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The Trigonometry Brain is similar
to the Algebra Brain, but lacks many of the features found only in the
Algebra Brain.Since Trigonometry is
usually only taught at one instruction level, there is no real need for
remediation.The Trigonometry Brain is
primarily aimed at students who are taking trigonometry at the collegiate
level.All of the topics in the
Trigonometry Brain are covered in UMR's Trigonometry course.
As with all our Brains, the Trigonomety Brain is composed of two primary
features:The Brain navigation window
and the content window. The active thought is located in the center of the
Brain 'plex.Clicking on any other thought will activate and move it to the center
of the Brain 'plex.Then the bottom window will load a different content page associated
with the activated thought.
For instance, following the path Trigonometric Functions Six Basic Trig Functions Graphs of Trig Functions Sine and Cosine CurvesPhase Shift will take you to a page
about the phase shift of a trigonometric function, an important concept in
Trigonometry
There are over 100 thoughts
contained in the Trigonometry Brain.Unlike the first incarnation of the Trigonometry Brain, much more
detail is included on each important trigonometric concept.All examples have detailed
explanations.Many more real world
applications have been included.
Trigonometry relies on a thorough
understanding of algebra for success.Therefore, we include a "Fundamentals of Trigonometry"
thread that details some of the basic knowledge required to be successful in
trigonometry, such as functions, an understanding of real numbers (both
rational and irrational), and a list of algebraic concepts that are useful to
know in Trigonometry.This list
includes reasons why each concept is important in trigonometry.For instance, being familiar with
arithmetic combinations of functions will help us to solve trigonometric
equations.Trigonometric equations can
be solved using algebraic techniques; we only apply trigonometry when
determining the exact solution after we have solved the trigonometric
equation for the appropriate function.
For fun, we include a brief
history of π, since π is a fundamental concept in
trigonometry.We start with the
origins of π as a ratio
between circumference and diameter back in Ancient Greece and work our way
forward through time to the computer era, where π has been calculated to over 200 billion digits (and still
counting!).
Feel free to explore the
Trigonometry Brain at your leisure.Like the Algebra and Calculus Brains, it is available 24 hours a day,
7 days a week.
Questions or comments about the Trigonometry
Brain can be directed via email to braintrax@umr.edu. | 677.169 | 1 |
TI-36X Pro Scientific Calculator TI's latest and most advanced scientific calculator features a high-quality MultiView™ display and MathPrint™ capability. Enhanced math functionality makes it ideal for computer science and engineering courses and topics in which graphing technology may not be permitted. | 677.169 | 1 |
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This unique book helps Class 4 aspirants to become Mathematics Olympiad champs by focussing on deep learning.
It has 18 Mock tests for Olympiad Maths. Also, it challenges your child at 2 levels. He / She can go to the advanced level after clearing…
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The book contains the descriptive study material covering detailed information about each topic of the prescribed syllabus along with examples and exercise. The book also contains various Sample Questions Papers based upon prescribed syllabus along wi | 677.169 | 1 |
Study Notebookcontains a note-taking guide for every lesson in the Student Edition. This notebook helps students: Preview the lesson, Build their mathematics vocabulary knowledge, Organize and take notes using graphic organizers, Increase their writing skills, and Prepare for chapter tests. | 677.169 | 1 |
ISBN-13: 9780201558029
Edition: 2nd 1994, updated and improved, introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills-the skills needed to solve complex problems, to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. It is an indispensable text and reference, not only for computer scientists but for all technical professionals in virtually every | 677.169 | 1 |
Elements of Plane and Solid Geometry Most persons do t possess, and do t easily acquire, the power of abstraction requisite for apprehending the Geometrical conceptions, and for keeping in mind the successive steps of a continuous argument. Hence, with a very large proportion of beginners in Geometry, it depends mainly upon the form in which the subject is presented whether they pursue the study with indifference, t to say aversion, or with increasing interest and pleasure. In compiling the present treatise, this fact has been kept constantly in view. All unnecessary discussions and scholia have been avoided; and such methods have been adopted as experience and attentive observation, combined with repeated trials, have shown, to be most readily comprehended. No attempt has been made to render more intelligible the simple tions of position, magnitude, and direction, which every child derives from observation; but it is believed that these tions have been limited and defined with mathematical precision. A few symbols, which stand for words and t for operations, have been used, but these are of so great utility in giving style and perspicuity to the demonstrations that apology seems necessary for their introduction. Great pains have been taken to make the page attractive. The figures are large and distinct, and are placed in the middle of the page, so that they fell directly under the eye in immediate connection with the corresponding text A Wentworth
Publisher
Forgotten Books
Date of Publication
27/09/2015
Language
English
Format
Paperback / softback
ISBN-10
133010840X
ISBN-13
9781330108406 | 677.169 | 1 |
The Year 11 syllabus is divided into two units, each of one semester duration, which are typically delivered as a pair. The notional time for each is 55 class contact hours.
Unit 1 contains the three topics:
I. Consumer arithmetic
II. Algebra and Matrices
III. Shape and measurement
"Consumer arithmetic" reviews concepts of rate and percentage change in the context of earning and managing money, and provides a context for the use of spreadsheets.
"Algebra and matrices" continues the Year 7-10 study of algebra and introduces the new topic of matrices. The emphasis of this topic is the symbolic representation and manipulation of information from real-life contexts using algebra and matrices.
"Shape and measurement" extends the knowledge and skills students developed in the Year 7-10 curriculum with the concept of similarity and the associated calculations involving simple and compound geometric shapes. The emphasis in this topic is on applying these skills in a range of practical contexts, including those involving three-dimensional shapes.
Unit 2 contains the three topics:
I. Univariate data analysis and the statistical investigation process
II. Applications of trigonometry
III. Linear equations and their graphs
"Univariate data analysis and the statistical investigation process" develop the students' ability to organise and summarise univariate data in the context of conducting a statistical investigation.
"Applications of trigonometry" extends students' knowledge of trigonometry to solve practical problems involving non-right-angled triangles in both two and three dimensions, including problems involving the use of angles of elevation and depression and bearings in navigation.
"Linear equations and their graphs" uses linear equations and straight -line graphs, as well as linear-piece-wise and step graphs, to model and analyse practical problems.
Course Assessment:
Response - 40%
Investigation - 20%
Examination - 40%
Note – A detailed assessment statement will be provided to students at the commencement of the course.
Further Study:
Mathematics Applications (Units 3 & 4) - ATAR
Additional Information:
The Mathematics Applications (Units 1 & 2) - ATAR course is designed for students who want to extend their mathematical skills beyond Year 10 level but whose future studies or employment pathways do not require knowledge of calculus. The course is designed for students who have wide range of educational and employment aspirations, including continuing their studies at university of TAFE. | 677.169 | 1 |
books.google.com - PRAXIS II Mathematics Content Knowledge (0061) For Teacher Certification Are you prepared to excel on the PRAXIS II? * Get to know the test, how it is scored, and much more. * Set up a study schedule by following our flexible, results-driven timeline * Take the first practice test to discover what... Best Teachers' Test Preparation for the Praxis II
* Set up a study schedule by following our flexible, results-driven timeline
* Take the first practice test to discover what you know and what you should know
* Use REA's advice to ready yourself for proper study and success
Sharpen your knowledge and skills
* The comprehensive review guides candidates through all the content and process categories on the official test, which is required in most states for certification. Content categories include: Algebra and Number Theory, Measurement, Geometry; Trigonometry, Functions, Calculus, Data Analysis and Statistics, Probability, Matrix Algebra, and Discrete Mathematics.
* Chart your progress with full and detailed explanations of all answers
* Boost confidence with test-taking strategies and experienced adviceErrors everywhere
User Review - kpolo23 - Borders
There is a lot of information presented in this book in a simple and easy-to-follow manner. The downside is that there are errors all over the text!! There are equations that are missing signs (or ...Read full review
Study guide
User Review - 5tu44 - Overstock.com
I was satisfied with the condition and speed of delivery. Experience would lead me to make future purchases.Read full review | 677.169 | 1 |
Algebra 2: Radical Functions Stations Activity
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Algebra 2: Radical Functions Stations Activity
This Algebra 2 Activity covers all the topics in the unit on Radical Functions and Rational Exponents. There are eight stations for students to work through in groups of 3 or 4 students. Time should be limited to 3 or 4 minutes per station, which allows a WILD CARD Round for students to go back to any station where they needed more time. | 677.169 | 1 |
From the people who brought you the Dummies instructional book series, brings you the same non-intimidating guides in video form. This is Mathematics for Dummies. Just watch this video tutorial to learn how to find approximate area using sigma notation, For Dummies.
Find the area under a curve with sigma notation with this tutorial. Calculating the approximate area with summation notation requires formulas, and these calculus instructions help. | 677.169 | 1 |
Countless people have relied on Anton to learn the difficult concepts of calculus. The new ninth edition continues the tradition of providing an accessible introduction to the field. It improves on the carefully worked and special problems to increase comprehension. New applied exercises demonstrate the usefulness of mathematics. More summary tables and step-by-step summaries are included to offer additional support when learning the concepts. And Quick Check exercises have been revised to more precisely focus on the most important ideas. This book will help anyone who needs to learn calculus and build a strong mathematical foundation.
"synopsis" may belong to another edition of this title.
From the Publisher:
The aim of this major revision is to create a contemporary text which incorporates the best features of calculus reform yet preserves the main structure of an established and well-tested calculus course. The multivariate calculus material is completely rewritten to include the concept of a vector field and focuses on major physics and engineering applications of vector analysis. Covers such new topics as Jacobians, Kepler's laws, conics in polar coordinates and parametric representation of surfaces. Contains expanded use of calculator computations and numerous exercises 40903 | 677.169 | 1 |
Key to Decimals Answers and Notes: Books 1-4 The Key to Decimals series begins with basic concepts and operations on decimals. Then it covers real-world uses of decimals in pricing, sports, metrics, calculators, and science. The success-oriented approach of Key to Decimals builds confidence and independence. You'll find this series to be a great way to prepare for standardized tests. This is the Answers and Notes book but it does include the complete text of all 4 of the student Key to Decimals books along with some teaching tips. | 677.169 | 1 |
Algebra
This course is aligned to state and common core standards. Our goal is to further enrich algebraic skills and the concepts necessary for students to succeed in advanced courses.
Topics include:
Algebraic Expressions
Quadratic Equations
Exponents
Sequence and Series
Polynomials
Solving Polynomial Equations
Polynomial Functions
Rational Expressions
Linear Equations
Writing Linear Equations
Equations
Formulas
Solving Simply Equations
Solve Quadratic Equations
System of Equations
Algebraic Solution to System of Equations
Graphic Solution to System of Equations
Coordinate Graphing
Graphing Linear Functions
Rational Functions
Functions
Graph linear Inequalities
Graph System of Linear Inequalities
Exponents and Roots
Exponents and Radicals
Real Numbers
Complex Numbers
Patterns
Mapping
Functions | 677.169 | 1 |
Modern Junior Mathematics, Vol. 1 (Classic Reprint)
Description
Excerpt from Modern Junior Mathematics, Vol. 1
Until recently upper elementary and high school work in mathematics was planned for the pupil who was expected to continue it in the university. Although logical, its arrangement was neither psychological nor pedagogical. Some progress, however, has been made recently in adapting the study to the needs and abilities Of pupils.
In the junior high or intermediate school, work in mathematics in the seventh, eighth, and ninth grades should be complete in itself and at the same tirne preparatory to senior high school work. NO effort should be made to finish arithmetic in the eighth grade and algebra in the ninth: while denying the child the interest and beauty that lie in geometry and trigonometry until his taste for mathematics has been destroyed. Nor will alternate bits of formal algebra, geometry, and trigonometry solve the problem. The result is a mastery of none and a confusion in all.
Experience has proved that the necessary elements of arithmetic can be taught and certain definite skill developed in the first six grades. In the seventh grade business applications of arithmetic with the Simplest elements of bookkeeping should be given. In the eighth grade mensuration Should be taught experimentally or through observational geometry, and, through that, in a natural and meaningful | 677.169 | 1 |
Pre-Calculus for Game Developers, 1st Edition
Successful game programming requires at least a rudimentary understanding of central math topics. While most books neglect the point-by-point details that are necessary to truly hone these skills, Beginning Pre-Calculus for Game Developers tackles each task head on, using easy-to-understand, hands-on exercises. You will conquer the basics of these essential math topics and will then learn how to specifically apply each skill to the field of game programming. Whether you are searching for an entertaining, engaging way to improve your math skills or you wish to develop the background skills necessary to boost your game programming, Beginning Pre-Calculus for Game Developers serves as the step-by-step guide that will help you tackle pre-calculus with confidence | 677.169 | 1 |
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This activity includes 8 rotations with 4 tasks each for a total of 32 student tasks.
In pairs or small groups, students rotate to each of the 8 pages, posted on your classroom walls. Students complete 1 of the 4 tasks at each rotation. The idea is to explore and practice graphing, creating tables, identifying intercepts, examining patterns, and more!
When I used this activity to review with my own students, the conversations that occurred at each station were priceless! Naturally, students justify, explain and provide peer teaching for one another while I walk around, intervening as necessary. They also said that this activity was "fun" - which is a big deal when you're in Algebra class... ;-)
I hope your students gain a deeper understanding of linear, quadratic and exponential functions! | 677.169 | 1 |
Durell's Advanced Arithmetic
Format: Hardcover
Language: English
Format: PDF / Kindle / ePub
Size: 8.28 MB
Downloadable formats: PDF
How did we — as a species and as a society — become so familiar with and totally reliant on these abstractions our ancestors invented just a few thousand years ago? He turned a laser-like focus on literacy. After a little training, most of the students are able to solve similar problems under timed test conditions. This tool helps teachers and their students by providing research-based strategies for teaching foundational reading skills to any beginning reader.
Pages: 458
Publisher: Charles E. Merrill Co. (1912)
ISBN: B002TTB9LE
A Treatise On the Differential Calculus and the Elements of the Integral Calculus: With Numerous Examples
Problem Solving, Grades 4-5 Workbook
MATH SKILLS: ARITHMETIC WITH INTRODUCTORY ALGEBRA AND GEOMETRY
Even though we use names like "hundred," "thousand," "million," etc., which are the same as the names of the columns higher than the ten's column, we are not really representing groupings; we are merely giving the number name, when we pronounce it, just as when we say "ten" or "eleven". "Eleven" is just a word that names a particular quantity , source: Instant Access Code Chapter 1 read for free rockxiao.com. The settling velocity and terminal location on the bottom of the tidal channel is computed and compared to the simulated flow in a channel without turbines. We have observed an enhanced sedimentation, and we will quantify the degree of enhancement and the parameter range within which it is significant , source: Math for Business Careers download here If this cannot be determined observations matter and the effect of the remaining observations can be ignored safely, then choose w such that the tail area is sufficiently small. [2] Weighted Standard Error and its Impact on Significance Testing (WinCross vs , cited: Vocabulary Card for download here Vocabulary Card for Tussy/Gustafson's. The test is not expensive, and for people who paid attention while earning their bachelor degree, it really isn't difficult. Furthermore, if you decide to teach in a private school, the NTE might not be required. Once you have completed all the requirements, your teaching certificate for your state will arrive in the mail Learn the Alphabet With the read online Learn the Alphabet With the Munch Bunch. Other times, web-native mathematical objects are created, remixed and shared within the integrated authoring and discussion environment, such as applets made with Scratch or Geogebra constructions Jada Makes Jewelry: Use Place download online Either that or she had a fear of plungers or something. And because the sight of a crying seven-year-old elbow deep in a toilet wasn't sad enough, she threatened to make him use his teeth next time The story of a piece of coal: download for free According to e: The Story of a Number by Eli Maor, In the second edition of Edward Wright's translation of Napier's Descripto (London, 1618), in an appendix probably written by William Oughtred, there appears the equivalent of the statement that loge10 = 2.302585. Since the actual tables contains no decimals it was probably given as 2302585 without the decimal point epub.
It is crucial check to that the calculations being done are the correct calculations. More Mathematical Challenges read here FREE benefits include Daily News, Developer Tips, Career Center, VB Forums & more. Discover The 5 Solution to a Wrinkle Free Face - ALL EXPOSED TODAY! Various sources across the internet have exposed a HUGE celebrity secret to erase wrinkles - without botox or surgery! How do Hollywood starlets look so radiant and youthful well into thier 40's, 50's, and even 60's Basic Fractions (Teachers read for free read for free?
A history of the mathematical theory of probability: from the time of Pascal to that of Laplace
Benjamin Franklin (January 17, 1706, Boston - April 17, 1790 Philadelphia), was an American polymath, printer, inventor, statesman, and one of the most. Any crop not growing to leaders in quantas gotas de rivotril equivale a dosagem de 0 25 all over the globe cross pollination herbicidepesticide drift Introduction to the National download here Introduction to the National Arithmetic,. According to various sources, the answer is NO! So if they aren't all using surgery to stay looking great, what is their secret? Keep reading, it's excitingly effective, safe, and cheap! A high profile doctor has been giving advice to clients (rumoured to include celebrities) to look 10 to 15 years younger fast, but are scared of the potential risks of surgery or botox. Many online sources have expressed suprise over how shockingly simple, cheap, and effective his technique was The Psychology of Arithmetic download for free Instead of being capital i's, they are lower-case L's and only appear to be i's. Also, due to the automatic formatting of WikiAnswers, the question mark is at the end of the sequence and no… How do you convert 6 pounds 11 oz to kilograms? There are about 0.454 kg in a pound. (or ~2.2 lb / kg which is slightly less accurate) Therefore 6 + (11/16) = 6.6875 6.6875 lbs * 0.454(kg/lb) = 3.036125kg (or 6.6875 / 2.2) Or, 3kg 36g Counting (Headstart 3-5) download pdf Counting (Headstart 3-5). As implied earlier, the trick to successfully earning an online degree is to, first, know what you already have, and, second, to know what your goals are. Perhaps you want to be a teacher but would prefer secondary education. That can also be done, but the procedure and requirements will be a little different from the elementary teacher's program Mathematics for Technical and Vocational Students (10th Edition) read pdf. Traders recorded their numerical data using Roman numerals, and performed calculations either by a fairly elaborate and widely used fingers procedure or with a mechanical abacus ref.: Multiplication: Worksheets download for free
Developing Decimal Concepts: Building Bridges Between Whole Numbers and Decimals
Painless Fractions (Painless...(Pb))
Adams's New Arithmetic.: Arithmetic, in which the principles of operating by numbers are analytically explained, and synthetically applied ...
Basic College Mathematics
Today horoscope refers to fortune telling, but the practice is rooted in the original meaning, measuring the aspect of the stars and planets to measure the seasons online. Some of us may feel uncomfortable with the notion that mathematics is fiction, but the concepts and procedures of mathematics are all constructions of our minds, products of our attempts to understand our worlds, real and imaginary , source: Enhanced WebAssign Homework Only LOE Printed Access Card for One-Term Math and Science Children eagerly anticipate their school's annual Sports Day. The entire student body practices intricate choreographed cheers and marching maneuvers. On the day of the event, parents and the neighborhood are invited to watch each class compete in races and other track and field events , e.g. Topology Sometimes the more specific phrase sinus rectus, or "vertical sine," was used; hence the phrase sinus versus, or our "versed sine," was applied to the "sagitta," or the "sine turned on its side." I find every news, reviews very informative and interesting. This site is indeed a great site for both teachers and learners. Thanks to EdTech for creating such an enriching site on education Mental Maths for Ages 7-8 site1373914966.provisorio.ws. For just $439, the Altair 8800 for the first time included everything in one kit - assembly instructions, metal case, power supply, and all of the boards and components required to build "the most powerful computer ever presented as a construction project in any electronics magazine". It took many days and nights of careful soldering and assembly to hopefully create a working Altair , e.g. Squaring & Area - In A Minute: download online Write on jour slate the numbers from 500 to 600 Insect Addition It will be more fun for them and they will be more accepting of singing. Seven Sailors: This is a tongue twister that the kids find challenging and enjoy singing. We sing "Seven Sassy Sailors Sailed the" on Do and then we go to Sol and sing, "Seven Salty Seas" and then we modulate to the next chord/key. This is tricky but using tongue twisters and alliteration in chorus is great for diction practice , source: A Treatise on the Analytic Geometry of Three Dimensions, Vol. 1 of 2 (Classic Reprint) Table 6 presents the results of the post-hoc procedure where the variables YC ("When I study, listening to classical music interferes with my concentration") and YP ("When I study, listening to popular music interferes with my concentration") were coded 1 for a yes and 0 for a no response. 33% of the respondents indicated that classical music interferes with their studying, while 43% of the subjects indicated that popular music interferes with their studying ref.: The Mickey Mouse Make-It Book (Disney's Wonderful World of Reading) read pdf. Gauss' Lemma expresses a Legendre symbol as a product of many signs. Eisenstein's Lemma: A variation of Gauss's lemma allows a simpler proof. Large partial quotients allow very precise approximations. Regular patterns in the continued fractions of some irrational numbers. Engel expansions of positive numbers are nondecreasing integer sequences. Pierce expansions of numbers from 0 to 1 The Complete Practical read online triumphwellbeing.co.uk. Recent studies have shown that the effect of stratospheric sudden warnings extends well into the upper atmosphere. A stratospheric sudden warming is often accompanied by an amplification of lunar tides in the ionosphere/theremosphere. However, there are occasionally winters when a stratospheric sudden warming occurs without an enhancement of the lunar tide in the upper atmosphere, and other winters when large lunar tides are observed without a strong stratospheric sudden warming , source: Collins Easy Learning read epub triumphwellbeing.co.uk. | 677.169 | 1 |
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The subject of real analysis dates to the mid-nineteenth century - the days of Riemann and Cauchy and Weierstrass. Real analysis grew up as a way to make the calculus rigorous. Today the two subjects are intertwined in most people's minds. Yet calculus is only the first step of a long journey, and real analysis is one of the first great triumphs along that road. In real analysis we learn the rigorous theories of sequences and series, and the profound new insights that these tools make possible. We learn of the completeness of the real number system, and how this property makes the real numbers the natural set of limit points for the rational numbers. We learn of compact sets and uniform convergence. The great classical examples, such as the Weierstrass nowhere-differentiable function and the Cantor set, are part of the bedrock of the subject. Of course complete and rigorous treatments of the derivative and the integral are essential parts of this process. The Weierstrass approximation theorem, the Riemann integral, the Cauchy property for sequences, and many other deep ideas round out the picture of a powerful set of tools.
Title:
Handbook of Real Variables
Author:
Edition:
Publisher:
Birkhauser Boston
Format:
ePub
Subject:
Length:
Width:
Sub Title:
With Applications to Differential Equations and Fourier Analysis | 677.169 | 1 |
A Computational Introduction to Number Theory and Algebra
A Computational Introduction to Number Theory and Algebra
Victor Shoup
Language: English
Pages: 600
ISBN: 0521516447
Format: PDF / Kindle (mobi) / ePub
This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory. This edition now includes over 150 new exercises, ranging from the routine to the challenging, that flesh out the material presented in the body of the text, and which further develop the theory and present new applications. The material has also been reorganized to improve clarity of exposition and presentation. Ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
some trivial aspects of our data structure for representing large integers. For example, it is clear that in constant time, we can determine the sign of a given integer a, the bit length of a, and any particular bit of the binary representation of a; moreover, as discussed in Exercises 3.17 and 3.18, multiplications and divisions by powers of 2 can be computed in linear time via "left shifts" and "right shifts." It is also clear that we can convert between the base-2 representation of a given
B (i.e., A ⊆ B but A = B); further, A ∪ B denotes the union of A and B, A ∩ B the intersection of A and B, and A \ B the set of all elements of A that are not in B. For sets S1 , . . . , Sn , we denote by S1 × · · · × Sn the Cartesian product xiv Preliminaries xv of S1 , . . . , Sn , that is, the set of all n-tuples (a1 , . . . , an ), where ai ∈ Si for i = 1, . . . , n. We use the notation S ×n to denote the Cartesian product of n copies of a set S, and for x ∈ S, we denote by x×n the
examine an even more specialized case of the above situation. Suppose that X1 , . . . , Xn are pairwise independent random variables, each of which takes the value 1 with probability p, and 0 with probability q := 1 − p. As before, let X be the sample mean of X1 , . . . , Xn . As we calculated in 6.5 Some useful bounds 119 Example 6.22, the Xi have a common expected value p and variance pq. Therefore, by (6.17), for any > 0, we have pq (6.19) P[|X − p| ≥ ] ≤ 2 . n The bound on the right-hand
1/n2 converges and the series 1/n diverges, the expectation E[X] exists, while E[X 2 ] does not. ✷ Theorems 6.6 and 6.7 hold under the additional hypothesis that E[X] and E[Y ] exist. If X1 , X2 , . . . is an infinite sequence of real random variables, then the ran∞ dom variable X := ∞ i=1 Xi is well defined provided the series i=1 Xi (u) ∞ converges for all u ∈ U. One might hope that E[X] = i=1 E[Xi ]; however, this is not in general true, even if the individual expectations E[Xi ] are | 677.169 | 1 |
This 5th variation of Lang's booklet covers all of the subject matters normally taught within the first-year calculus series. Divided into 5 components, every one portion of a primary path IN CALCULUS includes examples and purposes when it comes to the subject coated. furthermore, the rear of the ebook comprises certain ideas to various the workouts, letting them be used as worked-out examples -- one of many major advancements over earlier versions.
As an introductory clarification of the speculation of Fourier's sequence, this transparent, precise textual content is exceptional. The 3rd revised version, that is right here reprinted unabridged, includes checks for uniform convergence of sequence, a radical remedy of term-by-term integration and the second one theorem of suggest worth, enlarged units of examples on endless sequence and integrals, and a bit facing the Riemann Lebeague theorem and its effects.
"A convenient e-book like this," famous The Mathematical Gazette, "will fill an exceptional wish. " dedicated to totally labored out examples, this detailed textual content constitutes a self-contained introductory direction in vector research for undergraduate and graduate scholars of utilized arithmetic. starting chapters outline vector addition and subtraction, exhibit find out how to unravel and be sure the course of 2 or extra vectors, and clarify structures of coordinates, vector equations of a aircraft and immediately line, relative speed and acceleration, and infinitely small vectors.
Completely revised, up-to-date, extended, and reorganized to function a chief textual content for arithmetic classes, creation to Set thought, 3rd version covers the fundamentals: relatives direction layout, offers end-of-section difficulties, with tricks, of various levels of trouble, contains new fabric on basic varieties and Goodstein sequences, and provides very important fresh rules together with filters, ultrafilters, closed unbounded and desk bound units, and walls. | 677.169 | 1 |
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This comprehensive book introduces students to time series and forecasting techniques. The prerequisites are college algebra and basic statistics. It contains complete coverage of linear regression analysis, which provides much of the conceptual foundation of forecasting.
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This comprehensive book introduces students to time series and forecasting techniques. The prerequisites are college algebra and basic statistics. It contains complete coverage of linear regression analysis, which provides much of the conceptual foundation of forecasting | 677.169 | 1 |
Wednesday, August 9, 2017
High School Math. Three words that are always interesting whether you're a homeschooler or not. I absolutely love math, but my kids do not. I'm always up for reviewing math products because there are so many different ones and they all have something different about them. For the last few weeks we have been working through No-Nonsense Algebra by Math Essentials, and Edyn has really enjoyed it!
Math Essentials was developed by Rick Fisher, a math instructor with over 31 years of experience! He has devoted his time to not only teaching his students, but also developing award winning math materials.
What did we receive?
We were given the No-Nonsense Algebra book which is a soft bound book and approximately 175 pages. When you buy the book, you get free access to all of the teaching videos, so we were given our code to be able to access them.
How does No-Nonsense Algebra work?
I am using this program for Edyn as a full curriculum, and she has done very well with it. It is actually perfect for her because the teaching method works well for her. It's very thorough to insure that the student understands the concept being taught. It uses a different approach than other programs by having 5 key parts:
Introduction and Explanation
Helpful Hints
Examples
Written Exercises
Review
At the end of each chapter there is also a Chapter Review section and a Final Exam that is also included.
How did we use this in our school?
After opening up her book, and getting her pencil and paper ready, we read the Introduction to the concept she will be working on. Side note, I love how they stress the importance of writing the problems down and working them out on paper. I am a firm believer in this.
In the Introduction is where the concept is explained, and you will be able to find the Helpful Hints. These are super important to go over because they will contain the important tips and short cuts.
Next we watch the free video lesson that goes along with it. The videos are great. They are clear and very easy to understand. Each video that we have done runs somewhere in the neighborhood of around 10 minutes. It's nice to be able to stop, rewind, or completely rewatch the video if you need more instruction.
After she watches the video we move back to our book. We do go over the examples that are given because Edyn needs to be able to see those problems worked out. Also, those examples help her if she gets stuck on a problem that she's working out herself. It's just another tool she can go back and look at if she needs to.
From the Examples, we move on to the Exercises. The first thing I want to point out is that they give you the perfect amount of problems to work. I don't like when a program gives you 5 or 6 problems. That's not enough in my opinion for the student to become confident with. They need to be able to work enough problems that they can master the concept.
When she's done, we check them by finding the solutions in the back of the book. I love that!! It makes it so much easier to check.
Finally she works on the review.
What did we think?
I have to say I am very impressed with this program. It is simple and easy to understand for both parents and students. Not only do you get an ample amount of explanation in the book, you also get the videos with step by step instruction. I would call this program a solid program that is geared towards making sure the student understands what is being taught to them. I would definitely recommend No-Nonsense Algebra by Math Essentials to anyone who is looking for a complete Algebra curriculum.
If you've never had the pleasure of listening to an audio drama from Heirloom Audio Productions, then let me tell you a little bit about what to expect. Heirloom Audio Productions is known for recreating the stories of the legendary G.A. Henty. Mr. Henty was a war correspondent, a big guy with a big beard, who lived for adventure. Unless you've lived under a rock, then you know he was a master story teller. He loved to share his stories with his family, and throughout the years, he went on to write 122 books! Heirloom Audio Productions takes these stories and makes them come alive. I am an avid book lover, and I also love audio books. This is not your ordinary audio book. This is a true listening adventure that includes real actors and sound effects. It takes you to a whole different world while listening to one of these works of art! What did we receive for this review?
We were very excited to receive the 2 CD set along with all of the extra digital download features! The bonuses that come in the download are always amazing! In the Reign of Terror Adventure Playlist ~ This is how you can listen online. I love to have the option to listen on my phone and not have to worry about having a CD player. In the Reign of Terror Original E-book ~ This is the original e-book with all new colorful graphics. Official Soundtrack ~ The original music by Emmy-winning composer John Campbell. Printable Cast Poster ~ Printable promotion poster featuring the star studded cast. Inspirational Verse Poster ~ Printable copy of the inspirational verse quoted in In the Reign of Terror, "What man intends for evil, God intends for good." Desktop Wallpaper Download ~ Beautiful artwork for your computer background. Official Script Download ~ I LOVED this. It's super cool to see how the script was laid out. Study Guide and Discussion Starter ~ This is such an amazing bonus feature especially if you're wanting to turn this into more than just a "read aloud." It's perfect for helping younger kids understand and remember the story. I love how the study guide starts out giving you a little background on G.A. Henty, Maximilien Robespierre, and Marie Antoinette. Each set of questions is broken down into 3 parts.
Listening Well ~ This are great comprehension questions to keep your student listening all the time.
Thinking Further ~ These questions make your student think a little bit more. They may be asked about a character's thoughts or actions, or they may be asked to look up something in the story.
The Defining Words ~ This gives your student a change to broaden their vocabulary. It's a wonderful addition to the study guide.
Heirloom Audio Productions also has something new that seem like so much fun! It's called Live the Adventure Club. This club adds even more fun to your listening experience and includes super cool fun and engaging activities for your kids! It's definitely worth checking out.
In the Reign of Terror ~
This story. I almost don't have words for it. It's definitely the saddest of all of the G.A. Henty stories I've heard so far. It made me cry because of what innocent people had to endure just because of their lineage. Harry is 16 years old and moves to France to become a companion to a Nobleman's children. This is just a short time before the French Revolution. He quickly becomes part of their family by winning their trust and showing that he's willing to do what it takes to protect the family. As time goes on the mob is getting closer and the family must put in place their plans to flee. This takes Harry on whirlwind journey to protect his new family. This is a wonderful story about what man intends for evil, the Lord intends for good. The story talks about the differences in the American Revolution and the French Revolution. I like how it talks about that the American Revolution wasn't really a revolution at all because they did not revolt by using a mob. They had actually tried to solve it peacefully, and war was their last choice.
In the Intro Mr. George, the narrator talks about how the difference in the two was what was in their hearts. The American's turned their faces to God and the French turned away from God.
What did we think?
We always love anything that Heirloom Audio does. This story really spoke to my heart because I don't think I realized what these poor innocent people went through. It was definitely my favorite so far because of how it completely drew me in. These CD's are always perfect for long car rides or even if you want to have something different than a family movie night. You will not be disappointed in the star studded cast or the gripping sound track. Both are always amazing. If you are looking for an audio adventure, In the Reign of Terror by Heirloom Audio Productions won't disappoint.
It's finally August. I am pretty sure it was just January, but my life seems like a whirlwind lately. I have had so much going on the last few weeks, that taking the time to actually sit down and put my thoughts down here on my blog have been kind of put on the back burner.
So, as you know we really tried to get our school year going awhile back, but this summer has been crazy with lots of visitors, which we love, but it has gotten us a little behind on where I wanted to be already with this year. That just means that we will have to work extra hard, and maybe even have some work time on Fridays.
I really need to schedule some time to spend on my blog. My days just seem too short with not enough hours, and if you're alive then you know what I mean. I have to say that part of that is my fault. I have been on a backwards sleep schedule and I end up going to bed late, and waking up kind of late. I am trying to turn that around so that when we get back into our school year next week, we can get up and get started early. So I guess my first goal is go to bed early.
Also speaking of schedules, I have started using FlyLady to clean my house. I had tried it awhile back and it overwhelmed me, but now that I have the app it has really helped keep me on track. I love that she uses zones, so you are only working small spaces at a time. I love it!
Next up our goal is to start our budget. We are about to start the Dave Ramsey program, and I am super excited about it. I am ready for us to take control of our money and become debt free! I think that being on a budget, and a cash envelope system will help us keep our money and spending in check.
Last but not least, I'm going to hopefully start meal planning monthly rather than every two weeks. I'm hoping to even post a few of them here. I think it will be easier to not eat out those few times that we do a month. Every time we eat out it's about $40. We normally do about three times a month so you're easily looking at over a $100 a month for just three meals. I know I can do better than that!
So, if I missed some then I can add an update. Right now our goal is a house. We are wanting to put some roots down and buy the house we've always wanted, or something pretty close. I'm looking forward to this adventure!
Tuesday, August 1, 2017
For the last few weeks we have been working on a really fun and different English program. My kids love manipulatives when they are learning because it seems to help them remember things better. English Grammar Teaching Method from English on a Roll has been a really different experience for us in our homeschool.
Grammar is extremely important to me, so I will try almost any English or language arts type of program. I feel that I have a pretty good knowledge of grammar, but honestly there is so much to learn. Little rules here and there so I don't think that you can ever review it too much. I have always heard that English is one of the most complicated languages to learn, and I truly believe that.
If you have ever taught homeschool, grammar is normally going over the rules and maybe doing some worksheets or working online. English on a Roll is different because it uses MSL, or Multisensory Structured Language. This method, which has had a large amount of research, uses simultaneous teaching to the auditory, visual, and tactile learning styles. It starts with the basics and builds on them a little at a time to the more complex lessons. It also uses direct instruction which is continuous interaction between the teacher and the student. Another important facet is repetition and review. This is key to using this program! Last but not least, synthetic and analytic teaching which is building the whole with parts and breaking the whole into parts.
What did we receive?
The manipulatives are a block set of 40 different color coded all plastic cubes with case. They are very well made, and that was very impressive to me.
The teacher's manual is a 140 page soft bound book.
How did we use English on a Roll?
This program says that it can be used for anyone ages 5 and up. It is also geared for ESL students or anyone who needs extra help in grammar.
We decided to jump right in and use this a few times a week. When I first opened the book and thumbed through the first few lessons, I thought that this was entirely too easy for my kids, and it wouldn't really be anything new since they are 12 and 14. The first lesson honestly took us minutes to go over because it really was ONLY review for them. But, as the lessons progressed, they turned into more lengthy discussions, and I could really start seeing the benefits of the program.
There is very little preparation needed to get started. The book tells you everything you need for each lesson including which cubes that you will need to get out of the box for that particular lesson. I love anything that saves me time! There are pages in the front that also tells you which cubes are what so that you can find them quickly in the box. The book also tells you if you need to copy any of the pages for your student. This is covered in the copy right. There are even hints and tips on how to effectively teach each lesson.
The very first lesson is on pronouns. This was surprising to me considering lessons we've done in the past normally start with nouns and verbs. I do think that if you are trying to learn English as a second language then it makes complete sense. Anyway, I just wanted to mention that.
Like I said, the book tells you all that you need to prepare for each lesson. You will only give your students the cubes needed for the lesson that they are on. We would go over the lessons and worksheets, but their favorite part was definitely working with the manipulatives. They enjoy the section called Conversation and games. For instance, they may roll one of the cubes and then make a sentence with the cubes that are left. It was fun to see what they would come up with.
Our thoughts on the product was that it has been a really fun experience for us. I am going to continue with the book until it's done because it is great review and they have even learned a few new things. I would definitely recommend this to anyone who is teaching ESL or even someone that is just needing the extra help.
Tuesday, July 25, 2017
We love doing art projects, but like I've said before they always seem to get put on the back burner. When I see things come up for review that has to do with art, then I always get excited about it. We have been able to review something really fun for the last few weeks called Rigid Wrap and CelluClay Quik-Sculpting Kit by ACTÍVA Products.
What did we receive?
We were given two rolls of Rigid Wrap and one package of CelluClay.
They also sent us a very colorful FREE e-book, ACTÍVA Products' Favorite Sculpture KIDS CRAFTS. This book has tons of craft ideas so that you can make something fun with your new kit! How did we use it? When we received our kit, I was a little concerned that it was going to be really messy since the box had some white powder that would come out of it every time we moved it. Once we opened the box and got everything out to start our project, I realized that it probably wasn't going to be as bad as I had originally thought. We did cover our table with a big piece of plastic just so that it was easy clean up. We looked through the book and the kids decided on what project that they wanted to make. There are several different projects to choose from, and the book has plenty of colorful pictures showcasing each one.
They immediately decided that they wanted to make the bowl from the e-book. I have to point out that I am very happy that we received the e-book because although there was a paper included in our box, you couldn't read it. It had different ideas on it, but the quality wasn't good at all. We couldn't even read the back page because it was cut off.
Ok so the Rigid Wrap is really a neat product. It's strips of cloth that have plaster already on them. All you need is water to activate it!
First we wrapped our bowl in saran wrap. The kids then took the pieces of Rigid Wrap that they had cut into strips and dipped them in a bowl of warm water. They then laid the strips all around the bowl in different directions so that they were able to build up the layers on the bowl to make it nice and thick. This was so much fun for them!
When they were done they needed to let the bowl dry. I wasn't sure how long it would take so I decided to let it sit overnight. The next morning it was still a bit damp, so we set it outside in the hot Texas sun, and it dried right up and was ready for the next step.
They wanted to try out the CelluClay next. The only problem was that there were no instructions that I could find that explained how to mix it up. CelluClay is basically plaster mixed with bits of paper to be used like paper mache. I found a video on how to mix it up, but basically you just add water until it's the consistency of clay.
They took the CelluClay and added it as a rim to the bowl. It was a lot of fun to work with! They say it can keep fresh in the refrigerator and last longer.
We set our bowl out in the sun again, and it dried up nicely. Next they painted it with regular acrylic paint.
We had so much fun working with this product and the possibilities with it are endless!! | 677.169 | 1 |
Conceptual Mathematics: A First Introduction to Categories (Softcover)
"In the last fifty years, the use of the notion of 'category' has led to a remarkable unification and simplification of mathematics. Written by two of the best-known participants in this development, Conceptual Mathematics is the first book to serve both as a skeleton key to mathematics for the general reader or beginning student and as an introduction to categories for computer scientists, logicians, physicists, linguistics, etc." — From the back cover
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Continued from the back cover: "While the ideas and techniques of basic category theory are useful throughout modern mathematics, this book does not presuppose knowledge of specific fields but rather develops elementary categories such as directed graphs and discrete dynamical systems from the beginning. The fundamental ideas are then illuminated in an engaging way by examples in these categories."
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GRE Math Review
The Math skills required for GRE quantitative reasoning section are of a basic standard that should be within the reach of a tenth grade student. You don't need to learn up lots of new formulae but you will need to sharpen up your thinking skills.
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STAARS ALGEBRA 1 EOC RESOURCES
This file contains 13 worksheets for each TEKS covered in reporting category 1. Each worksheet has 18 problems. The worksheets are designed so that the student can practice the skills that they will need to solve STAAR EOC problems for this category. This is a great resource for first time testers or re-testers.
The student will demonstrate an understanding of how to use algebraic methods to manipulate numbers, expressions, and equations.
The following TEKS are covered in this document:
A.10A – add and subtract polynomials of degree one and degree two (supporting standard)
A.10B – multiply polynomials of degree one and degree two (supporting standard)
A.10C – determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend (supporting standard)
A.10D – rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property (supporting standard)
A.10E – factor, if possible, trinomials with real factors in the form ax^2 + bx + c, including perfect square trinomials of degree two (readiness standard)
A.10F – decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial (supporting standard) | 677.169 | 1 |
Summary
THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! Glencoe Algebra 1is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
Table of Contents
Foundations for Functions
The Language and Tools of Algebra
Solving Linear Equations
Linear Functions
Functions and Patterns
Analyzing Linear Equations
Solving Systems of Linear Equations
Solving Linear Inequalities
Polynomials and Nonlinear Functions
Polynomials
Factoring
Quadratic and Exponential Functions
Advanced Expressions and Data Analysis
Radical Expressions and Triangles
Rational Expressions and Equations
Statistics and Probability
Table of Contents provided by Publisher. All Rights Reserved.
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TeacherMarch 30, 2016
by RUBEN
Nice book
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This course gives you a broad overview on several concepts and real world examples of Algebra. Students who want to learn concepts from scratch, would find it helpful to kick start their preparation and the course helps them to overcome any hurdles in their homework assignments or any competitive exams (GMAT, SAT, GRE, etc).
The course is designed for students to start with fundamental concepts and walk you through complex exercises in each section. My goal is to provide an interactive learning experience for you and I would like to encourage students to post any questions or if they need any extra guidance on any concept. | 677.169 | 1 |
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.This module provides a proficiency exam for the chapter "Basic Operations with Real Numbers". | 677.169 | 1 |
Catalog Record: Euclid, book V. proved algebraically so far as it relates to commensurable magnitudes. To which is prefixed a summary of all the necessary algebraical operations, arranged in order of difficulty | Hathi Trust Digital Library
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Euclid, book V.
proved algebraically so far as it relates to commensurable magnitudes. To which is prefixed a summary of all the necessary algebraical operations, arranged in order of difficulty.
By Charles L. Dodgson | 677.169 | 1 |
Overview
Geometry from Euclid to Knots by Saul Stahl
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Book Cover designing + formatting 6 print ready Math books
We require a graphic designer to work on formatting and layout of 6 Math books and create a front cover and back cover for these books (Similar cover / 6 variations). The content to be put in the books is in PowerPoint format and each book is about 150 pages long with just one question on each page. Sample of 5 pages of the book is attached.
What we need to get done is in 2 parts:
A. Cover Design: Design a front and back cover for these books. This is a series of books on math problems for students in Grades 1 to 6. The cover has to reflect the intent of the book plus the target audience (children in the specific grades) and the decision maker (parents) who will decide to buy the book. The cover for all these books need to reflect that they are part of a series.
B.: Making a standard template for content Layout and Formatting of 6 books. Specific tasks are:
1. Preparing the standard template of the book to 8" x 10" with 0.5" margin on top, bottom and side and [url removed, login to view]" gutter. There will be one question per page. More specific details will be discussed prior to the project commencement.
2. A logo has to be added to each page
3. Page numbering will have to be done
4. An index has to be created.
5. Preface/ Introduction pages will need to be added (will be provided)
6. Solutions of questions have to be put in the end. (Will be provided)
7. About 10 simple Math Graphics(geometry) have to be made per book.
The final output will need to be in PDF format, 300 dpi and must be ready to print with all the necessary technical printing specifications in place.
You should be willing to accept feedback if we require any changes to your output prior to submission of the final file. In case any specific things have been left out in this description you should be ready to accommodate those as we work along the project.
After submission of the final file, it'll take about 4 days to process the last milestone payment as we'll need to verify by proofreading/printing that you followed all the formatting requirements.
You will be requested to sign non-disclosure form as all discussions/emails regarding the book are confidential. You will not be entitled to any copyright rights, royalties, claim or privileges to the book. You will release total and complete rights to the book, images and illustrations.
Please send samples so we can see your design work to assess suitability for cover design. You may also prepare a template of the pages attached with this description. A prior experience with book publishing would certainly be preferred.
This is very urgent work and we need high quality output with a fast turnaround.
Hello,
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"The book NCERT Handbook Term 2 Mathematics Class 10 is exclusively written for CBSE students of class 10.
The book provides Quick Revision/ Notes All the in-chapter questions of the NCERT books, wherever found, have been fully solved.
The solutions have been designed in such a manner (Step-by-Step) that it would bring 100% Concept Clarity for the students.
The solutions are Complete (each and every question is solved), Inflow (exactly on the flow of questions in the NCERT book) and Correct (Errorless).
This is followed by 3 Sample Question Papers with detailed solutions and Marking Scheme. The Sample papers have been designed on the latest CBSE pattern. Each Sample paper contains value based questions as per the format of CBSE Board. | 677.169 | 1 |
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
Introduction to Differentiation (Differential Calculus)
A great way to start learning Calculus through video lectures and quizzes introductory course on Differential Calculus. It comprises of a total of close to 13 hours worth of videos and quizzes. This is perfect for secondary school students seeking a good primer on Calculus. It is also great as a refresher for everyone else.
The course is arranged from the very basic introduction and progresses swiftly with increasing depth and complexity on the subject. It is recommended that the students do not skip any part of the lectures, or jump back and forth, because good understanding of the fundamental is important as you progress.
Quizzes are included on 15 subtopics to strengthen your understanding and fluency on this topic. So it is advisable that you attempt all the questions.
The course is delivered by an experienced teacher with five years of experienceHave fun learning!
Who is the target audience?
Secondary and High Schools students taking Calculus 1 (Differential Calculus)
Students preparing for Calculus 1 (Differential Calculus) tests / exams at 'O' Level or its equivalence | 677.169 | 1 |
Files
Description
A co-publication of the AMS and IAS/Park City Mathematics Institute
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute.
But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves.
The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics—rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism. | 677.169 | 1 |
8th Grade Math Practice Workbook and Full length Online Assessments has been writing in one form or another for most of life. You can find so many inspiration from FSA Test Prep 8th Grade Math Practice Workbook and Full length Online Assessments also informative, and entertaining. Click DOWNLOAD or Read Online button to get full FSA Test Prep 8Introducing an essential addition to the 5-million-copy bestselling Brain Quest Workbook series! Finally, 6th graders canOur 1st edition Florida 8th Grade Math Test Prep for Common Core State Standards is an excellent resource to assess and manage student's understanding of concepts outlined in the Common Core State Standards Initiative. This resource is formatted into three sections: Diagnostic, Practice, and Assessment with multiple choice in each section. The material covered includesknowing that there are numbers that are not rational, and approximate them by rational numbers; expressions and equations work with radicals and integer exponents; understanding the connections between proportional relationships, lines, and linear equations; analyzing and solving linear equations and pairs of simultaneous linear equations; defining, evaluating, and comparing functions; using functions to model relationships between quantities; understanding congruence and similarity using physical models, transparencies, or geometry software; understanding and apply the Pythagorean Theorem; solving real-world and mathematical problems involving volume of cylinders, cones, and spheres; and investigating patterns of association in bivariate data. These standards are covered extensively by the practice problems. This book contains over600 practice problems aligned to each Common Core State Standard. In addition the book contains an answer key to practice problems. Paperback: 241From analyzing scarcity and opportunity cost to assessing the growth of nationalism, this state-aligned study guide will provide you with the content you need to succeed on your certification test. Covering the major areas of geography, economics, political science, world history, American history, and social science, this comprehensive guide also includes 186 sample-test questions with full answer rationale. If you need FTCE Social Science 6-12 certification the first time, you need this XAMonline guide!
IT is a great advantage to have been born one of a large family group of healthy, active children, surrounded by wholesome influences. The natural and healthy discipline which children exercise upon one another, the variety of tastes and talents, the cheerful companionship, even the rivalries, misunderstandings, and reconciliations where free play is given to natural disposition, under wise but not too rigid oversight, form an excellent discipline for after-life. Being the third daughter in a family of nine brothers and sisters, who grew up to adult life with strong ties of natural affection, I enjoyed this advantage. My earliest recollections are connected with the house in Bristol, No. 1 Wilson Street, near Portman Square, to which the family removed from Counterslip, where I was born, when I was about three page years old. My childish remembrances are chiefly associated with my elder sisters, for being born between two baby brothers, who both died in infancy, I naturally followed my sisters' lead, and was allowed to be their playmate. Our Wilson Street home had the advantage of possessing a garden behind it, containing fine trees; and also a large walled garden opposite to it, with fruit trees and many flowers and shrubs, which afforded us endless delight and helped to create an early love of Nature. I cannot recall the sequel of incidents in this period of my life, for being so young when we moved to Wilson Street, the recollections of those early years are confused; but some things stand out, distinctly impressed on the memory. My eldest sister had become possessed of a small telescope, and gazing through one of the garret windows, we thought we could spy the Duchess of Beaufort's woods over the tops of the houses. There was a parapet running along the front of the house, and we were seized with a desire for a more extensive view through the precious telescope than the garret window afforded, so a petition for liberty to go on to the roof was sent to papa in our names by my lively eldest sister | 677.169 | 1 |
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This book addresses a neglected mathematical area where basic geometry underpins undergraduate and graduate courses. Its interdisciplinary portfolio of applications includes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architecture. Professor Barry, from his long experience of teaching and research, here delivers a modern and coherent exposition of this subject area for varying levels in mathematics, applied mathematics, engineering mathematics and other areas of application. Euclidean geometry is neglected in university courses or scattered over a number of them. This text emphasises a systematic and complete build-up of material, moving from pure geometrical reasoning aided by algebra to a blend of analytic geometry and vector methods with trigonometry, always with a view to efficiency. The text starts with a selection of material from the essentials of Euclidean geometry at A level, and ends with an introduction to trigonometric functions in calculus.Very many geometric diagrams are provided for a clear understanding of the text, with abundant Problem Exercises for each chapter. Students, researchers and industrial practitioners would benefit from this sustained mathematisation of shapes and magnitude from the real world of science which can raise and help their mathematical awareness and ability.Provides a modern and coherent exposition of geometry with trigonometry for varying levels in mathematics, applied mathematics, engineering mathematics and other areas of applicationDescribes computational geometry, differential geometry, mathematical modelling, computer science, computer-aided design of systems in mechanical, structural and other engineering, and architectureProvides many geometric diagrams for a clear understanding of the text and includes problem exercises for each del | 677.169 | 1 |
The Complete Idiot's Guide® to Algebra has been updated to include easier-to-read graphs and additional practice problems. It covers variationsof standard problems that will assist students with their algebra courses, along with all the basic concepts, including linear equations and inequalities, polynomials, exponents and logarithms, conic sections, discrete math, word problemsand more.
-Written in an easy-to-comprehend style to make math concepts approachable
-Award-winning math teacher and author of The Complete Idiot's Guide® to Calculus and the bestselling advanced placement book in ARCO's "Master" series
W. Michael Kelley taught high school math for seven years; during that time he received the Outstanding High School Mathematics Teacher award from the Maryland Council of Teachers of Mathematics. Additionally, he taught calculus for five years at the college level. He currently works at the University of Maryland as an Academic Technology Coordinator for the College of Education. He runs a Web site for calculus help at | 677.169 | 1 |
A Little Calculus1.22
Publisher Description
A Little Calculus is a free trial software application from the Kids subcategory, part of the Education category.
The app is currently available in English and it was last updated on 2013-04-10. The program can be installed on iOS.
A LITTLE CALCULUS is a collection of more than 70 interactive topics from a first year calculus course. To be used by both teachers and students, this app is designed to aid in the teaching and learning of calculus and should serve as a nice supplement to any introductory calculus textbook. While this app cannot be used to obtain solutions to calculus problems, it can be used to numerically and/or graphically verify computations for a wide variety of problems. Ultimately, the purpose of this app is to interact with and to gain a conceptual understanding of the fundamental topics of calculus.
TOPICS:
Graph functions of one variable, as well as parametric and polar curves.
Investigate precalculus topics such as the equation of a line, graphing polynomials, Pythagorean Theorem, trigonometric functions, etc.
Understand the fundamental notion of a limit from a formal or informal point of view.
Study rates of change using the ideas from differential calculus (e.g., secant and tangent lines, derivatives, Mean Value Theorem, Newton's method, etc.)
Calculate the area of a region or surface, length of a curve, and volume of a solid using the techniques of integral calculus.
Interact with parametric and polar curves (e.g., slopes, areas, arc lengths, etc.)
Learn about sequences and series (geometric, harmonic, alternating, etc.) and approximate functions using Taylor polynomials.
Future releases to include many more features, topics, and background information on each topic.
FEATURES:
Customize each topic by changing any function, variable, and/or interval and by selecting from a variety of options.
Interact with every graph (drag to change the value of a variable or to move/rotate the graph, pinch to zoom, etc.)
Universal App (requires iOS 7.0 or later running on iPad, iPhone, or iPod Touch.)
Fully functional, built-in calculator.
No internet required, except for initial download and updates.
No in-app purchases or advertising.
A Little Calculus (version 1.22) has a file size of 11 bytes bytes
Total downloads
3
Pricing
License model
Free Trial
Price
$0.99
Version History
Here you can find the changelog of A Little Calculus since it was posted on our website on 2016-09-27.
The latest version is 1.22 and it was updated on soft112.com on 2017-06-30.
See below the changes in each version: | 677.169 | 1 |
Math Models for Hydraulics Coming to ISO (.PDF Download)
Jan 23, 2017
Brought to you by
A mathematical model is an equation or set of equations used to predict the behavior or performance of some machine at a specified set of conditions. Thus, when we say that the force (F) is calculated by multiplying a cylinder pressure (P) times its piston area, and its speed (v) is calculated by dividing the input flow by the cylinder area, we are in fact using the ideal math model of a cylinder...
Register or Sign in below to download the full ar | 677.169 | 1 |
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Logarithmic and Trigonometric Tables: To Seven Places of
It is free to home schooled students upon proof of purchase of the book. ONLINE STORE: Purchase revision notes and prelims for National 4 and National 5 Mathematics, National 4 and National 5 Lifeskills Mathematics, (new) Higher Mathematics and (new) Advanced Higher Mathematics exams online. Choose a specific addition topic below to view all of our worksheets in that content area. Each pair The area of the diagram, Fig. 65, is considered to be divided into four quadrants as shown.
Pages: 332
Publisher: Nabu Press (March 15, 2010)
ISBN: 1147304904
Trigonometry
Trigonometry
However, these inverse trigonometric functions are very important in calculus , cited: 100 Worksheets - Finding Larger Number of 8 Digits: Math Practice Workbook (100 Days Math Greater Numbers Series) (Volume 7) As a model of randomness or ignorance, probability theory plays a critical role in the development of statistical theory. The word statistics comes from the modern Latin phrase statisticum collegium (lecture about state affairs), from which came the Italian word statista, which means "statesman" or "politician" (compare to status ) and the German Statistik, originally designating the analysis of data about the state CliffsQuickReview Trigonometry read online read online. Ideal for middle school and upper elementary students, grades 3-8. Addresses number and operations standards established by the National Council of Teachers of Mathematics (NCTM), including: => Understand and represent commonly used fractions. => Understand fractions as part of unit wholes and as locations on number lines. => Compare and order fractions, and find their approximate locations on the number line , e.g. Logarithmic and trigonometric tables, by Edward A. Bowser Surely one of the most remarkable relations in mathematics is Euler's Formula that connects trigonometric functions with exponential functions: eix = cos x + i sin x epub. These Geometry and Trigonometry Song lyrics are available from a variety of albums: The subject content (above) matches that set out in the Department for Education's Mathematics GCSE subject content and assessment objectives document epub. Both Pappus and Proclus call him Menelaus of Alexandria (Heath 260), so we may assume that he spent some of his time in Rome, and much of his time in Alexandria Natural Trigonometric FunctionsTo Seven Decimal Places For Every Ten Seconds Of Arc read for free. Similarly coverage of algebra, quadratic equations and number theory is either absent or just for namesake. Geometry coverage is mostly confined to area-volume-perimeter (=mensuration) Graphing Calculator Resource Guide subtractionrecords.com. Each solution step is provided with its objective, related definition, rule and underlying trig formula. Test preparation options automate development of printable math tests Theory of Equations: Polynomial equations; Imaginary and irrational roots; Symmetric functions of roots in terms of coefficients; Sum of rth powers of roots; Reciprocal equations; Transformations of equations pdf.
Topics include factorization in Dedekind domains, integers in a number field, prime factorization, basic properties of ramification, and local degree. This course covers the projective line and plane curves, both affine and projective. We also study conics and cubics, as well as the group law on the cubic ref.: Elements of Plane Trigonometry download online Winners of the 2016 CAS University Award Program were determined by a panel of judges from companies across the property and casualty insurance industry. Three members of the mathematics department have received 2015-16 LAS teaching awards. They are Karen Mortensen, Associate Director of Graduate Studies in Mathematics has been awarded the 2015-16 LAS Academic Professional Award , cited: A system of geometry and read epub play2.batsinbelfries.com. Another rule important later in determining geometric unsharpness in radiology is the ratio of sides. The ratio of the two sides a is the same as the ratio of the two sides b and is also the same as the two sides c , cited: Elements of geometry and download for free
PLANE TRIGONOMETRY
Elements of Trigonometry, Plane and Spherical By Lefebure De Fourcy
If we substitute for sin b and then cancel sin c, we find cos A = cos a sin B, which also gives cos B = cos b sin A. Five more identities are found involving tangents and cotangents from these , e.g. Tables Logarithmic And download for free Tables Logarithmic And Trigonometric. download. The study of Precalculus deepens students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students Introduction to Electric Circuits Introduction to Electric Circuits. Amy and the Professor try it first, but realize they can't switch back directly (since Amy and the Professor's minds have already been switched). In trying to figure out if they can switch back to their proper bodies with 4 or more bodies, the Professor announces that they'll have to use math to figure it out , e.g. Epitome Elementorum Matheseos download online
Mathematics for the practical man: Explaining simply and quickly all the elements of algebra, geometry, trigonometry, logarithms, coordinate geometry, calculus; with answers to problems,
The Elements of Algebra and Trigonometry
By Cynthia Y. Young - Trigonometry: 2nd (second) Edition
Fab Five for Trigonometry Level Nine: Graphing Vertical Shifts of Sine and Cosine Functions Using Fab Five
EBENE UND SPHARISCHE TRIGONOMETRIE
If the points are the same and the distance therefore zero and all waypoints therefore identical, the first point (either point) is returned Modern Algebra and Trigonometry nikafadul.com. Ashley Whitfield (supervisor Ted Johnson): Nonlinear dynamics of wave packets within the framework of the Ostrovsky equation and its generalisations. 2 Algebra 1, Chapter 8: download for free Algebra 1, Chapter 8: Exponents and. When they see advanced math on your transcript, college admissions officials will be impressed Student Solutions Manual download here Combination probability free worksheet, multiplying positive and negative numbers worksheet, Mcdougal Littell algebra 2 answer key, options problems examples Algebra With Trigonometry Book 2 Algebra With Trigonometry Book 2. Our free trigonometry help also include problems which you can work on to understand the topic better. Developed by Math experts, these tutorials are just what you need to get your trigonometry fundamentals right. These tutorials shows us how to do trigonometry. Besides using Math Captain's detailed and free tutorials, we also recommend you explore online tutoring and trigonometry homework help options to get better at Math online. Texere. 2004. 0812975219 This last work appears to present a contrary view to Random Walk (Malkiel) but is not nearly as contrary as its title suggests. Perhaps I should have included it with the first four. Wiley. 2003. 0471430161 Two books about crashes (kind of). He can be vague on mathematical details download. The cosine, cotangent, and cosecant are so named because they are respectively the sine, tangent, and secant of the complementary angle abbreviated to "co-". With these functions, one can answer virtually all questions about arbitrary triangles by using the law of sines and the law of cosines , source: College Algebra and read online read online. The scalar product a·b = cos c (et cycl.). The product (c x b)·(a x c) can be expanded in two ways. First, it is equal to sin a sin b cos C from evaluating the cross products Plane Trigonometry Use Code: ZAZZPAPERFUN Ends Thursday See Details The value you specified is invalid. You are viewing zazzle's Trigonometry posters section where you can find many shapes, sizes, and styles of Trigonometry posters available for customization or ready to buy as is A Textbook On Advanced Algebra And Trigonometry: With Tables (1910) Of unknown authorship and now preserved in the Bodleian Library in Oxford University, the manuscript has been variously dated—sometimes as early as the "early centuries of the Christian era." [55] The 7th century CE is now considered a plausible date. [56] The surviving manuscript has seventy leaves, some of which are in fragments Elements of plane and spherical trigonometry; with their applications to mensuration, surveying and navigation Elements of plane and spherical. Students shall be awarded one-half to one credit for successful completion of this course , source: Trigonometry: A Unit Circle download online Algebra & Trigonometry, INSTRUCTOR'S EDITION, w/ CD-ROM, 8th edition, hc, 2006 Algebra & Trigonometry, INSTRUCTOR'S. Hosmer, The Principles and Practice of Surveying, Vol I, 10th ed. (New York: John Wiley & Sons, 1970) , e.g. Seven Place Full Natural Trigonometric Tables Well, for one thing it allowed them to estimate the distance to the Sun! It all starts with a triangle, specifically a right-angled one: A right-angle is 90°, rather like the corner of a square ref.: Algebra and Trigonometry Enhanced with Graphing Utilities Sixth Edition | 677.169 | 1 |
operation matrix - always had trouble with those difficult matrices sums?
here's help-operation matrix! that performs matrix operations for you
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Dec2Bin Converter binary number to decimal;
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Graphviewer scientific equation solver You can calculate the function inflection points
Multiple functions can be plotted in different colors at once
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mPustakSubtract Mathematics Practice app that lets you learn with a lot of fun!
Complex Numbers Calculator Using the complex numbers calculator the answers to algebra problems covering this topic is only as far as your mobile phoneGreenfish Plot Greenfish Plot - This program is an advanced curve plotting application for mobile Java devices. It supports plotting multiple explicite, polar or parametric function curves. It can also perform numeric calculations such as calculating the value, derivative, integral, roots, minimum or maximum of a given function
mPustakMultiply Mathematics Practice app that lets you learn with a lot of fun! | 677.169 | 1 |
Applied mathematics vs. pure mathematics in high school?
I've just started working through "Basic Mathematics" by Serge Lang. It immediately struck me, when I skimmed through the pages, that there is a large emphasize on proving things and manipulating expressions, and very little exercises that is applying the mathematical theory to the physical world.
In my country, it's quite the opposite. In high school, about 80% of the exercises are basically applied math. For example, when we learn functions, most of the exercises are of the type:
"The resistance of a metal wire with a definite length is inversely proportional to the square of the wire's diameter. If one reduces the diameter by 25%, with how many percent will the resistance increase" (My own loose, unauthorized translation)
In Basic Mathematics, most of the exercises are of the type:
"Show that any function defined for all numbers can be written as a sum of an even function and an odd function."
The subject of this thread is: What do you think is the most advantegous way of learning mathematics? Would you even make a distinction between these two approaches like I've done, and if so, how would you describe the distinction? Is the latter approach (the "Serge Lang-approach") more popular in America?
...
The subject of this thread is: What do you think is the most advantegous way of learning mathematics?
This depends on what you're planning to do. If you want a degree in mathematics, you'll need to be comfortable with both approaches. If your plans are for something else, then you won't be as concerned with proving things.
Would you even make a distinction between these two approaches like I've done, and if so, how would you describe the distinction?
While the training for each distinction will have some overlap, the goals are often different. Pure/theoretical mathematicians are not usually concerned with the physical implications of whatever they're working on.
Is the latter approach (the "Serge Lang-approach") more popular in America?
I don't know what you mean by "more popular," so I can't really answer the question. More popular with whom: school systems, teachers, students, research? | 677.169 | 1 |
Finite Mathematics
Browse related Subjects ...
Read More section material.A wealth of pedagogy includes the following distinctive features: Worked-out Examples with Annotations to help students through the more challenging concepts; Practice Problems, offered as extra exercises after the more difficult worked-out examples; Section Summaries, briefly restating essential formulas and key concepts; Chapter Summary with Hints and Suggestions included at the end of every chapter to unify the chapter, give specific reminders, and reference problems in the review exercises suitable for a practice test; and Cumulative Review Exercises appearing at the end of groups of chapters to reinforce previously learned concepts and | 677.169 | 1 |
What's in this pack?
This pack contains 48 exam style question cards covering the new curriculum for the top grades of the new gcse in algebra. The design of a card means you can use these in a variety of ways in your classroom; as a starter or a plenary, as extension work, as homework or as a revision tool. An answer key is included.
The questions feature some challenging topics including rearranging fractional equations, expanding more than one brackets, manipulating and solving algebraic fractions with both addition and division, algebraic proofs that include some well known theories, as well as some rewriting of equation questions, factorising, completing the square and solving of quadratic equations and inequalities where the coefficient of x^2 is greater than one, as well as where the question is set up through scenarios, finding the nth term of quadratic sequences and working with the Fibonacci sequence, working with quadratic simultaneous equations, composite and inverse functions, and a variety of graph transformation questions.
Topics are as follows:
-Rearranging Equations
-Binomials
-Algebraic Fractions
-Algebraic Proof
-Quadratics Sequences
-Quadratic Inequalities
-Simultaneous Equations
-Functions
-Transformations
**This resource has been recommended by the TES Resource Team**
*UPDATED JANUARY 2017* Added a crossword puzzle with answers.
This resource pack will get your learners thinking about electricity and electric circuits. It includes:
• A lucid and logical 69-slide PowerPoint which includes many visual aids. The slides are thoughtfully animated (not over-animated) to allow opportunities for learners to participate and promote class discussions.
• Seven pages of interactive notes (scaffolded notes). These notes fit perfectly with the presentation. I find this activity keeps lower-level students engaged during the lessons while allowing differentiation for higher achievers.
• A crossword (with answers), some homework questions and a quiz.
**Just print and go! Or customize to fit the needs of your class.**
Learning objectives covered in this resources are listed below.
• By the end of these lessons, pupils should know:
1. that electricity is a form of energy.
2. that current electricity can be produced from cells, batteries or the mains
3. that there are a range of appliances in the home, which use electricity.
4. that we can represent components by symbols.
5. that current electricity flows in conductors but not in insulators.
6. that a complete path is needed from one side of the battery to the other for electricity to flow.
7. how a switch works.
8. that there are two types of circuit, series and parallel.
9. that current is measured in Amps.
10. that current is measured using an ammeter.
11. how to connect and use an ammeter.
12. that in a series circuit, the current is the same all the way round the circuit.
13. that in a parallel circuit, the current is shared but not lost or used up.
14. that the current in a series circuit depends upon the number and type of components used.
15. that a battery is a store of electrical energy.
16. that voltage is a measure of the amount of energy or push given to the current.
17. that more cells in series equals more voltage.
18. that the effect of voltage upon current and bulb brightness.
19. that an electric current causes a wire to become hot. .
20. that the bigger the current, the higher the temperature of the wire.
21. that if too much current flows, the wire will melt.
Hope you find it useful. Your feedback is much appreciated.
It's back for 2017 with a fresh new look!
All 48 booster packs (over 190 pages of content!) have been updated with the Sample paper and 2016 Reasoning and Arithmetic questions. The new video tutorials on YouTube for these questions are only accessible via this resource: a MUST for all KS2 primary schools, children and parents preparing for SATs!
This resource allows a student to choose a weak topic area of theirs (personalised learning) from a menu of 48 topics and instantly opens a printable PDF of past SATs questions specific to that topic. All 48 topic PDFs are housed on Genius Maths' Google drive account which can only be accessed via this single file. All questions contain a Youtube Button next to them, so if a student needs help, they simply HIT THE YOUTUBE button to zoom off to a mini Youtube tutorial specific to that question on our Youtube channel. The Youtube channel has over 180,000 hits and rising from those who used it during the last two year's SATs.
Also included are the One-A-Day Mini Maths Vidamins for Y5 + and links to Thinking Outside the Box puzzle videos! This single PDF could easily be placed on a teacher's computer for whiteboard projection. It could be used in whole class lessons in an ICT suite or from the comfort of a student's own living room on their tablet.
Schools placing this on their own website will be giving students the ability to access and revise for their SATs from home across multiple platforms - laptops, tablets and phones.
Students could even revise on their phone on a car journey!
The school promo posters are included to help you advertise the launch of the Organiser on your school corridors/walls.
*updated 04/12/16 to include KS2 Launch assembly and parent information letter to send home.
**updated 03/03/17 to include Answer Booklet PDF. Now you can quickly check answers to all questions in the PDF, in addition to viewing solution and answer via the YouTube video.
***Technical support: You do not need a google account to use this resource, if you are asked to sign in this it is because google has detected that someone has previously logged into a google account on your machine- in this case please first clear out cookies from your web browser. Thanks**
TRY BEFORE YOU BUY HERE:
just copy and paste the link!
Many thanks
Copyright T.Taylor
NOTE: Following its success in the summer sale, I have decided to keep the sale price - so grab a bargain! Used to be £5. Many thanks.
A self-contained game to be played in pairs.
Use to revise reading coordinates on a grid. Best played once coordinates have already been introduced, as a consolidating activity.
Differentiated versions of the game within this pack, including use of the first quadrant only, as well as all four quadrants. You will also find instructions on how to play the game within your pack. Suitable for Years 4 and 5 (on one quadrant) and Year 6 and KS3 (on all four quadrants).
YEAR 6 MASTERY MATHSCOVERS EVERY OBJECTIVE IN THE NATIONAL CURRICULUM WITH:CONCRETE, PICTORIAL, ABSTRACT, FLUENCY, REASONING AND PROBLEM SOLVINGOVER 120 IDEAS, ACTIVITIES AND TASKS.
objectives include:
Year 6 objectives
•solve problems involving the calculation and conversion of units of measure, using decimal notation up to 3 decimal places where appropriate
•use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to 3 decimal places
•convert between miles and kilometres
•recognise that shapes with the same areas can have different perimeters and vice versa
•recognise when it is possible to use formulae for area and volume of shapes
•calculate the area of parallelograms and triangles
•calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³]
•express missing number problems algebraically
•find pairs of numbers that satisfy an equation with 2 unknowns
•enumerate possibilities of combinations of 2 variables
•draw 2-D shapes using given dimensions and angles
•recognise, describe and build simple 3-D shapes, including making nets
•compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
•illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
•recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
•describe positions on the full coordinate grid (all 4 quadrants)
•draw and translate simple shapes on the coordinate plane, and reflect them in the axes
•interpret and construct pie charts and line graphs and use these to solve problems
•calculate and interpret the mean as an average
•read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
•round any whole number to a required degree of accuracy
and more!
YEAR 5 PACK NOW AVAILABLE!
find this resource and more at:
New for 2017! A pack of 5 Revision sheets/tests for the new Foundation curriculum plus some included in the Higher curriculum, and are aimed at students targeting grade 5. Hence this pack is suitable for top end Foundation students and also for great for grade 5 and generalA game that can be played in pairs, threes or independently. Please note that this game focuses on times tables facts from 2 to 10 to ensure children are confident in these tables before progressing to the 11s and 12s, which will need to be taught subsequently.
Children need a 'Table Splat' mat and counters (different coloured counters for each child). Children take turns to turn over a card, revealing a times tables question. The child who is the first to place their counter on the correct answer (whilst shouting 'SPLAT!') can leave their counter on the board. The winner is the player with the most counters on the board once all of the times table cards have been used.
Differentiate by choosing the multiplication cards relevant for that child, depending on which times table they are currently working on.
*Update: 6s and 9s have been underlined, to avoid confusion.*
Save money when bought as part of a bundle. Click the button on the right for more information.
YEAR 5 MASTERY MATHS COVERS EVERY OBJECTIVE IN THE NATIONAL CURRICULUM WITH: CONCRETE, PICTORIAL, ABSTRACT, FLUENCY, REASONING AND PROBLEM SOLVING OVER 120 IDEAS, ACTIVITIES AND TASKS.
OBJECTIVES INCLUDE:
Year 5 objectives
•read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit
•count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
•interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through 0
•round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000
•solve number problems and practical problems that involve all of the above
•read Roman numerals to 1,000 (M) and recognise years written in Roman numerals
•add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
•add and subtract numbers mentally with increasingly large numbers
•use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
•solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
•identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
•know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
•establish whether a number up to 100 is prime and recall prime numbers up to 19
•multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
•multiply and divide numbers mentally, drawing upon known facts
•divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
•multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
•recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
•solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
•solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
•solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates
•compare and order fractions whose denominators are all multiples of the same number
•identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
AND MORE!
*UPDATED January 2017 - More support worksheets added*
This resource includes a 56 slide PowerPoint presentation, four activity worksheets, a mind map, a short quiz and a 34-question unit test. Everything is ready to be used or easily edited to suit your learners.
• Includes sound clips to bring the learning to life
• Animations have been thoughtfully used to promote participation from lower achieving students and discussion from higher ability ones.
• 26 learning outcomes listed below
By the end of these lessons, pupils will:
1. recognise that sound is made by objects that vibrate
2. define that the frequency of vibration of the source is measured in Hertz (Hz)
3. discuss how sound is made in different musical instruments
4. know that a vibrating source causes the layers of air around it to move
5. discover that sound travels by compressing and expanding the surroundings
6. express that sound travels as a longitudinal wave
7. discover that sound travels best through solids and worst through gases because of the arrangement of the particles
8. explore the relative speed of sound in different mediums
9. explain that sound waves cannot travel through a vacuum because there are no molecules
10. know that sound waves detected by the ear cause the ear drum to vibrate
11. explore the structure of the ear
12. describe how sound is transmitted through the ear to the brain
13. know that different people have different ranges of hearing
14. know that the average human range of hearing is 20 to 20,000 Hz
15. define that loudness is measured in decibels (dB's)
16. discuss that 0 dB is the threshold of hearing and 130 dB's is the threshold of pain whilst 140 dB's causes damage
17. discuss that loud sounds can have permanent and temporary effect on the ear
18. discuss some common causes of ear damage
19. define that noise is unwanted sound
20. discover that a loud sound is produced by a large vibration and vice versa
21. discover that a high pitched sound is produced by a very frequent (quick) vibration and vice versa
22. know that an microphone can change sound to electricity and that this can then be displayed on an oscilloscope
23. know that the wave displayed on an oscilloscope is a transverse wave
24. demonstrate how to identify the amplitude, the wavelength and the frequency of a wave
25. recognise the link between the loudness of the sound and the amplitude of the wave
26. recognise the link between the pitch of the sound and the frequency/wavelength of the wave
Cheers!
Written by Outstanding Practitioner leading on Mastery.
Great for revision or Whole Lesson activities as it is well planned and in depth.
This contains 1 PowerPoint.
PowerPoint 1 - Lesson on Comparing and Ordering Fractions. It has 28 Comparing and Ordering Fractions, one of them is a worded problem worksheet.
Enough for minimum of 2 Lessons about 100 Minutes worth of resources.
Kindly review when you purchased this resource.
Suitable for GCSE Mathematics, GCSE Maths or any other International Qualification.
New for 2017! A pack of 5 Revision sheets/tests for the new Higher Higher curriculum, and are aimed at students targeting grade 7. Great as mixed topicVery engaging and interactive lessons. Great for whole lesson or quick fire revision.
Fraction - Equivalent Fractions Understanding equivalent fractions. (Contains 30 slides)
I have put down how many slides each PowerPoint contains as the preview slides do not do the resources justice that it deserves.
Kindly review the resource once you have purchased it. Thank you in advance.
Fraction - Adding and Subtracting Fraction.
Great for whole lesson or quick fire revision as it is well planned and in depth Adding and Subtracting Fractions. (Contains 32 Slides)
I have put down how many slides each PowerPoint contains as the preview slides do not do the resources justice that it deserves.
Kindly review the resource once you have purchased it. Thank you in advance.
Suitable for GCSE Maths, GCSE Mathematics or other International Course.
Written by an outstanding practitioner on Mastery in Mathematics.
Great for whole lesson or quick fire revision as it is well planned and in depth.
This contains 1 PowerPoint.
PowerPoint 1 - Lesson on Improper Fractions and Mixed Numbers. 42 Improper Fractions and Mixed Numbers.
Enough for minimum of 2 Lessons about 100 Minutes worth of resources
Fraction - Fraction of a Quantity.
Great for whole lesson or quick fire revision as it well planned and in detailSuitable for GCSE Maths, GCSE Mathematics or other international course.
Assessment questions included to check on understanding.
Challenge Questions included.
Presentation on: Working out Fraction of an Amount. (Contains 32 slides)
I have put down how many slides each PowerPoint contains as the preview slides do not do the resources justice that it deserves.
Kindly review the resource once you have purchased it. Thank you in advance.
3 worksheets for translations.
The first one is for them to draw the translated shape and the second is for the pupils to write the translation themselves.
The third contains both of the above plus a few blank grids for pupils to create their own shape and translation and to pass to a friend to translate the shape. | 677.169 | 1 |
Bond 11 How to Do Maths Author: Elisabeth Heesom
ISBN: 9780192742278 Format: Paperback Number Of Pages: 124 Published: 5 March 2015 Country of Publication: GB Dimensions (cm): 29.6 x 21.1 x 0.7 Description: Bond is the number 1 provider of 11+ practice, helping millions of children pass selective entrance exams. Bond How To Do Maths is a practical guide, designed for use by children but containing a wealth of information for parents. Packed with worked examples for each question type, and with practice questions to check progress in each section, this book contains expert advice and step-by-step strategies for success in 11+ and Common Entrance tests | 677.169 | 1 |
Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics)
Basic Abstract Algebra: For Graduate Students and Advanced Undergraduates (Dover Books on Mathematics)
Robert B. Ash
Language: English
Pages: 432
ISBN: 0486453561
Format: PDF / Kindle (mobi) / ePub
Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible. The early chapters provide students with background by investigating the basic properties of groups, rings, fields, and modules. Later chapters examine the relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of algebraic number theory, algebraic geometry, noncommutative algebra, and homological algebra, including categories and functors. An extensive supplement to the text delves much further into homological algebra than most introductory texts, offering applications-oriented results. Solutions to all problems appear in the text.
of this material in an undergraduate algebra course. [It should be possible to base an undergraduate course on Chapters 1-4, traversed at a suitable pace with detailed coverage of the exercises.] In Chapter 4, the fundamental structure theorems for finitely generated modules over a principal ideal domain are developed concretely with the aid of the Smith normal form. Students will undoubtedly be comfortable with elementary row and column operations, and this will significantly aid the learning
and G are inclusion-reversing by definition, the proof of (1) is complete. (3) The fixed field of σH σ −1 is the set of all x ∈ E such that στσ −1(x) = x for every τ ∈ H. Thus F (σHσ −1 ) = {x ∈ E : σ −1 (x) ∈ F (H)} = σ(F (H)). (2a) This was observed in the proof of (1). (2b) If σ is an F -monomorphism of K into E, then by (3.5.2) and (3.5.6), σ extends to an F -monomorphism of E into itself, in other words (see (3.5.6)), an F -automorphism of E. Thus each such σ is the restriction to K of a
and rs. [The product of fractional ideals is defined exactly as in (7.6.1).] Proof. (i) If x1 = a1 /b1 , . . . , xn = an /bn generate I and b = b1 · · · bn , then bI ⊆ R. (ii) If rI ⊆ R, then I ⊆ r−1 R. As an R-module, r−1 R is isomorphic to R and is therefore Noetherian. Consequently, I is finitely generated. (iii) It follows from the definition (7.6.5) that the intersection, sum and product of fractional ideals are fractional ideals. The assertions about denominators are proved by noting that r(I | 677.169 | 1 |
Elimination - Systems of Equations - PowerPoint Introduction Lesson
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This is a zipped file that contains a 6 slide PowerPoint file and a 2 page pdf file.
The PowerPoint has 6 fully animated example problems. You can explain steps and walk around the room instead of writing on the board. The pdf file is for students work along as you solve the 6 problems together.
Each problem has two linear equations given in standard form and the answer is reported as an ordered pair. The complexity of the problems increases throughout the slideshow. The first two problems do not require either equation to be multiplied by a number, the last two problems require both equations to be multiplied by a number. | 677.169 | 1 |
Project Gutenberg's Vector Analysis and Quaternions, by Alexander Macfarlane
Produced by David Starner, Joshua Hutchinson, John Hagerson, and the Project Gutenberg On-line Distributed Proofreaders.
i
MATHEMATICAL MONOGRAPHS.
EDITED BY
MANSFIELD MERRIMAN and ROBERT S. WOODWARD.
No. 8. VECTOR ANALYSIS
and
QUATERNIONS.
by
ALEXANDER MACFARLANE,
Secretary of International Association for Promoting the Study of Quaternions.
NEW YORK: JOHN WILEY & SONS. London: CHAPMAN & HALL, Limited. 1906.
Transcriber's Notes: This material was originally published in a book by Merriman and Woodward titled Higher Mathematics. I believe that some of the page number cross-references have been retained from that presentation of this material. I did my best to recreate the index.
the theory of numbers. This plan of publication has been arranged in order to meet the demand of teachers and the convenience of classes. mechanics. the first edition of which was published in 1896. each chapter being independent of the others. contained eleven chapters by eleven authors. possibly also monographs on branches of astronomy. It is the intention of the publishers and editors to add other monographs to the series from time to time. In these reissues it will generally be found that the monographs are enlarged by additional articles or appendices which either amplify the former presentation or record recent advances. and non-Euclidean geometry.Editors' Preface
The volume called Higher Mathematics. if the call for the same seems to warrant it. the group theory. It is the hope of the editors that this form of publication may tend to promote mathematical study and research over a wider field than that which the former volume has occupied. Among the topics which are under consideration are those of elliptic functions. the calculus of variations. 1905. but all supposing the reader to have at least a mathematical training equivalent to that given in classical and engineering colleges. but it is also thought that it may prove advantageous to readers in special lines of mathematical literature.
December. The publication of that volume is now discontinued and the chapters are issued in separate form.
iii
. and mathematical physics may be included.
it is now recognized as a necessity for the exact student of physics or engineering. December. In America. For those who desire information on the literature of the subject a Bibliography has been published by the Association for the promotion of the study of Quaternions and Allied Mathematics (Dublin. 1898. 1896). has been prepared by Professor Joly (London. There is still much variety in the matter of notation. Dr. Tait's Scientific Papers have been reprinted in collected form (Cambridge. 1899.Author's Preface
Since this Introduction to Vector Analysis and Quaternions was first published in 1896. 1903) which has now reached a second edition. 1904). In Great Britain. Also the writings of the great masters have been rendered more accessible. Wilson has amplified and extended Professor Gibbs' lectures on vector analysis into a text-book for the use of students of mathematics and physics (New York. 1894–). 1900). and Professor Joly has realized Hamilton's idea of a Manual of Quaternions (London. Turner have published a manual for students entitled Vectors and Rotors (London. pamphlets. Bucherer has published Elemente der Vektoranalysis (Leipzig. Knott has prepared a new edition of Kelland and Tait's Introduction to Quaternions (London. 1901). 1905. and whereas some reviewers then regarded the analysis as a luxury. Ontario. In the same interval many papers. and the relation of Vector Analysis to Quaternions is still the subject of discussion (see Journal of the Deutsche Mathematiker-Vereinigung for 1904 and 1905). 1905). 1901). In Germany Dr. and a complete edition of Grassmann's mathematical and physical works has been edited by Friedrich Engel with the assistance of several of the eminent mathematicians of Germany (Leipzig.
iv
. and Dr. and discussions have appeared. 1904). the Elements of Quaternions. Canada. A new edition of Hamilton's classic.
Chatham. the study of the subject has become much more general. Professor Henrici and Mr. 1903). Professor Hathaway has published a Primer of Quaternions (New York.
This space analysis is a universal Cartesian analysis. Arts. or quaternion in nature. in the same manner as algebra is a universal arithmetic. whether rectangular. The different views of this extension of analysis which have been held by independent writers are briefly indicated by the titles of their works:
• Argand. By providing an explicit notation for directed quantities. 2–4 treat of the more restricted analysis. by "Quaternions" is meant a space-analysis in which the quaternion is the fundamental idea. 1806. Calcolo delle Equipollenze.Article 1
Introduction.
1
. 1827. Treatise on the geometrical representation of the square roots of negative quantities. or polar. • Moebius. or of a still different nature. 1835. and developed so as to harmonize with one another and with the Cartesian Analysis1 . Essai sur une mani´ ere de repr´ esenter les quantit´ es imaginaires dans les constructions g´ eom´ etriques. • Bellavitis. while Arts. just as propositions about quantities in a plane remain true when restricted to a straight line. • Warren. Hence in the following articles the ascent to the algebra of space is made through the intermediate algebra of the plane. The subject to be treated is the analysis of quantities in space. see Nature. 1891–1893. or are of such a kind that they can be adequately represented by space quantities.
1 For
a discussion of the relation of Vector Analysis to Quaternions. Der barycentrische Calcul. whether they are vector in nature. cylindrical. Every proposition about quantities in space ought to remain true when restricted to a plane. instead of in a roundabout way by means of a quadratic function. 5–10 treat of the general analysis. They are in truth complementary parts of one whole. it enables their general properties to be investigated independently of any particular system of coordinates. and in this chapter they will be treated as such. It also has this advantage that it can express the directed quantity by a linear function of the coordinates.
By "Vector Analysis" is meant a space analysis in which the vector is the fundamental idea. 1828.
2 The dot was used for this purpose in the author's Note on Plane Algebra. as usual. and explains readily many things which are difficult to explain by the other analysis. and its direction by a small Greek letter.Article 2
Addition of Coplanar Vectors.2 but in such simple expressions as the above. the difference is sufficiently indicated by the difference of type. each component starting from the end of its
1 This notation is found convenient by electrical writers in order to harmonize with the Hospitalier system of symbols and abbreviations. as b. A system of three mutually rectangular axes will be indicated. Though a vector is represented by a line.1 its magnitude by a small italic letter. a directed area which is of two dimensions in length. A vector quantity may be such that its components have a common point of application and are applied simultaneously.
By a "vector" is meant a quantity which has magnitude and direction. The analysis of a vector here supposed is that into magnitude and direction. as β .
3
. or it may be such that its components are applied in succession. k . Kennelly has since used for the same purpose in his electrical papers. as B . R = rρ. Examples are a linear velocity which is of one dimension in length. But it will be found that the analysis into magnitude and direction is much more in accord with physical ideas. A vector will be denoted by a capital italic letter. For example. the vector is analyzed into tensor and unit-vector. 1883. and whose direction coincides with or represents the direction of the vector. B = bβ . It is graphically represented by a line whose length represents the magnitude on some convenient scale. an axis which is of no dimensions in length. which means that the tensor is a mere ratio destitute of dimensions. Sometimes it is necessary to introduce a dot or a mark to separate the specification of the direction from the expression for the magnitude. its physical dimensions may be different from that of a line. According to Hamilton and Tait and other writers on Quaternions. while the unit-vector is the physical magnitude. j . by the letters i.
36/36◦ 30 . then we have the more symmetrical formula OC =
2 + f 2 + 2f f cos(θ − θ ) f1 1 2 2 1 2
tan−1
f1 sin θ1 + f2 sin θ2 . and AC parallel to OB .—Let OA and OB represent two vectors of the same kind simultaneously applied at the point O.—Let the forces applied at a point be 2/0◦ and 3/60◦ . f1 cos θ1 + f2 cos θ2
When the components are equal. and join OC . This principle was discovered with reference to force. Take the direction of OA for the initial direction. and an example of the latter in two rectilinear displacements made in succession to one another. Thus OA may be denoted by f1 /0. OB by f2 /θ2 . f1 + f2 cos θ2
Example. OC by f /θ. ADDITION OF COPLANAR VECTORS. From the geometry of the figure it follows that
2 2 f 2 = f1 + f2 + 2f1 f2 cos θ2
and tan θ = hence OC =
2 + f 2 + 2f f cos θ 2 f1 1 2 2
f2 sin θ2 . Then the resultant is 4 + 9 + 12 ×
1 2
tan−1
√ 3 3 7
= 4.
If the first component is given as f1 /θ1 .ARTICLE 2. f1 + f2 cos θ2
tan−1
f2 sin θ2 . but it applies to any vector quantity coming under the above conditions. The diagonal OC represents in magnitude and direction and point of application the resultant of OA and OB .
4
predecessor. and the magnitude of the resultant is twice the projection of either component on the bisecting line. OC = 2f1 cos 2 2
. Draw BC parallel to OA. the direction of the resultant bisects the angle formed by the vectors. An example of the former is found in two forces applied simultaneously at the same point.
Composition of Components having a common Point of Application. The above formula reduces to θ2 θ2 . the direction of any other vector will be sufficiently denoted by the angle round which the initial direction has to be turned in order to coincide with it.
f1 cos(θ2 − θ1 ) + f2 = f cos(θ2 − θ). and there is only one set of two components which produces a given resultant. then the other component is f2 /θ2 =
2 − 2f f cos θ f 2 + f1 1
tan−1
f sin θ −f1 + f cos θ
Given the resultant and the directions of the two components.—The resultant of two equal alternating electromotive forces which differ 120◦ in phase is equal in magnitude to either and has a phase of 60◦ . 1 − cos2 (θ2 − θ1 )
. Join AC and draw OB equal and parallel to AC . The line OB represents the component required. from which it follows that f1 = f {cos(θ − θ1 ) − cos(θ2 − θ) cos(θ2 − θ1 )} . It is evident that OA and OB when compounded produce the given resultant OC ." Let f /θ be the vector and f1 /0 one component. then compound it with the given resultant to find the required component. the lines OA and OB cut off represent the required components. The line OB is identical with the diagonal of the parallelogram formed by OC and OA reversed. hence the rule is. to find the other component. and CB parallel to OX . hence they are the only pair of components having the given directions.
Given a vector and one component.—Let OC represent the resultant. for it is the only line which combined with OA gives OC as resultant.
5
Example.—The resultant is represented by OC .ARTICLE 2. Then f1 + f2 cos(θ2 − θ1 ) = f cos(θ − θ1 ). ADDITION OF COPLANAR VECTORS. Let f /θ be the vector and /θ1 and /θ2 the given directions. "Reverse the direction of the component. to find the magnitude of the components. From C draw CA parallel to OY . and OA the component. and the directions by OX and OY .
let 100/60◦ . 2
π . ADDITION OF COPLANAR VECTORS. as A. f cos θ
f cos θ
+
f sin θ
. 2
π . 1 + cos 60◦
6
Composition of any Number of Vectors applied at a common Point. C . For example.—The resultant may be found by the following graphic construction: Take the vectors in any order. Now f1 /θ1 = f1 cos θ1 /0 + f1 sin θ1 Similarly f2 /θ2 = f2 cos θ2 /0 + f2 sin θ2 and fn /θn = fn cos θn /0 + fn sin θn Hence f /θ = = f cos θ /0 +
2
π . The resultant obtained is the same. whatever the order. the vector from the beginning of A to the end of C is the resultant of the given vectors. and as the order is arbitrary. The result may be obtained analytically as follows: Given f1 /θ1 + f2 /θ2 + f3 /θ3 + · · · + fn /θn . B . From the end of A draw B equal and parallel to B . This follows by continued application of the parallelogram construction. 2
f
θ
2
π 2 · tan−1 f sin θ . /30◦ . then f1 = 100 cos 30◦ . and /90◦ be given.ARTICLE 2. and from the end of B draw C equal and parallel to C . the area enclosed has no physical meaning.
3
Composition of Successive Vectors.) Prob. For any number of successive vectors. 4/40◦ . 3 h/nt. and has a physical meaning. 2
3 This does not hold true of a sum of vectors having a real order of succession.ARTICLE 2. 3/30◦ . then A + B = −C . and B a vector starting from the end of A. The line OP is not the complete equivalent of A + B . The resultant vector is 123/45◦ . (Ans. Zero. ADDITION OF COPLANAR VECTORS.—The composition of successive vectors partakes more of the nature of multiplication than of addition. In this chapter no attempt is made to apply formal laws to directed quantities. but each pair differs in phase by 120◦ . Calculate the resultant vector of 1/10◦ . etc. the ordinary rule about the transposition of a term in an equation holds good. This is permissible because there is no real order of succession among the given components. The diagonal OP represents A + B only so far as it is considered independent of path. But A + B and B + A determine different paths. 1. and from O draw a vector equal to B . 2/20◦ . it would also be the complete equivalent of B + A.
Prob. and A + C = −B . Find the components of the vector 100/70◦ in the directions 20◦ and 100◦ . and B + C = −A. the areas they determine with OP have different signs. if it were so. Prob. the sum so far as it is independent of path is the vector from the initial point of the first to the final point of the last. 4. The velocity of a body in a given plane is 200/75◦ . Prob. Prob. It is a mistake to attempt to found space-analysis upon arbitrary formal laws. Three alternating magnetomotive forces are of equal virtual value. Compound the following magnetic fluxes: h sin nt + h sin(nt − 120◦ )/120◦ + (Ans. Prob. 6. and from its extremity a vector equal to A. 2. find the other component. 3. 5. What is attempted is an analysis of these quantities. This is also true when the successive vectors become so small as to form a continuous curve. find the resultant. if A + B + C = 0. For example. The area between the curve OP Q and the vector OQ depends on the path. the fundamental rules must be made to express universal properties of the thing denoted. Let A be a vector starting from the point O. and one component is 100/25◦ . Draw the third side OP .
7
In the case of a sum of simultaneous vectors applied at a common point. and one component is 100/0◦ .
. find the other component.) h sin(nt − 240◦ )/240◦ . and as they go oppositely around.
ADDITION OF COPLANAR VECTORS. a/nt. 8. 9. Prob. Compound two alternating magnetic fluxes at a point a cos nt/0 and a sin nt/ π .
.
8
Prob. Find the resultant of two simple alternating electromotive forces 100/20◦ and 50/75◦ . Prove that a uniform circular motion is obtained by compounding two equal simple harmonic motions which have the space-phase of their angular positions equal to the supplement of the time-phase of their motions. 7.ARTICLE 2. 2 (Ans.) Prob.
9
.
When all the vectors considered are confined to a common plane. Thus the complete product breaks up into two partial products. namely. that the square of a sign of direction is +. but unfortunately it does not explain ii = +. each may be expressed as the sum of two rectangular components. as suggested by ordinary algebra. it is supposed not to be an axis. R = xi + yj . j an operand. The kind of operator which i is supposed to denote is a quadrant of turning round the axis i. Here i and j are not unit-vectors. not necessarily of the same kind physically. Hence AB = (a1 i + a2 j )(b1 i + b2 j ) = a1 b1 ii + a2 b2 jj + a1 b2 ij + a2 b2 ji. and (a1 b2 − a2 b1 )k which has the axis of the plane for direction.—Let A = a1 i + a2 j and B = b1 i + b2 j be any two vectors. If we assume. and k the result. Let i and j denote two directions in the plane at right angles to one another. but a quadrant of rotation round an axis. but we do not assume that the order of the factors is indifferent. then the above reduces to AB = a1 b1 + a2 b2 + (a1 b2 − a2 b1 )k.Article 3
Products of Coplanar Vectors. This explains the result ij = k. We assume that their product is obtained by applying the distributive law. and further that the product of two directions at right angles to one another is the direction normal to both. then A = a1 i + a2 j . but rather signs of direction. Product of two Vectors. a1 b1 + a2 b2 which is independent of direction. B = b1 i + b2 j .1
1 A common explanation which is given of ij = k is that i is an operator. for it would give ii = i.
it is an essentially positive or signless quantity. 2 × 4 + 3 × 5 = 23 foot-pounds per second. The former partial product is so called because it is of such a nature.
2 2 Corollary 2. the direction of the other A must be the same.—SBA = SAB . draw QM and N L perpendicular to OP . It is denoted by SAB where the symbol S. PRODUCTS OF COPLANAR VECTORS. denotes. then SAB denotes the rate of working of the force. The kinetic energy due to the downward 642 10 velocity is 10 × and that due to the horizontal velocity is × 1002 . for whatever the direction of A. Then (OP )(OM ) = (OP )(OL) + (OP )(LM ). a a = a1 b1 + a2 b2 .
10
Scalar Product of two Vectors. Corollary 1.ARTICLE 3. Let OP and OQ represent the vectors A and B . For instance. being in Roman type. Its kinetic energy then is 10 (642 + 1002 ) foot-poundals. 2 a quantity which has no direction.—By a scalar quantity is meant a quantity which has magnitude and may be positive or negative but is destitute of direction.
Example 2.—A2 = a2 1 + a2 = a . let A denote a force and B the velocity of its point of application. The result is the same whether the force is projected on the velocity or the velocity on the force. hence the scalar product cannot be negative. a1 a2 = a b1 + b2 . but a function of the vectors A and B . The square of any vector is independent of direction. Example 1.—A force of 2 pounds East + 3 pounds North is moved with a velocity of 4 feet East per second + 5 feet North per second. find the rate at which work is done. not a vector. The geometrical meaning of SAB is the product of A and the orthogonal projection of B upon A.—A stone of 10 pounds mass is moving with a velocity 64 feet down per second + 100 feet horizontal per second. the 2 2
.
—Let A = (10i + 11j ) inches and B = (5i + 12j ) inches. and is denoted by VAB . then SAB = ab cos αβ . Example. It is to be observed that the coordinates of A and B are mere component vectors. their pole. and draw the lines indicated by the figure. when the components are rectangular. It is then evident 1 1 a2 a2 − 2 b1 b2 − 1 that the area of the triangle OP Q = a1 b2 − 2 2 (a1 − b1 )(b2 − a2 ) = 1 ( a b − a b ). that is. Its geometrical meaning is the product of A and the projection of B which is perpendicular to A. 800 cos 45◦ volts. but by simple addition. PRODUCTS OF COPLANAR VECTORS. where αβ denotes the angle between the directions α and β .
. the area of the parallelogram formed upon A and B . Example.
11
whole kinetic energy is obtained. The two together written as above specify the normal k . that is. where αβ denotes the direction which is normal to both α and β . Also VAB = ab sin αβ · αβ . not by vector. that is. Example. 65 square inches in the plane which has the direction k for axis.
Vector Product of two Vectors. Here /45◦ indicates the direction α and /90◦ the direction β . 1 2 2 1 2 Thus (a1 b2 − a2 b1 )k denotes the magnitude of the parallelogram formed by A and B and also the axis of the plane in which it lies. whereas A and B themselves are taken in a real order.ARTICLE 3.—At a distance of 10 feet /30◦ there is a force of 100 pounds /60◦ The moment is VAB = 10 × 100 sin /30◦ /60◦ pound-feet 90◦ //90◦ = 1000 sin 30◦ pound feet 90◦ //90◦ Here 90◦ / specifies the plane of the angle and /90◦ the angle. then VAB = (120 − 55)k square inches.—The other partial product from its nature is called the vector product. If A is expressed as aα and B as bβ .—The effective electromotive force of 100 volts per inch /90◦ along a conductor 8 inch /45◦ is SAB = 8 × 100 cos /45◦ /90◦ volts. and /45◦ /90◦ means the angle between the direction of 45◦ and the direction of 90◦ . It follows that VBA = −VAB . that is. Let OP and OQ represent the vectors A and B .
A−1 = α = 2 = 2 a a a1 + a2 2
The reciprocal and opposite vector is −A−1 . a a
2 Writers who identify a vector with a quadrantal versor are logically led to define the reciprocal of a vector as being opposite in direction as well as reciprocal in magnitude.ARTICLE 3. In the figure let OP = 2β 1 be the given vector. A−1 = feet East + 125 5 10 5 feet North and −A−1 = − feet East − feet North.—If A = 10 feet East + 5 feet North. a b = (cos αβ + sin αβ · αβ ).—By the reciprocal of a vector is meant the vector which combined with the original vector produces the product +1. and OR = 2 (−β ) is its reciprocal and opposite. 125 125 125 Product of the reciprocal of a vector and another vector.2 10 Example. then OQ = 1 2 β is its reciprocal. The reciprocal of A is denoted by A−1 . b must equal a−1 and β must be identical with α in order that the product may be 1. a
Hence SA−1 B =
b b cos αβ and VA−1 B = sin αβ · αβ . Since AB = ab(cos αβ + sin αβ · αβ ). a2 1 = 2 a1 b1 + a2 b2 + (a1 b2 − a2 b1 )αβ .
. PRODUCTS OF COPLANAR VECTORS.— A−1 B = 1 AB.
12
Reciprocal of a Vector. It follows that a1 i + a2 j aα 1 .
2/90◦ . B = 3/0◦ + 4/90◦ . the total product will be represented by OR. If the product is formed after the other mode of association we have A(BC ) = (a1 i + a2 j )(b1 c1 + b2 c2 ) + (a1 i + a2 j )(b1 c2 − b2 c1 )k = (b1 c1 + b2 c2 )(a1 i + a2 j ) + (b1 c2 − b2 c1 )(a2 i − a1 j ) = SBC · A + VA(VBC ).—Let A = 1/0◦ + 2/90◦ . where αβγ denotes the direction which is perpendicular to the perpendicular to α and β and γ . Hence the latter partial product differs with the mode of association. where the point separates the vectors to which the S refers.—Let A = a1 i + a2 j . The latter product is also expressed by (VAB )C . B = b1 i + b2 j . C = 5/0◦ + 6/90◦ .
Square of a Binomial of Vectors.
The former partial product means the vector C multiplied by the scalar product of A and B .—If A + B denotes a sum of non-successive vectors. The fourth proportional to A. B. the resultant of OP and OQ. Then (AB )C = (a1 b1 + a2 b2 ) + (a1 b2 − a2 b1 )k (c1 i + c2 j ) = (a1 b1 + a2 b2 )(c1 i + c2 j ) + (a1 b2 − a2 b1 )(−c2 i + c1 j ). If these partial products (represented by OP and OQ) unite to form a total product.
13
Product of three Coplanar Vectors.ARTICLE 3. while the latter partial product means the complementary vector of C multiplied by the magnitude of the vector product of A and B . and more analytically by abc cos αβ · γ . The vector a2 i − a1 j is the opposite of the complementary vector of a1 i + a2 j . But the square of
. It is also expressed by abc sin αβ · αβγ . which is equivalent to V(VAB )C . C is (A−1 B )C = 1×3+2×4 5/0◦ + 6/90◦ 12 + 22 1×4−2×3 + −6/0◦ + 5/90◦ 12 + 22 = 13. it is entirely equivalent to the resultant vector C . because VAB is at right angles to C . PRODUCTS OF COPLANAR VECTORS.4/0◦ + 11. Example. C = c1 i + c2 j denote any three vectors in a common plane. The former product is also expressed by SAB · C .
—Let A + B + C denote a sum of successive vectors. PRODUCTS OF COPLANAR VECTORS. while the vector part gives four times the area included between the path and the third side. The product terms must be formed so as to preserve the order of the vectors in the trinomial. = A2 + AB + BA + B 2 . + 2(VAB + VAC + VBC ). Hence S(A + B + C )2 = (1) = a2 + b2 + c2 + 2ab cos αβ + 2ac cos αγ + 2bc cos βγ and V(A + B + C )2 = (2) = {2ab sin αβ + 2ac sin αγ + 2bc sin βγ } · αβ (1) (2)
. Hence (A + B )2 = (A + B )(A + B ). = A2 + B 2 + 2SAB.
14
any vector is a positive scalar. The scalar part gives the square of the length of the third side. that is. giving (A + B )2 = A2 + 2AB + B 2 = A2 + B 2 + 2SAB + 2VAB. and consequently we need not expect the square to be a scalar quantity. This may also be written in the form a2 + b2 + 2ab cos αβ. not of the factors. A is prior to B and C . there is no third vector C which is the complete equivalent. but of the terms in the binomial. and B is prior to C . = A2 + B 2 + SAB + SBA + VAB + VBA. = A2 + B 2 + C 2 + 2(SAB + SAC + SBC ). Square of a Trinomial of Coplanar Vectors. hence the square of A + B must be a positive scalar. the square must be formed after the rules for the products of rectangular components (p. We observe that there is a real order. Since A and B are in reality components of one vector. 432). this causes both product terms to be AB .ARTICLE 3. But when A + B denotes a sum of successive vectors. Hence (A + B + C )2 = A2 + B 2 + C 2 + 2AB + 2AC + 2BC.
PRODUCTS OF COPLANAR VECTORS. find the area of the polygon. 12. or vector product. Find the sine and cosine of the angle between the directions 0. A force of 10 pounds /45◦ is acting at the end of 8 feet /200◦ . .) Prob. and 6/0◦ + 5/90◦ . find the torque. which is the theorem of moments. 7/225◦ ..5807 N.8141 E. Find the fourth proportional to 10/0◦ + 2/90◦ .17/90◦ . but in accordance with the order of the vectors in the trinomial. C = 7/45◦ . 1 1 V(AB + AC + BC ) = {15 sin /0◦ /30◦ + 21 sin /0◦ /45◦ + 35/30◦ /45◦ }. find the moment.75 + 7.04 × 107 lines per inch per second. and 0.000 lines per square inch /0◦ .53 = 15.03/0◦ + .—Let A = 3/0◦ . find the vector product. (Ans. 11.5060 E. Prob.7. 13. 16. At a distance of 25 centimeters /20◦ there is a force of 1000 dynes /80◦ . what is the work done (scalar product)? What is the meaning of the negative sign in the scalar product? Prob. Prob. (Ans. + 0. 8/180◦ .
. + 0. B = 5/30◦ . The radius of curvature of a curve is 2/0◦ + 5/90◦ . per second. Prob.ARTICLE 3. 14.) Prob. 15. 8/0◦ − 3/90◦ . 1. Also that the product terms are not formed in cyclical order. Prob. The vector part is four times the area included between the successive sides and the resultant side of the polygon. Note that it is here assumed that V(A + B )C = VAC + VBC . 9/100◦ . find the curvature. A conductor in an armature has a velocity of 240 inches per second /300◦ and the magnetic flux is 50. 10.42 + 4. per second + 50 feet SE. A mass of 100 pounds is moving with a velocity of 30 feet E.
Prob. find its kinetic energy. 2 2 = 3. 18.
15
The scalar part gives the square of the vector from the beginning of A to the end of C and is all that exists when the vectors are non-successive. 17.8625 N. Find the area of the polygon whose successive sides are 10/30◦ . When a force of 200 pounds /270◦ is displaced by 10 feet /30◦ . Prob. Example.
for the two vectors may or may not be of the same physical kind. where θ denotes the angle in radians. It is the most important key to the extension of analysis to space. it is not conical. Etymologically "quaternion" means defined by four elements. but the above form shows that the equation is homogeneous. Also R = rβ θ and A = β −θ . hence all the quaternions considered have a common axis. that is to say. the turning-factor may be omitted. a quantity destitute of physical dimensions. The magnitude may or may not be a mere ratio. The operator which changes A into R consists of a scalar multiplier and a turning round the axis β . and expresses nothing but the
1 The idea of the "quaternion" is due to Hamilton. When the angle is naught. Thus π β θ = cos θ · β θ + sin θ · β 2 . which is true in space. The turning is in a plane. that is.
16
. in plane analysis it is defined by two.
By a "quaternion" is meant the operator which changes one vector into another. the direction normal to the plane may be denoted by β . one of which has a zero angle and the other an angle of a quadrant. Thus R = rβ θ A and 1 1 1 1 reciprocally A = β −θ R. For the present all the vectors considered lie in a common plane.Article 4
Coaxial Quaternions. Let the former be denoted by r and the latter by β θ . r A R r The turning factor β θ may be expressed as the sum of two component operators. Its importance may be judged from the fact that it has made solid trigonometrical analysis possible.1
Let A and R be two coinitial vectors. It is composed of a magnitude and a turning factor.
n the alternations per unit of time. that is. the operator which changes the current into the electromotive force is a quaternion. Components of the Reciprocal of a Quaternion. p θ = tan−1 . where r is the resistance. also that I −1 E = r + 2πnl · β 2 . are given by r= p2 + q 2 . COAXIAL QUATERNIONS. The resistance is the scalar part of the quaternion. which stands for −1. and I the alternating current in magnitude and phase. l the self-induction. The relations between r and θ.
2 In
. and p and q .—Let E denote a sine alternating electromotive force in magnitude and phase. and the inductance is the vector part.2 Hence rβ θ = r cos θ + r sin θ · β 2 =p+q·β2 and rβ θ A = pA + qβ 2 A = pa · α + qa · β 2 α.—Given R = p + q · β 2 A. and that it also serves to specify the general turning factor β θ as well as the quadrantal turning π factor β 2 . q
π π π π
17
Example. equivalence of a given quaternion to two component quaternions. The advantages of using the above notation are that it is capable of being applied to space. and β denotes the axis of the plane of representation. then E = r + 2πnl · β 2 I.
√ π the method of complex numbers β 2 is expressed by i.ARTICLE 4. It follows that π E = rI + 2πnl · β 2 I . then A= 1 π R p+q·β2 π p−q·β2 R = π π p+q·β2 p−q·β2 p−q·β2 R p2 + q 2 π p q = − 2 ·β2 2 2 2 p +q p +q
π π π π
=
R.
ARTICLE 4. then R = r θ −θ β R." treat this product of coaxial quaternions as if it were the product of vectors. and R to R . The angles are summed because they are indices of the common base β . p + q2 π (pp + qq ) + (pq − p q ) · β 2 = R. p+q·β2 π π p − q · β 2 = (p + q · β 2 ) 2 R. and A to R . Given R = rβ θ A = (p + q · β 2 )A and R = r β θ A = (p + q · β 2 )A. The impressed alternating electromotive force is 200 volts. COAXIAL QUATERNIONS.4 Quotient of two Coaxial Quaternions. required the current. the resistance of the 1 circuit is 10 ohms.7 amperes / − 20◦ 42 .
19
Product of Coaxial Quaternions. 19.—If the given quaternions are those which change A to R. such as Hayward in "Vector Algebra and Trigonometry. the quaternion which changes A to R is obtained by taking the product of the given quaternions. are given. r
π π π π π π
1 π R.
. and likewise the product of the turning factors.)
4 Many writers. Given R = rβ θ A = p + q · β 2 A and R = r β θ A = p + q · β 2 R. p2 + q 2 = (p + q · β 2 )
Prob. then that which changes R to R is obtained by taking the quotient of the latter by the former.—If the quaternions which change A to R. (Ans. then R = rr β θ+θ A = (pp − qq ) + (pq + p q ) · β 2 A. 18. and there are 60 alternations per second." and Stringham in "Uniplanar Algebra. This is the fundamental error in the Argand method. the self-induction is 100 henry. Note that the product is formed by taking the product of the magnitudes.
r2 . find the impressed voltage. 22. 21. and self-inductions l1 . etc. A number of coils having resistances r1 .
.. If the electromotive force is 110 volts /θ and the current is 10 amperes /θ − 4 find the resistance and the self-induction.
Prob.
Prob. 20. etc. there being 120 alternations per second. l2 .
20
1 π.ARTICLE 4. COAXIAL QUATERNIONS. and reciprocally. are placed in series.. find the impressed electromotive force in terms of the current. If in the above circuit the current is 10 amperes. Prob.
It may be specified as xi + yj + zk ρ= 2 . then we deduce the other form thus: R = r cos θ · i + r sin θ cos φ · j + r sin θ sin φ · k. x
For example. The additional angle φ/ is introduced to specify the plane in which the angle from the initial line lies. B = 10 30◦ //45◦ = 10 cos 45◦ · i + 10 sin 45◦ cos 30◦ · j + 10 sin 45◦ sin 30◦ · k. x + y2 + z2 where the three squares are subject to the condition that their sum is unity.
A vector in space can be expressed in terms of three independent components. If we are given R in the form rφ//θ. we deduce R= x2 + y 2 + z 2 tan−1 z y tan−1 y2 + z2 . If R is given in the form xi + yj + zk .Article 5
Addition of Vectors in Space. and any constant vector B may be expressed as B = bβ = b1 i + b2 j + b3 k. and when these form a rectangular set the directions of resolution are expressed by i. k . In space the symbol ρ for the direction involves two elements. 21
. Any variable vector R may be expressed as R = rρ = xi + yj + zk . Or it may be specified by this notation. j . a generalization of the notation for a plane. φ//θ.
and the vector of electromotive force. and consequently are summed by simple addition. and ji = −k we obtained (p. In the dynamo three principal vectors have to be considered: the velocity of the conductor at any instant. j 2 = +. ij = k. Frequently all that is demanded is. because k is in tri-dimensional space the axis which is complementary to i and j . We also observe that the three rules ij = k . ik = −j .
The square combinations give results which are independent of direction. The figure shows that these rules are made to represent the relation of the advance to the rotation in the right-handed screw. The area vector determined by i and j can be represented in direction by k .Article 6
Product of Two Vectors.—By the rules i2 = +. from the symmetry of space we assume that the following rules are true for the product of two vectors in space: i2 = +. jk = i. The physical meaning of these rules is made clearer by an application to the dynamo and the electric motor. ki = j . Accordingly. jk = i. ik = −j . kj = −i.
Rules of Signs for Vectors in Space. j 2 = +. k2 = + . given two of these directions to determine 23
. the intensity of magnetic flux. each of which has the highest importance in mathematical and physical analysis. kj = −i. ki = j are derived from one another by cyclical permutation. ij = k . likewise the three rules ji = −k . ji = −k. 432) a product of two vectors containing two partial products.
and that the magnetic flux is to the left. for it compares the three directions directly with the right-handed screw. is AB = (a1 i + a2 j + a3 k )(b1 i + b2 j + b3 k ). corresponding to the rotation from the velocity to the flux in the righthanded screw we have advance into the paper: that then is the direction of the electromotive force. corresponding to current flux we have advance towards the bottom of the page. The corresponding formula for the electric motor is current flux = mechanical-force. and force current = flux. Complete Product of two Vectors. Suppose that the direction of the velocity is i. The formula ij = k becomes velocity flux = electromotive-force. that its velocity is towards the bottom. Example. not necessarily of the same kind physically.
24
the third. = a1 b1 ii + a2 b2 jj + a3 b3 kk + a2 b3 jk + a3 b2 kj + a3 b1 ki + a1 b3 ik + a1 b2 ij + a2 b1 ji = a1 b1 + a2 b2 + a3 b3 + (a2 b3 )i + (a3 b1 − a1 b3 )j + (a1 b2 − a2 b1 )k a1 = a1 b1 + a2 b2 + a3 b3 + b1 i a2 b2 j a3 b3 k
. Their product. from which we derive by cyclical permutation flux force = current. and that the magnetic flux is towards the left. and electromotive-force velocity = flux. and that of the flux j . from which we deduce flux electromotive-force = velocity. which therefore must be the direction of the mechanical force which is applied to the conductor.ARTICLE 6. then the direction of the electromotive force is k . 444). suppose that in a motor the direction of the current along the conductor is up from the paper. according to the rules (p.
The formula velocity flux = electromotive-force is much handier than any thumb-and-finger rule.—Suppose that the conductor is normal to the plane of the paper. PRODUCT OF TWO VECTORS.—Let A = a1 i + a2 j + a3 k and B = b1 i + b2 j + b3 k be any two vectors. Again.
PRODUCT OF TWO VECTORS. Corollary 2. the vectors are necessarily homogeneous.—Hence SBA = SAB . for the two factors have the same direction. namely. b3 k respectively. and OP × ON = OP × (OL + LM + M N ). but in a product the vectors may be heterogeneous. and OQ represent B . The square of A must be positive. and let OL. For b1 a1 + b2 a2 + b3 a3 = a1 b1 + a2 b2 + a3 b3 .
25
Thus the product breaks up into two partial products. In a sum of vectors. Example. Corollary 1.—The vector product as before is denoted by VAB .
Scalar Product of two Vectors. Its geometrical meaning is the product of A and the orthogonal projection of B upon A. and negative when they have opposite directions. The former is called the scalar product.—Let the intensity of a magnetic flux be B = b1 i + b2 j + b3 k . The product is positive when the vector and the projection have the same direction. Then ON is the orthogonal projection of OQ. a a a = a1 b1 + a2 b2 + a3 b3 = SAB.—The scalar product is denoted as before by SAB . a1 a2 a3 = a b1 + b2 + b3 . which has the direci j k tion normal to the plane of A and B .ARTICLE 6.—Hence A2 = a1 2 + a2 2 + a3 2 = a2 . then the flux through the area is SSB = bl sl + b2 s2 + b3 s3 . By making a3 = b3 = 0. and the latter the vector product. Vector Product of two Vectors. LM . b2 j . we deduce the results already obtained for a plane. Let OP represent A. The product of B and the orthogonal projection on it of A is equal to the product of A and the orthogonal projection on it of B . and let the area be S = s1 i + s2 j + s3 k . It means the product of A and the component of B which is perpendicular
. and M N be the orthogonal projections upon OP of the coordinates b1 i. which is independent of direction. and b1 b2 b3 . a1 b1 + a2 b2 + a1 a2 a3 a3 b3 .
and is represented by the area of the parallelogram formed by A and B . and let C denote any other vector having the same point of application.
. and ij represent the respective components of the product. PRODUCT OF TWO VECTORS. Product of two Sums of non-successive Vectors.—Given A = r φ//θ and B = r φ //θ . Thus (a1 b2 − a2 b1 )k denotes the magnitude and direction of is 2 the parallelogram formed by the projections of A and B on the plane of i and j .—If A is expressed as aα and B as bβ . The orthogonal projections of this area upon the planes of jk .—Hence VBA = −VAB . and (a3 b1 − a1 b3 )j that on the plane of k and i. Example.—Let A and B be two component vectors. C = c1 i + c2 j + c3 k.
Let A = a1 j + a2 j + a3 k. where αβ denotes the direction which is normal to both α and β .—Given two lines A = 7i − 10j + 3k and B = −9i + 4j − 6k .ARTICLE 6. Example. then the triangle OP Q is the projection of half of the parallelogram formed by A and B . giving the resultant A + B . to find the rectangular projections of the parallelogram which they define: VAB = (60 − 12)i + (−27 + 42)j + (28 − 90)k = 48i + 15j − 62k. Corollary 1. For. Corollary 2. Then SAB = rr cos φ//θ φ //θ = rr {cos θ cos θ + sin θ sin θ cos(φ − φ)}. let OP and OQ (see second figure of Art. Similarly (a2 b3 − a3 b2 )i denotes in magnitude and direction the projection on the plane of j and k . B = b1 i + b2 j + b3 k. ki.
26
to A. 3) be the orthogonal projections of A and B on the plane of i and j . and drawn in the sense given by the right-handed screw. then SAB = ab cos αβ and VAB = ab sin αβ · αβ . But it is there shown that the area of the triangle OP Q 1 (a1 b2 − a2 b1 ).
A body of 1000 pounds mass has linear velocities of 50 feet per second 30◦ //45◦ and 60 feet per second 60◦ //22◦ . and the magnetic flux is N. find the difference of potential at the ends. then (A + B )(C + D) = AC + AD + BC + BD. Prob. Show that if a system of area-vectors can be represented by the faces of a polyhedron. find the direction of the mechanical force on the conductor. what is the direction of the electromotive force in the conductor? Prob. Prob. Prob. Prob. 31.ARTICLE 6.
27
Hence (A + B )C = AC + BC . C and D. 37. their resultant vanishes. PRODUCT OF TWO VECTORS. The arm is 9i + 11j + 13k feet. A conductor 8i + 9j + 10k inches long is subject to an electromotive force of 11i + 12j + 13k volts per inch. A + B = (a1 + b1 )i + (a2 + b2 )j + (a3 + b3 )k. and the force applied at either end is 17i + 19j + 23k pounds weight.5.
. In the same way it may be shown that if the second factor consists of two components. The relative velocity of a conductor is S. 30. Find the rectangular projections of the area of the parallelogram defined by the vectors A = 12i − 23j − 34k and B = −45i − 56j + 67k. 35.. Show that work done by the resultant velocity is equal to the sum of the works done by its components. Prob. find its kinetic energy. that of the magnetic flux is West. The direction of the current is vertically downward. Since A and B are independent of order. which are non-successive in their nature.W.W. When A + B is a sum of component vectors (A + B )2 = A2 + B 2 + AB + BA = A2 + B 2 + 2SAB.) Prob. 326 volts. Similarly V(A + B )C = {(a2 + b2 )c3 − (a3 + b3 )c2 }i + etc. 32. (Ans. 29. Prob. 28. A body to which a force of 2i + 3j + 4k pounds is applied moves with a velocity of 5i + 6j + 7k feet per second.
Prob. Prob. 33. find the torque. 34.. = (a2 c3 − a3 c2 )i + (b2 c3 − b3 c2 )i + · · · = VAC + VBC. 36. consequently by the principle already established S(A + B )C = (a1 + b1 )c1 + (a2 + b2 )c2 + (a3 + b3 )c3 = a1 c1 + a2 c2 + a3 c3 + b1 c1 + b2 c2 + b3 c3 = SAC + SBC. find the rate at which work is done. Show that the moment of the velocity of a body with respect to a point is equal to the sum of the moments of its component velocities with respect to the same point.
Example. we know that S(VAB )C = S(VBC )A = S(VCA)B = −S(VBA)C = −S(VCB )A = −S(VAC )B. Hence the volume formed by the three vectors has no direction in space.—From the determinant expression for the third product. Hence any of the three former may be expressed by SABC . and let the straight wire L = 15 centimeters 60◦ //45◦ . in the usual formula for the volume of a parallelepiped. PRODUCT OF THREE VECTORS. C taken in that order. and cos αβγ to cos φ. B. Sum of the Partial Vector Products.ARTICLE 7.—Let the velocity of a straight wire parallel to itself be V = 1000 /30◦ centimeters per second. and the product of VAB with the projection of C upon it is the measure of the volume in magnitude and sign.—By adding the first and second partial products we obtain the total vector product of ABC . Third Partial Product. The line VAB represents in magnitude and direction the area formed by A and B .
The third product S(VAB )C is represented by the volume of the parallelepiped formed by the vectors A. which is denoted by V(ABC ). By decomposing the second product we obtain V(ABC ) = SAB · C − SBC · A + SCA · B. Then VV B = 6000000 sin 60◦ 90◦ //90◦ lines per centimeter per second.
30
The determinant expression for this partial product may also be written in the form a1 b1 a2 c1 b2 i a c2 + 2 b2 j a3 c2 b3 j a c3 + 3 b3 k a1 c3 b1 k c1 i
It follows that the frequently occurring determinant expression a1 b1 a2 c1 b2 d 1 a c2 + 2 b2 d2 a3 c2 b3 d 2 a c3 + 3 b3 d3 a1 c3 b1 d 3 c1 d1
means S(VAB )(VCD). Hence S(VV B )L = 15 × 6000000 sin 60◦ cos φ lines per second where cos φ = sin 45◦ sin 60◦ . but it is positive or negative according to the cyclical order of the vectors. let the intensity of the magnetic flux be B = 6000 /90◦ lines per square centimeter. In the expression abc sin αβ cos αβγ it is evident that sin αβ corresponds to sin θ.
. and any of the three latter by −SABC .
m2 at the extremity of A2 . The equation expresses a physical of mechanical principle. A mass m − m may be introduced at the extremity of any radius-vector R. it is required to find how to add or compound them.Article 8
Composition of Quantities. and means the directed moment of m with respect to the extremity of R. together with the said mass-vector applied at the extremity of R. etc.
Addition of a Located Scalar Quantity. The equation states that the mass m at the extremity of the vector A is equivalent to the equal mass at the extremity of R. The product m(A − R) is what Clerk Maxwell called a mass-vector. so that mA = (m − m)R + mA = mR + mA − mR = mR + m(A − R). mA = mR + m(A − R) . Here A − R is a simultaneous sum. m1 at the extremity of A1 ..
A number of homogeneous quantities are simultaneously located at different points. and denotes the radius-vector from the extremity of R to the extremity of A.
32
.—Let mA denote a mass m situated at the extremity of the radius-vector A. Hence for any number of masses.
and a force of 7i + 9j + 11k pounds weight at 10i + 12j + 14k feet. F2 at A2 . COMPOSITION OF QUANTITIES. etc.
+
the condition for no resultant couple is VR which requires F = VAF.ARTICLE 8. so that the
. such as F1 at A1 . find the torque which must be supplied when both are transferred to 2i + 5j + 3k . This equation asserts that a force F applied at the extremity of A is equivalent to an equal force applied at the extremity of R together with a couple whose magnitude and direction are given by the vector product of the radius-vector from the extremity of R to the extremity of A and the force.—Let FA denote a force applied at the extremity of the radius-vector A.. As a force F − F may introduced at the extremity of any radius-vector R.—Given a force 1i + 2j + 3k pounds weight at 4i + 5j + 6k feet. Hence for a system of forces applied at different points.
F to be normal to
Example. VAF . we have FA = (F − F ) + FA = FR + V(A − R)F. we obtain (FA ) = = Since V (A − R) F = = VAF − VAF − VR VRF F (FR ) + F
R
V (A − R) F V (A − R) F.
34
Composition of a Located Vector Quantity.
ARTICLE 8. 44. VAF − VR F F = 0. Find the torque for 4i +3j +2k pounds weight at 2i − 3j +1k feet. hence it is given by V that is V VR F F =V AF F. we obtain 2 − F R + SR F· F =V AF F. Since F = 8i + 11j + 14k . the perpendicular
8i + 11j + 14k 1 9i − 18j + 9k = {351i + 54j − 243k }. Example. 381 381
Prob. hence there always is a central axis. 47.
This is the same straight line as before. Find the moment at 90◦ //270◦ of 10 pounds at 4 feet 10◦ //20◦ and 20 pounds at 5 feet 30◦ //120◦ . Prob. 64 + 121 + 196 8i + 11j + 14k 1 = and F 381 to the line is Since V VAF = 9i − 18j +9k . 46.
36
The condition for the central axis is that the resultant force and the resultant couple should have the same direction. COMPOSITION OF QUANTITIES. 45. and 2i − 1k − 1k pounds weight at −3i + 4j + 5k feet when transferred to −3i − 2j − 4k feet. the direction of the line is 8i + 11j + 14k √ .
. therefore R= 1 ( F) 1 =V F
2V
F V (V
AF +
SR (
F F)
2
·
F
AF ) + SR
1 · F
F. Prob. only no relation is now imposed on the directions of F and VAF . Prob. Find the central axis in the above case.
By expanding the left member according to the same principle as above. Prove that the mass-vector drawn from any origin to a mass equal to that of the whole system placed at the center of mass of the system is equal to the sum of the mass-vectors drawn from the same origin to all the particles of the system.—Find the central axis for the system of forces in the previous example.
To prove that β b ρ coincides with the axis of β 2 ρ 2 β 2 . Take the more general −b versor ρθ . Let OP represent the axis β , AB the versor β 2 , BC the versor ρθ . Then (AB )(BC ) = AC = DA, therefore (AB )(BC )(AE ) = (DA)(AE ) = DE . Now DE has the same angle as BC , but its axis has been rotated round P by −b π b 2 ρ 2 β 2 will coincide with β b ρ.1 the angle b. Hence if θ = π 2 , the axis of β The exponential expression for β 2 ρ 2 β 2 is e− 2 bβ 2 + 2 πρ 2 + 2 bβ 2 which may be expanded according to the exponential theorem, the successive powers of the
1 This theorem was discovered by Cayley. It indicates that quaternion multiplication in the most general sense has its physical meaning in the composition of rotations.
−b π b 1 π 1 π 1 π
−b
π
b
ARTICLE 10. COMPOSITION OF ROTATIONS.
46
trinomial being formed according to the multinomial theorem, the order of the factors being preserved. Composition of Finite Rotations round Axes which Intersect.—Let β and γ denote the two axes in space round which the successive rotations take place, and let β b denote the first and γ c the second. Let β b × γ c denote the single rotation which is equivalent to the two given rotations applied in succession; the sign × is introduced to distinguish from the product of versors. It has been shown in the preceding paragraph that βbρ = β
−b 2
ρ2 β2;
π
b
and as the result is a line, the same principle applies to the subsequent rotation. Hence γ c (β b ρ) = γ
−c 2
unless you receive specific permission. complying with the rules is very easy. Special rules.Article 11
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Showing 1 to 30 of 98
Linear Algebra
The words linear and algebra dont always appear together. The
word
linear is an adjective used in many settings: linear equations, linear
regression, linear programming, linear technology, and so on.
The word algebra, of course, is famil
Getting Systematic with
Systems of Equations
Investigating Solutions for Systems
A system of equations has a solution when you
have at least one set of numbers that replaces
the variables in the equations and makes each
equation read as a true statement.
Mastering Matrices
and Matrix Algebra
Matrices have their own arithmetic. What you think
of when you hear multiplication has just a slight
resemblance to matrix multiplication.
When working with matrices, youll find just enough
familiarity to let you fe
Vektor
A vector is a special type of matrix (rectangular array
of numbers)
When you create a vector, you write the
numbers in a column surrounded by brackets.
Vectors have names
The names of vectors are usually written as
single, boldfaced, lowercase le
AINU & BASQUE LANGUAGE *
CORRELATION
INTRODUCTION
An ancient language form that originated in the North African area of our most ancient
civilizations has been studied by Nyland (2001). He found that many words used to describe names
of places and things
TKI163612 Teori Keputusan
Dawi Karomati B, S.T., M.Sc
Semester Ganjil 2016/2017
8/13/2016
STUDY CASE
A company is to decide if it should fund a 5-year R&D program to develop a new
product for the market. Depending on the outcome of the research, the
compa
Probabilistic thinking (II)
Factorization rule for joint probability
Changing the order of conditioning
Suppose in the previous tree we have
There is no reason why we should always conditioned G on B. suppose we want to
draw the tree in the order G to B | 677.169 | 1 |
Showing 1 to 6 of 6
Y = mx + b Word Problems
1. Suppose that the water level of a river is 34 feet and that it is receding at a
rate of 0.5 foot per day. Write an equation for the water level, L, after d days. In
how many days will the water level be 26 feet?
2. Seths father
INTERMEDIATE ALGEBRA Advice
Showing 1 to 3 of 6
The teacher is so patient that she'll answer multiple questions from the same person. She'll also answer emails. She even did for that me. (I didn't answer it because, I figured out what I was supposed to do).
Course highlights:
I got more practice in this area.
Hours per week:
6-8 hours
Advice for students:
I recommend working on MOM as soon as you can ,so if you encounter any problems, then the teacher can answer any questions you have.
Course Term:Summer 2017
Professor:Ms. Kejika Riley
Course Required?Yes
Course Tags:Math-heavyMany Small AssignmentsParticipation Counts
Jul 15, 2017
| No strong feelings either way.
This class was tough.
Course Overview:
I took her online course, where I had to use Youtube videos. The man, John Salak, was quite knowledgeable. They just got boring to watch.
Course highlights:
I guess I got a little bit better at some types of problems.
Hours per week:
3-5 hours
Advice for students:
I suggest trying to take a regular lecture class because, I've read some good things on her. (I've read that she is fast paced, though.)
Course Term:Spring 2017
Professor:Raksha Patel
Course Required?Yes
Course Tags:Math-heavy
May 05, 2017
| Would recommend.
Not too easy. Not too difficult.
Course Overview:
yes I would recommend it the professor is a good person to work with and really helps you understand if you have questions.
Course highlights:
I learned a lot in this course I was struggling 1st semester and she was able to help me out a lot | 677.169 | 1 |
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Device Combines Features Of Computer & Calculator
11/01/95
Expressly designed for high-school and college mathematics instruction, the TI-92 combines the power of computer software and the independence of a calculator. The portable, hand-held unit sports a full QWERTY keyboard, numeric keypad, eight-direction cursor and function keys that operate pull-down menus. It supports NCTM standards and accommodates a broad range of math subjects from algebra through calculus. For example, the TI-92's interactive geometry applications allow students to build objects using points, lines, triangles, polygons, circles, arcs and other basic shapes. Objects can be translated, rotated and dilated. Its symbolic manipulation features, meanwhile, were developed in conjunction with Soft Warehouse, authors of DERIVE. Students may explore polynomial factors, roots of equation, indefinite integrals, derivatives, limits and Taylor polynomials. Expressions appear on the screen just as they would in a printed textbook. The device graphs functions, parametric equations, polar equations, recursively defined sequences and 3D surfaces. With optional TI-GRAPH LINK software, one may transfer data and programs between the TI-92 and a computer. The TI-92 is also compatible with the firm's Calculator-Based Laboratory (CBL) System, for analyzing real-world data. Texas Instruments, Dallas, TX, (800) TI-CARES | 677.169 | 1 |
Mathematics
Below you can browse and buy physical and digital products for the Edexcel Mathematics curriculum. Check out the bestselling physical books for the latest GCSE (9-1) specification and look at the current A Level top titles. Remember to check back for the new publishing in A Level Mathematics for teaching from September 2017.
Have you spotted our next day delivery truck on a product? Order these items before midday on a school account and get delivery next working day.
Remember, if you can't find what you're looking for below you can useExam Board: AQALevel & Subject: GCSE MathsFirst teaching: September 2015 First exams: June 2017This Maths all-in-one revision and practice book is guaranteed to help you achieve the best results. Containing clear and accessible explanations of all the GCSE content, there are lots of practice opportunities for each topic throughout the book.
Contains sample exam papers for Edexcel AS and A Level exam preparation. This work also includes a revision planner and checklist as well as a fully worked examination-style paper with chief examiner's commentaryWritten by Chief Examiners and providing the best match to the specification, this title motivates students by making maths easier to learn. Suitable for the GCE specification, it features student-friendly worked examples and solutions, leading up to a wealth of practice questions. It also includes sample exam papers for exam preparation.
Presenting worked examples and solutions leading to practice questions, this helps students to learn maths. It features sample past exam papers for exam preparation, and includes regular review sections. It includes a CD ROM which contains what students need to motivate and prepare themselves.
Offering worked examples and solutions leading to practice questions, this book helps students to learn maths. It features sample past exam papers for exam preparation, and regular review sections. It includes a CD ROM which contains what students need to motivate and prepare themselves. | 677.169 | 1 |
College Algebra: Concepts and Models was the first college algebra text to be developed specifically for students who may not be proceeding on to calculus or upper-level math courses, but who need a solid understanding of algebra for their social sciences and liberal arts majors. It encourages student understanding of algebra through the use of modeling techniques and real-data applications. Optional use of technology is carefully integrated throughout the text.
A text-specific web site offers instructor and student resources, including chapter-by-chapter online tutorials for the student. Also available on the web site are the Programs appendix and Career Interviews section.
Chapter Openers and Chapter Projects have been updated to reflect current topics and data.
Section Openers now include a set of learning objectives for each section.
Real Data Application examples have been updated or replaced with new applications.
Technology Boxes have been revised to remove references to specific programs or calculator models.
Exercise Sets include additional and updated skill exercises and applications.
Chapter Summaries have been rewritten to link the section objectives to the Review Exercises He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson. | 677.169 | 1 |
Order of Math and Physics Courses
Hello, I am preparing to start college and I'm looking for assistance in how to order my courses. Before taking any Physics courses, my school requires you complete Calculus 1. After taking Calculus 1, I will be eligible for Physics 1. Would it be wise to complete Calculus 2 before beginning Physics 1, or should succeeding in Calculus 1 adequately prepare me for Physics 1?
A description of Physics 1: This course is a calculus-based study of the mechanics of rigid bodies, emphasizing Newton's laws and its applications. This course includes an introduction to fluids. It is designed for engineering, physical science, and computer science majors.
Also, after Calculus 2, I'll need to take Ordinary Differential Equations, Multivariable Calculus, and Linear Algebra. What would be the preferable order to take these classes?
My planned major is Aerospace Engineering. I'm starting at a community college and expecting to spend 3 years competing prerequisite transfer classes, so taking extra time to get everything done doesn't worry me.
Calculus 1 should adequately prepare you for an introductory, calculus-based physics course. As for ODEs, multivariable calculus, and linear algebra, I don't think order should be important. I did multivariable calculus first, and then ODEs and linear algebra concurrently, which worked out well for me.
Staff: Mentor
Would it be wise to complete Calculus 2 before beginning Physics 1, or should succeeding in Calculus 1 adequately prepare me for Physics 1?
Assuming your Calc 1 covers both basic derivatives and basic integrals, you'll be OK. This is a common prerequisite for Physics 1 at many colleges/universities. You probably won't actually use much calculus in Physics 1 for working out problems, and when you do, it will probably involve only simple derivatives and integrals like polynomials and maybe sines, cosines or exponentials. The calculus is mainly used to make basic relationships between physical quantities simpler or more general, i.e. acceleration is the derivative of velocity, etc. | 677.169 | 1 |
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Summary
Introduction to Linear Algebra, Sixth Edition, is a foundation text that bridges both practical computation and theoretical principles. This bookrs"s flexible table of contents makes it suitable for readers interested in science and engineering as well as readers who want an introduction to mathematical abstraction and logical reasoning. To achieve this flexibility, the authors focus on three principle topics: matrix theory and systems of linear equations, elementary vector space concepts, and the eigenvalue problem. For all readers interested in linear algebra. | 677.169 | 1 |
books.google.com - Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative... and Understanding Mathematics | 677.169 | 1 |
Download and read online Algebra 2 Trigonometry in PDF and EPUB Presents past Regents exams on algebra and trigonometry, offers explanations of right and wrong answers, and reviews general concepts in the subjects.
Download and read online Barron s Regents Exams and Answers Geometry in PDF and EPUB ThisDownload and read online Barron s Regents Exams and Answers in PDF and EPUB "The section on how to answer Part C questions and the glossary were adapted from Let's review: physics, by Miriam A. Lazar and Albert S. Tarendash, published by Barron's Educational Series, Inc., 1996"--T.p. verso.
Download and read online Barron s Regents Exam and Answers Algebra I in PDF and EPUB As of 2014, the New York State Algebra I curriculum is completely aligned with Common Core standards. This up-to-date book will prepare students for the new Algebra I (Common Core) Regents exam. It features: the first two actual Regents exams administered for the updated Algebra 1 course; all answers fully explained; comprehensive review questions, grouped by topic; study tips, test-taking strategies, score analysis charts, and more valuable features. Students will find a review of all pertinent math topics, including sets, algebraic language, linear equations and formulas, ratios, rates, and proportions, polynomials and factoring, radicals and right triangles, area and volume, quadratic and exponential functions, and much more. It's an essential, must-have guide to preparing for the Algebra I Regents.
Download and read online Let s Review Integrated Algebra in PDF and EPUB (Download and read online Alpha Teach Yourself Algebra I in 24 Hours in PDF and EPUB A one-volume, one-day algebra course. Alpha ? Covers classifying number sets, expressions, polynomials, factoring, radicals, exponents and logarithms, and much more ? Each chapter ends with a quiz so readers can identify where they may need more help | 677.169 | 1 |
Showing 1 to 25 of 25
Determine the domain of a function
A function f is a rule that assigns to each element x in a set A (called the domain
of f ) exactly one element f (x) in a set B (called the range of f ). If a function f is given by
a formula and the domain is not specie
Chapter 1Functions
1.4Trigonometric Functions and Their Inverses
In this section we review some of the basic ideas and properties associated with
trigonometric functions.
Radian Measure
Angles are measured in degrees or radian. In Calculus, typically ang
Chapter 1Functions
1.2Representing Functions
In this section we will explore different ways to define and represent functions
formulas, graphs, tables, and words.
Using Formulas
There are a number of functions that typically are defined by a formuls. The
Chapter 3Derivatives
3.10Related Rates
In related rates problems we compare the rate of change of one quantity in terms of the rate of
change of another quantity. For example, if you blow up a balloon, both the volume and the
radius of the balloon are in
Chapter 3
3.2
Derivatives
Rules of Differentiation
Up to this point you have learned how to compute a derivative using the limit definition. Now we
will learn some rules that will help you compute derivatives of certain functionsconstant
functions, power
Math 1131
Spring 2012
Exponentials, Trig Functions, and their
Inverses
1. A variable star is one whose brightness alternately increases and decreases. For the most
visible variable star, Delta Cephei, the time between periods of maximum brightness is
5.4
Chapter 1Functions
One of the most basic building blocks of the calculus is functions. In this chapter we will
explore the basic properties of a function, the graph of a function, and ways of combining
and transforming functions. Generally there are four
Chapter 3Derivatives
3.1Introducing the Derivative
We now begin our discussion of one of the most fundamental ideas of the Calculusthe
Derivative. We will approach the Derivative from two perspectives: 1) finding the tangent line
to a curve at a particul
Chapter 3
3.3
Derivatives
The Product and Quotient Rules
Previously we learned that the derivative of a sum of functions is the sum of the derivatives of the
functions and that the derivative of the difference of functions is the difference of the deriva
Chapter 2Limits
2.7Precise Definition of Limits
The intuitive definition of a limit, that is, as x approaches a ,
f ( x) approaches some number L is a bit vague in mathematical terms. In order to be able to
prove that the limit of f ( x) is L as x appro
Graphing Rational Function Rules
Rule for Domain
Set each factor of the denominator equal to zero. This is where the function will be undefined.
The domain for the function will be all real numbers except those that make the denominator
zero.
Rule for Ver
Chapter 1Functions
1.3Inverse, Exponential, and Logarithmic Functions
We begin this section with a study of exponential functions. Many real-world
phenomena are modeled by exponential functions, for example, in finance, medicine,
biology, economics, and
Chapter 2Limits
2.2Definitions of Limits
In this section we begin the process of defining the idea of a limit in a more formal
mathematical way. To begin we examine the behavior of a linear function around some
values of .
Suppose we want to investigate
Chapter 2Limits
2.3Techniques for Computing Limits
Previously we learned how to estimate limits using graphs and tables. In this section we
learn analytical methods in order to calculate limits precisely. We befin with limits of
linear functions.
Limits
Chapter 2Limits
2.5Limits at Infinity
Previously we learned about infinite limits and vertical asymptotes. Limits at infinity occur when
the independent variable
increases or decreases without bound, that is
.
In this
section we examine limits at
Chapter 2Limits
2.4Infinite Limits
An infinite limit occurs when functional values increase or decrease without bound, that is, the
values tend to +!"! . In this section we will examine such limits.
An Overview
1
(if it exists).
x 0 x 2
1
We begin by fir
Chapter 2Limits
2.6Continuity
Continuity, an important mathematical concept of the Calculus, is term that is associated with
continuous functions. Essentially, continuous functions are functions that can be drawn without
any brakes, jumps, or holes in it
Chapter 2Limits
Limits represent one of the first big ideas of the Calculus. Limits are important since they
provide a foundation for the two main branches of the Calculusthe Differential
Calculus and the Integral Calculus. In this chapter we will examine | 677.169 | 1 |
Education - Mathematics
Year 7
Semester 1
The focus in term one is on numerical skills. Students will work independently and in small groups to develop skills in number operations, mapping and statistics in semester one. The mode of delivery will be varied, including teacher directed, student directed, and will also include use of technology to enhance the learning experience.
Semester 2
The focus in Semester Two is on problem solving. Students will work independently and in small groups to develop their skills in introductory formula writing in algebra, patterns, identifying angles, calculating area of basic shapes, becoming familiar with measurement and time and transformations. The mode of delivery will be varied, including teacher directed, student directed, and will also include use of technology to enhance the learning experience.
Year 8
Semester One
In this unit of work students will develop number skills with specific unit focus on Number and Algebra, Location & Measurement. An emphasis will be placed on developing numeracy skills and the ability to work mathematically through extended investigation.
Semester Two
By the end of this semester students will have developed skills in Statistics and Probability by collecting, analysing and interpreting data and the effect on averages of outliers. They will have determined complimentary events and probabilities to solve problems. In studying Measurement and Geometry they will recognise the features of circles and solve problems including circumference and area and use correct units in all aspects of measurement. An emphasis has been placed on developing numeracy skills and the ability to work mathematically through extended investigation.
Year 9
Semester One
Students will extend understanding of Number and Algebra by building on knowledge of Index Laws and simplifying a range of algebraic expressions. They will also describe the relationship between graphs and equations through a review of Co-ordinate Geometry. They will use proportionality both in graphs of rate and of financial mathematics and interpret ratio and scale factor. They will also follow mathematical arguments to develop strategies in investigating similarity. Students also study Measurement and Geometry and are introduced to Pythagoras' Theorem and its application in problem solving.
Semester Two
Statistics and Probability and Data Representation are linked when students collect data from secondary sources to investigate an issue and construct histograms and back-to-back stem-and-leaf plots. They will also make sense of the position of the mean and median in skewed, symmetric and bi-modal displays to describe and interpret data. Students will also build on knowledge developed earlier in the year and apply similarity to problem solving with Trigonometry. They extend their knowledge of Pythagoras and linear graphing, along with applying distance formula, finding the gradient and midpoint of a line segment and developing reasoning to sketch linear and non-linear relations to solve expressions involving binomials. | 677.169 | 1 |
Math News
October 09, 2016
With the first quarter nearly over, the various math classes have several concepts under their collective belts.
Algebra class has taken a look at classifying numbers, working with signed numbers, following the order of operations and converting from one unit to another, among other things. Speaking of unit conversions, one of the most difficult concepts for students to understand is how to convert cubic units back and forth. For example, when converting from cubic yards to cubic feet, one does not simply multiply by 3 (even though we all know that 1 yard is 3 feet). Since a cubic yard has three dimensions (length, width, height), it is necessary to instead multiply by 27 (which is 3 x 3 x 3). Essentially you are multiplying by 3 once for each of those dimensions.
Geometry began their year by looking at the three basic "building blocks" of geometry, also known as "points, lines and planes." From the walls of a house to a stop sign to the more complex hexagonal prism (which is the official term for the six-walled classrooms at OHS), it's truly amazing how many real life objects are simply combinations of these three fundamental geometric principles. Since then, students have moved on to other concepts like perimeter, area and angle measurement.
The General Math classes are currently spending their time studying geometric concepts, before eventually moving on to some algebraic concepts during the third quarter. Finally, they will spend the fourth quarter learning how to apply math in the job environment.
Algebra 2 have been studying matrices recently. While that sounds terribly irrelevant, a matrix (singular form of matrices) is simply a group of numbers arranged in rows and columns. If you've ever looked at a baseball box score, you've probably seen the score broken down inning by inning, ie. the two rows of numbers where you see the number of runs each team scored each inning. Yeah, that's a matrix. And people say algebra isn't used in real life. Baseball says otherwise :)
Both the Trigonometry and Calculus classes have had their work cut out for them, as they have spent their first quarter solving math problems reserved for those who are college bound, and not faint of heart where math is concerned. Critical thinking and problem solving abound. (Fortunately for them, critical thinking and problem solving are two skills Nebraska employers are looking for in their potential employees, according to a recent study). Simple math is in the rearview mirror. Gone are the days when a math problem can be solved in a few seconds. Most of the problems they tackle take several minutes and multiple strategies.
Here's a sample of the problems our students tackle. If you can get all these correct, you get an A :)
Algebra: Your living room is 12 feet long and 10 feet long. How many square yards of carpet would you need to cover it?
Geometry: Why do photographers use a tripod when they take pictures?
General Math: You are filling up the 15-gallon tank of your car with gas. Gas is on sale in Osceola for $2.36/gallon. Gas is on sale in York for $1.99/gallon. Would you save more money by purchasing your gas in Osceola or York? (Keep in mind that driving to York involves the additional cost of the gas you would use driving there and back).
Algebra 2: A store purchases a TV for $115. They plan to markup the TV by 500%. What price will they sell it for?
Trig/Pre-Calc: Ten workers can complete a road project in 15 days. How long would it take 25 workers to complete five of the same road projects? | 677.169 | 1 |
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
Word Problems Made Easy 2.0
Word problems don't have to be hard - in here I give some tips that I use in my own classroom knowledge of Algebra and/or be enrolled in an Elementary or Intermediate Algebra (Algebra 1 or Algebra 2) course.
Students should have some experience solving linear equations. Some lessons will involve more advanced equations such as polynomial and rational equations.
Some lessons will involve use of the quadratic formula. For the Elementary/Algebra 1 student, this may not apply to you so you could still watch most other lessons.
Description
Word problems, also called story problems, are understandably a source of frustration for many students taking an Algebra course. But it doesn't have to be that way. In this course, I put together ten years of classroom teaching experience in Mathematics into a unified strategy that will help you solve most common Algebra class word problems. Although all word problems are different, there are commonalities among them. An emphasis here is put in on how to read the word problem, how to organize and analyze the information given, and not be overwhelmed by all the numbers being thrown at you.
Who is the target audience?
This course is for students who are enrolled in an Algebra course and want help with solving word problems.
I have been teaching College Mathematics and Statistics since 2006. I've taught college math courses ranging from Basic Math and Algebra to Precalculus, Calculus, and Statistics. My core belief is that math is everywhere, and should be accessible to everyone. I never accept the words "I'm just bad at math" because it IS within the reach of everyone! | 677.169 | 1 |
MatBasic Desciption:
The MatBasic is the language of mathematical calculations. Strong mathematical base: full complex arithmetic's, linear algebra and operations, nonlinear methods and graphical visualization.
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MatBasic is a calculating, programming and debugging environment using special high-level programming language designed for solving mathematical problems. MatBasic programming language allows execution of difficult mathematical calculations, involving an exhaustive set of tools for the purpose of creation of algorithmic programs. It also allows a user to abstract his mind from the type of working data which can be either real-valued, or complex numbers, or matrices, or strings, or structures, etc. The MatBasic supports both the text and the graphical data visualization.
MatBasic is fast language interpreter and its environment application field is wide: from solving the school problem to executing different engineering and mathematical computations. The MatBasic programming language combines; simplicity of BASIC language, flexibility of high-level languages such as C or Pascal and at the same time turns up to be a powerful calculation tool. By means of a special operating mode, Matbasic it is possible to use as the powerful calculator. Also the MatBasic can be used for educational purpose as a matter of studying the bases of programming and raising algorithmization skills.
Efficient Java Matrix Library or EJML is an Java based linear algebra library designed to help you with the manipulation of dense matrices. Its design goals are: to be as computationally efficient as possible for both small and large matrices and to be...
Differential Equations is a handy application designed to help you solve equations with minimum effort. The program enables you to specify the coefficients by using the keyboard on the main window.It is designed to calculate the solution to homogeneous...
Linear Algebra Decoded is a program designed to assist students in the subject of Linear Algebra, although it has features for professors, including the ability to generate tests where problems are customized and solutions are in the field of integers....
This script defines the Matrix class, an implementation of a linear algebra matrix. Arithmetic operations, trace, determinant, and minors are defined for it. This is a lightweight alternative to a numerical Python package for people who need to do...
STIMATH is a high-level tool for mathematics, linear algebra, plotting and expression evaluation that can be used from any programming environment or even from a command line interface. It is an executable that takes a single argument, the name of a...
Diofantos is a library for the solution of equations that arise in physics. It deals with ordinary differential equations (ODE), partial differential equations (PDE), including grid generation, and integral equations.
centralApp Controller was built as a small and useful app that uses Ordinary Differential Equations to find a solution to a body under a central force.centralApp Controller was developed with the help of the Java programming language and can run | 677.169 | 1 |
Harrap's Mathematics Mini Dictionary
Description
A concise guide to more than 7000 mathematical terms and concepts. Tailored to GCSE and SCE syllabus requirements, the book seeks to clarify theory and practice in arithmetic, geometry, set theory, calculations, functions, algebra, bases, logarithms, basic astronomy and mathematical tools.show more | 677.169 | 1 |
Algebra I Simplifying Expressions for use with Expressions
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this file type before downloading and/or purchasing.
2 MB|29 pages
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Product Description
This is a 29 page flipchart with 27 pages set with questions. These 14 slides are preset for the questions to be used with the ActivExpression devices. However, the flipchart can certainly be used for review even if you do not have Expressions in your classroom. About half of the questions have a numeric answer and about half are multiple choice.
The questions consist of:
Simplifying expressions with positive and negative exponents
Simplifying expressions with zero as the exponent
Changing from scientific notation to standard form
Scientific notation with both positive and negative exponents
Finding a common ratio
Identifying arithmetic and geometric sequences
Finding future terms in a sequence
Each slide is set with the question and the correct answer programmed. Also included is a page with directions for exporting your assessment results to Excel. | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
8 MB|44 pages
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Product Description
This lesson is designed to reinforce prime factorization with the goal of memorizing the factorization of numbers under 50. After tracking data for over twenty years on algebra skills, I have learned this is one of the most important fundamentals for students in Pre-Algebra, Algebra and even Advanced Algebra. Prime Factorization is an automatic response that must occur for Exponent Operations, Polynomial Factoring and Division, and Logarithms. The data strongly suggests students who struggle with the second semester of Advanced Algebra often have struggles with Prime Factorization or the seeing of numbers as prime factors. Here, the lesson takes prime factorization further by teaching students how to find the LCM and GCF of two or more numbers. | 677.169 | 1 |
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
Getting started with MATLAB
The ultimate introduction to Matlab for (absolute) beginners install Matlab on your computer to follow the course by reproducing the codes we are discussing during the course and by solving the exercises. Most universities offer a free software version of Matlab, please ask your university if such a license is available. You could also get a trial version of Matlab at the official Matlab website.
Basic knowledge in Mathematics
The will to learn Matlab
Description
This course is designed to help you get started working with Matlab. Following topics are going to be covered: | 677.169 | 1 |
Welcome to A Level!
How would you like to learn?
Why Study A Level Maths?
A Level Maths is a respectable qualification, notorious for its difficulty. However, beyond this, the qualification is home to a tonne of rigour and fun. You have an ability to encounter new ideas and explore already-known ones in greater depth. So, if you enjoy maths or want to be challenged, then this qualification is definitely for you. The content on the site is designed to help guide you through your A Level Maths or Further Maths studies, so simply choose a module and start learning.
Watch the videos
Core One
Learn how to differentiate and integrate, how to do advanced problems in coordinate geometry and how to work with arithmetic sequences and series.
Core Two
Coming soon.
Further Pure 1
Explore the new concept of complex numbers, how to prove a recurrence relationship by induction and work with matrices in the first unit of further maths.
Below you can find FP1 worksheets that are stratified by chapter.
These do not have solutions and the likelihood is that I will not be able to upload solutions until the exams finish. I know this is not going to be any use to you, but feel free to send me solutions you have and if I receive enough, I will put them into worked solutions booklets for others to learn from. You can email me solutions or queries at: info@crashmaths.com
Mechanics 1
Coming soon.
Use our resources!
We have dedicated a lot of time to create a variety of different resources for you to use. On the site, you can find an exclusive range of unique, homemade past papers for you to try, containing questions that span the entire grade range and ones that you haven't come across before. We have also took a lot of time to create worksheets in the hope that they will help you consolidate your understanding of particular areas of maths and cement any gaps you may have. Besides the maths, our revision resources may also be helpful to you. | 677.169 | 1 |
Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications The Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing.
He also uses the philosophy to analyze the history of games and modern trends as well as to design games. Providing a robust, useful philosophy for game design, this book gives you real answers about what games are and how they work.
While familiarity with LaTeX and HTML is helpful, the book requires no prior experience with advanced programs or languages. For beginners, the text provides enough features to get started on basic applications.
In addition, most of the brain imaging data sets and MATLAB codes are available on the author's website. By supplying the data and codes, this book enables researchers to start their statistical analyses immediately.
Using real-life applications, this graduate-level textbook introduces different mathematical methods of scientific computation to solve minimization problems using examples ranging from locating an aircraft, finding the best time to replace ... | 677.169 | 1 |
Anfangsgründe Der Ebenen Und Sphärischen Trigonometrie, Und
If A is the angle under consideration, then the side AB is the base. The student is expected to: (A) analyze and compare coverage options and rates in insurance; (B) investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans; and (C) analyze types of savings options involving simple and compound interest and compare relative advantages of these options. (5) Mathematical modeling in science and engineering.
The. You can use three trigonometric ratios to help you solve for missing side lengths and angle measurements. The formulas of these three ratios will be provided to you during the test on the formula sheet pdf , cited:
Understand that mathematics consists of a broad range of topics and is not a single subject. The following steps detail the different areas with which you will need to become familiar as you are studying mathematics. Arithmetic is the first branch of mathematics that you will have studied in elementary and middle school ref.:. Discover printables, worksheets, thematic units, elementary lesson plans. Over 1000 math lessons for all grade levels D., Xiannan became a JL Doob Research Assistant Professor at University of Illinois at Urbana-Champaign, and then a postdoctoral fellow at University of Oxford. His research area is analytic number theory. "So far, I have worked on L-functions and the arithmetic objects attached to them, as well as in sieve theory and prime number theory," Xiannan says. This area is famous for having old, simply stated, and extremely difficult problems, but it has seen some exciting new advances in recent decades. "There are deep connections to various areas of analysis, algebra and representation theory," he adds Pre Algrbra Topic Order, how to find vertex on ti-89, algebra power calc. Entering log other than base 2 on TI, binomial function calculator, examples of permutations in real life, free online middle school math with pizzazz book c topic 4-e, solving 3rd order polynomials. Geometry intro second grade, factoring and simplifying factered, TI 83-plus pc emulator software, conceptual physics pearson education 9-2 worksheet answers, type in adding and subtracting positive and negative math questions, pre-algebra 5-7 prentice hall worksheets If we note that this triangle is half of the larger equilateral triangle shown below, however, things get much easier. We're going to let each side of the equilateral triangle equal 2a. Since the base of our original triangle is half the length of the base of the equilateral triangle, it has length a. We can then use the Pythagoren theorem to determine the height of our original triangle, which we'll call b: Now that we have the complete triangle, we can use the definitions of sine, cosine, and tangent to calculate their values at 30˚ and 60˚ ref.: For an accuracy equivalent to seconds of arc, four decimal places should be kept. The natural unit for angles in trigonometry is the radian, which is always divided decimally. Only when radians are used is the sine of an angle approximately equal to the angle for small angles Take an online test and test your concepts covered in our lesson. It will be conducted in real time, helping you prepare more effectively for real tests , source: As explained earlier, the main texts were composed in Sanskrit verse, and were followed by prose commentaries. [45] Though its authorship is unknown, the Surya Siddhanta (c. 400) contains the roots of modern trigonometry .[ citation needed ] Because it contains many words of foreign origin, some authors consider that it was written under the influence of Mesopotamia and Greece. [59] Brahmagupta's theorem states that AF = FD | 677.169 | 1 |
Dan Anderson
Here's a breakdown of some of the Course Feedback from my PreCalc H students
-1. If you had a friend taking this class next year, what advice would you give them?
Challenge yourself with problems you don't know the answer to yet. Try to figure things out on your own before you learn the real formulas and methods.
Make sure you study the feedback keys and know the technique/skill instead of just memorizing the questions on the feedback quizzes.
Don't be afraid of this course. Mr. Anderson has an amazing teaching style that makes this course a lot less intimidating so don't be scared. Also, take advantage of reassessments and don't leave them till the last couple weeks of the quarter.
I would tell them that throughout the year, Danderson is going to teach you things that are just way above your head. He is going to use these complex examples that make no sense to you… at first. Soon enough, he'll explain how he is getting all of these crazy formulas and all the shortcuts to get the answer. So, the biggest thing is that you can't give up during class. You have to stay focused and try to understand even if you have no idea what is going on, because later on, you'll be able to look back and understand everything that he did and learning the material is much more easier.
0. What could we do differently in class (and out) so that you could learn better?
Have more time practicing, or go over a few things before quizes.
I would try your best in class, even if you thi k you are messing up. You learn from your mistakes. Come afterschool if you need help on anything.
I think maybe before we take b quizzes we could do some practice problems the class before so we are able to ask questions on the material if we have any.
If we do homework, I would like it if we went over the material a bit more.
Assign questions for homework that would be checked.
… Out of class, assigning mandatory homework would be great as it allows you to try problems totally by yourself. Then, we should make it a point to go over it the next day in class.
I would like to have a recap at the end of each class, maybe 2 minutes to review what we did.
5. In this class, we learn to correct our mistakes.
If you make a mistake, most of the time Danderson won't tell you what the mistake is exactly, he will tell you where you made a mistake, but it is up to you to find out how to fix your mistake. I like this because it helps me to not make the same mistake again.
Whiteboards are great because we can erase and fix our mistakes.
Even when Mr. Anderson makes a mistake he encourages us to correct him, this sets a good example for the rest of us
Definitely. We always are learning from our mistakes.
It is hard when you don' t always answer questions (gave a 2 out of 4 on this question)
6. Any last comments?
This was by far my favorite year of math yet!!
For a person who doesn't particularly excel at math, I really enjoyed this class. It made math more likable and doable for me, especially with the standards based grading.
This was the most enjoyable math class I have ever taken and I am looking forward to another year of it.
Hopefully next year will be just as fun and i will gain more knowledge of the subject that i enjoy most which is math
Thank you for the year. This class was the most fun I've ever had in a classroom. The way you run your classroom makes it engaging and fun to learn the material, and it taught me the hard work that I will need to carry on into my senior year, college, and everything that comes after.
0B. What is working well in class? What would you like to see more of?
Grid Responses:
This post is mostly for myself, but maybe there is some value for you too (isn't this the case for all blogging)?
I gave out this 2nd quarter feedback form to my Precalc honors and AP Calculus BC classes:
My comments will be in italics. The rest will be verbatim or summarized.
Similarities for Q1: What activities/methods/strategies have we done in class that have worked well for you?
Standing Groupwork on Whiteboards (HUGE positive response here. Loud and clear, at least for those who like it.)
(PreCalc H) Take Homes (they enjoy working together on tough problems. The students actively liking this is a new one for me, I think it's because I've given more classtime for these takehomes).
Marbleslides (A set of Desmos activities) (We didn't do many other Desmos activities this quarter, the topics didn't warrant the need.)
Writing down examples in notebooks and having the classnotes in a shared google drive. (There is a significant group of students who would rather work on paper than whiteboards, I'd put it at 1 in 5 students. They find some solace in printing out my written notes from the tablet, or at least having those notes available, but I think they'd rather do everything on paper.)
Similarities for Q2: What activities/methods/strategies have we done in class that have NOT worked well for you?
Writing more things down in notebook (This is nicely paired from the last bullet in Q1)
Seated Whiteboards (They really do like the standing aspect!!)
Desmos Activities (This was a small amount of feedback, but they had some great points. A lot of their feedback is talking about my custom activities, so this is not a shot across the bow for Desmos, only for my custom activities. Quick take: I think I make them too dense for some students. There is a high load that they're being asked to lift on some of these, and there are students who don't thrive in that environment, depending on the timing of the activity and their (random) partner).
Not going over homework consistently (Yep. Not too much volume on it, but it's dead on. I think their volume was turned down because I figured it out in December and have been improving on it in January).
Similarities for Q3: What can we do to help you learn better in this class?
Scattershot mostly, but hand back work quicker. (Yep.)
Some requests to slow down. (This is a hard one. I know where we need to be to put the majority of students in a good spot for May of their senior year when they'll take the IB or AP exam. I don't have a great response for this. Do you?)
Excerpts from Q4: Anything else you want to say about class to me? Suggestions?
I enjoy the music keep that up.
I love whiteboards and take homes!!
It would be nice if reassessments could be done on other days than just Thursday or during school study halls.
I really like this class. It is fun and interactive. Cool music btw.
I enjoy doing whiteboard work and take home work in class.
Nothing additional other than stand is great.
Love the background music when we work.
Great learning efficiency, but sometimes comes with dreadfulness from repetition or notes.
Its actually quite enjoyable
Are there any good videos to explain some of the methods? Even if they were just linked to classroom that'd be good.
Hey teachers, if you don't do some sort of feedback form, consider it. Some fantastic feedback, a nice mix of stuff for me to chew on, and some nice motivational stuff from what is working well too.
We covered the midterm exam today (40 multiple choice) in groups today. They knew their grade but not which problems that they got right/wrong. In groups of 5 problems, they tried to find the correct answers, and after a couple minutes of discussion for each group questions, I gave the answers and showed solutions for those who had questions.
Worked quite well. Lots of natural discussion and students helping students.
Next the students worked on finding trig graphs that went through given points. After fiddling with it on their whiteboards, they wrote down a set of steps to themselves in their notebooks.
We're working on power series in Calc. Every year I love setting them up with the following series to find the convergence/divergence of:
They work on whiteboards, wander their way through the tough algebra and to the answer (converges everywhere), and are (generally) very happy to have made it through a tricky problem unscathed. Inevitibly, a student asks what the power series looks like. YES.
It all leads to an amazing conclusion. That mess of a series with alternating terms, odd polynomials, and factorials leads to …… (check the graph to see!)!
Part 3 of the feedback conclusions (Part 1 and Part 2).
Here's some sample responses to the prompt:
Anything else you want to say about class to me? Suggestions?
I'll address these one by one because they're so scattered.Awesome. Chalk another point to whiteboards. Whiteboarding is really running up the score… very unsportsmanlike.
I really enjoy this class. The fact that we aren't taking this class because we have to, rather because we want to makes it really enjoyable, and although it is challenging, makes it fun and interesting.
This is exciting to me! I wish I had more freedom with the curriculum, but after we switched over to IB and it's two year exam (PreCalc and Calc), we've had less control over the PreCalculus class. I'm happy to get this kind of comment.
I really like working in groups because you're not as embarrassed when you don't understand something because then your classmates can help you.
Awesome, chalk another point to groupwork too.
I suggest that you go over the a quizzes after we check the answer key, because me may notice that we got something wrong, but we may not know why we got that wrong or what to do to fix the issue.
This is a good idea. I'm not sure how to build it in yet, but I'll try some stuff out. I purposely don't help them right after the quiz because I want them to help each other, but I bet there is a way for me to interact but not take over as the King of all Knowledge.
Maybe offer some kind of challenge problems to the class, that requires thinking beyond just what we're learning. I think this could be enjoyable at least, and possibly beneficial.
Agreed! My use of puzzles and extensions ebbs and flows, and I'm definitely in an ebb cycle right now. Might be good to keep them on their mental toes and work on some puzzles before the holiday break.
More individual explaining would be helpful to some students because working with peers doesn't have the same efficiency sometimes.
This is an interesting comment. I wonder if efficiency == speed in terms of learning… My guess is no, at least with challenging topics.
I really like the colored notes that are accessible on the classroom and google drive. Very helpful for review.
I need to blog about my workflow for notes and sharing the class notes. Basically I'm writing worked examples and notes on an iPad pro (with an apple pencil), and exporting a pdf of the notes to a shared google drive folder. Love it.
This is an interesting comment. Five years ago I did lots of review games and games in general. But I think whiteboarding has replaced this kind of activity for me. Part of it is my guess at the implied penalty of speed on many student's learning. Some students just do not work well with speed as a component. Competition can also be a deterrent to learning for some students. It wouldn't have been for me as a student, but as I teach more, I'm getting to know the students a bit better (as learners at least).
make it simpler sometimes
Yea. About that. I suppose I can work on this a teacher, but the material we are learning isn't simple, so I'm not sure how I could effectively make it much simpler to learn.
Subset of Nice Comments That I'll Make No Comments On Because I'm EmbarrassedI really enjoy this class. The fact that we aren't taking this class because we have to, rather because we want to makes it really enjoyable, and although it is challenging, makes it fun and interesting.
What can we do to help you learn better in this class?
Do more practice problems and study what we are going to be tested on the class before
More worksheets? Working primarily on whiteboards doesn't help all that much because it get's wiped away so you can't go back and look at it
I feel like sometimes we don go over the homework even though I know it isn't mandatory.
I would like to have a little more time so I can copy more example problems from whiteboards into my notebook so I can look back at them to study.
I would like to spend more time going over homework questions as a class that were difficult. I would also like to put more practice problems into our notebooks.
I'm in between if I like how you do activities on different topics more loosely or not. I enjoy some structure. Like if you just said, "we are working on standard #__" before we started an activity. That helps it solidify in my brain.
DO more practice problems and explain the notes more clearly.
Maybe going through the practice problems a bit slower, or at least leaving up the answers so that those that do not understand well enough to move on can focus on one thing at a time.
I think I am learning well in this class. It helps me to have more problems after completing tasks in class, and these are sometimes provided. Even without these, I believe this class is working very well for me.
Ok, so the feedback on the not covering the homework rings loud in my ears, because I've had that feeling for a couple of weeks now. I'm going to be more intentional about what homework is assigned and how we cover it in the beginning of class. I've let this particular rope slip out of my hands a bit, and I (and the students) want it tightened up a bit. Check.
Also the feedback for giving more structure to what topic we're covering and why is important and I'll do a better job of being consistent with that task. These students wow me with their self knowledge on what they think works best for them. We don't always agree, but I love that we both have opinions and I can address at least some of their needs by modifying how I do things in class.
Here's a word cloud for feedback on the following question:
Grading System Feedback. Got any?
At the end of most quarters, I ask students to fill out an anonymous feedback form about what is working and what is not in our class. I use these feedback forms for many reasons, but most directly so that I can modify and tweak my instruction based on their ideas. Here is a word cloud and some selected quotes from the following question:
What activities/methods/strategies have we done in class that have worked well for you?
Working on the white board, usually standing up helps me a lot. Another thing that helps me do better in class is having A quizzes because i can reflect on them before we take the B quiz and i am more confident in the material
I like doing math in notebooks for example but then using the white boards for further practice. Also the online questionnaires are very helpful and interactive.
(I think the student's "online questionnaires" comment is referring to the Desmos Activities.)
I really like when we use the standing white boards because I like the fact that we have a ton of space so I can see all of my work and erase little mistakes without the annoying marks that an eraser leaves on paper. Also I like it because it gives us the opportunity to move around and work with other people outside of our seated groups and I think standing helps me think better.
Whiteboard work is really beneficial to me. It allows us to work together on problems and work without it being permanent, allowing us to make mistakes. I also enjoy the Desmos activities.
I liked using Desmos and working off of white boards. I also like changing groups every two weeks.
Reassessing works well with me. Desmos is a great website. Standing up in class works very well
… So the loudest pings were: whiteboards (loud and clear!), group work, the use of feedback quizzes before a "B" (graded) quiz, and Desmos Activites.
Now some feedback on the following question:
What activities/methods/strategies have we done in class that have NOT worked well for you?
I find that taking notes in my own notebook rarely helps me, and so I don't usually record things here. Since personal notes are not required, this isn't much of an issue, but I learn much more efficiently by actively doing problems.
seated whiteboards and I don't like that there's no mandatory homework to help me
The small amount of homework doesn't push me to review what we've learned in class and leaves me more lost during standards and take homes. I don't necessarily mean give large amount of home but 3-5 questions when take homes aren't assigned would be helpful.
It is sometimes hard to study for our tests because most of our practice problems are done on the boards.
"The Desmos activities are a little too quickly sped over, it would be better to either go over more or just not do them.
Puzzles need an appearance."
Sometimes it's hard to do the seated whiteboards when the work takes up a lot of space because depending on who you are sitting with that week some people like myself prefer to write everything out individually and you can run out of room so maybe to fix that we could always have the option to stand if our group decides that that would work better for the problem that we are trying to solve.
Sometimes the online desmos do not work well for me. If its at the beginning of the new topic and I am still not grasping the concepts I am sometimes lost (doing more work with peers may be more helpful for me).
I feel rushed when doing group activities if somebody in my group understnads it better. This is just dependent on the person. Like when asking for help, they just quickly explain instead of helping me really understand how to do it.
I tend to remember things through watching HOW something is done then learning it and then examples. Following instructions to arrive at an answer is more my thing. Although, I am adjusting to the figuring things out on my own. It is just taking time.
I like using whiteboards but I really like having example problems in my notebook so that I can look back to them to help me on homework and to study.
Desmos can be really hard at some points, and really easy at others, I haven't really found an in-between.
The take home tests haven't really helped me all that much
So it was a bit more scattered. Some nice notes from the students about the lack of permanency of the whiteboards. I'll partly address this concern by encouraging them to print out the class notes for the day (they have all the worked examples that I did on the tablet in a pdf in a shared google drive folder). Another small set of concerns on the Desmos Activities, and I think I can address those concerns by administrating the activities better, and making better activities in the first place. Some group dynamic issues of a group moving too fast (or too slow). This is harder to address as a whole class, but I'll keep my eye out for it more as I go around the room and make sure everyone is on the same page.
I strongly encourage you to give a similar feedback to your students. Some really important stuff gets shared by the students. I love it.
This is the PreCalculus H class working together on their problem set. I really value our use of problems sets in class. They are more challenging problems that require more time to process, and require working with other students. The anonymous student feedback at the end of the year continually mentions how much the students come to value these assessments.
To set the class up for success, I gave them 15 min at the end of a block to work together on the problem set. They can choose to work however they'd like. My only rule? No writing on paper. They can work together on whiteboards and then take pictures if they'd like to record the work done. This rule worked as anticipated, they naturally broke into groups and had some fantastic discussions. | 677.169 | 1 |
AN EXAMPLE OF REINFORCEMENT OF THE IMPLICIT AND EXPLICIT MATHEMATICAL CURRICULUM IN A CIVIL ENGINEER DEGREE
In this note, it is proposed a joint initiative between the areas of Applied Mathematics and of Continuum Mechanics to reinforce the mathematical skills of the students, in such a way that a better understanding of both the engineering and mathematical concepts can be achieved. To this end we have integrated a lecture subject that combines the analysis of soil strain in a raw materials storing zone during the different phases of a civil engineering work with the basic ideas related with first order differential equations. The aim is two-fold: on the one hand, it allows the students focusing their attention in the development of the technological methods, without feeling overwhelmed by the mathematical arsenal employed.
On the other hand, it reinforces the basic explicit Mathematical curriculum of Civil Engineering that has as a fundamental part a proper knowledge of the topic of ordinary differential equations. It also develops the capability of the student of modelling a realistic, or quasi-realistic, problem. As it is pointed out by the European Society for Engineering Education (SEFI) "the ability to formulate a mathematical model of a given physical situation, to solve the model, interpret the solution and refine the model is a key aspect of the mathematical development of an engineer".
The material corresponding to the lecture "Rheologic models application in Civil Engineering" is presented. This lecture can be tackled within the first two years of the degree. In particular, it is considered the instantaneous and delay strain in quasi-static loading system for a determined period of execution of the works (2 years). To model this situation, the instantaneous strain is represented by a spring whereas the delay strain is a combined system of spring and dashpot (viscoelastic model) both in a serial mode. We will consider two different kinds of soil: clay and gravel, analyzing the distinct responses along the time accordingly with the different types of charges. From a mathematical point of view, that is translated into the establishment of a first order differential equation, whose solution allows determining the movement of the soil, including the negative effects during the distinct phases of the work. In this way, the student can analyze the behaviour of the soil, understanding the relationship between the model and the real case (rheology). Finally, an analysis of the possible benefits of carrying out these kinds of methods in the learning process of the future engineer will be performed, discussing some recommendations in order to improve the integration between the Engineering and Mathematics approaches | 677.169 | 1 |
Synopsis
Winner of several awards for both fantasy and education, A Gebra Named Al has been acknowledged nationwide as both an enjoyable tale and a tool for helping teach young adults the fundamentals of algebra and chemistry. The story was written when the author was 14 years old. Julie struggles with homework until a mysterious Imaginary Number leads her into the Land of Mathematics. There she meets Al the gebra (who is like a zebra), and horses who represent different elements. In the process, she learns the foundations of algebra and chemistry. Join Julie in her journey through Mathematics, where the Orders of Operations are actual places and chemistrees are real plants with atomic fruit. Will she ever get home?
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27 Feb 2015
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published:01 Oct 2013
views:39231424 Feb 2017
views:70015Jo Boaler
Jo Boaler is a British education author, and is Professor of Mathematics Education at the Stanford Graduate School of Education. Boaler is involved in promoting mathematics education reform and equitable mathematics classrooms.
She is the CEO and co-founder of Youcubed, a non-profit organization that provides mathematics education resources to parent and educators of K–12 students. She is the author of seven books including, What's Math Got To Do With It? (2009) and The Elephant in the Classroom (2010), both written for teachers and parents with the goal of improving mathematics education in both the US and UK. Her 1997/2002 book, Experiencing School Mathematics won the "Outstanding Book of the Year" award for education in Britain.
Currently she is the Research Commentary Editor for the Journal for Research in Mathematics EducationOnline Classes: The Difference Between Online and Classrooms & Should You Take An Online Class?
Online Classes: The Difference Between Online and Classrooms & Should You Take An Online Class?
Online Classes: The Difference Between Online and Classrooms & Should You Take An Online Class?
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Math 2B. Calculus. Lecture 01.
Math 2B. Calculus. Lecture 01.
Math 2B. Calculus. Lecture 01.
25:59
Khan Academy Live: SAT Math Class
Khan Academy Live: SAT Math ClassBasic Math: Lesson 1 - NumbersTestmasters SAT Subject Test Mathematics Online Course Sample mathematics solutionsThis math video tutorial provides a basic overview of concepts covered in a typical high school algebra 1 & 2 course or a college algebra course. This video contains plenty of lessons, notes, examples, and practice problems for you to get a good 26 Nov 2008
Math 2B. Calculus. Lecture 01 tea inu andFree GED Math Preparation 2016 - 2017 Study Guide...
Advanced Algorithms (COMPSCI 224), Lecture. elegans roundworm sees by eating, sucking in big gulps of bacteria to learn about its surrounding environment. As researchers watched, they noticed an odd pattern marked by "bursts" of eating ... ....
One of the biggest names in mathematical computing has built a new tool to help skywatchers prepare for the total solar eclipse of Aug. 21, and penned a deep dive into how eclipses have driven mathematics... ....
The workshop was the first in a series being organized at campuses nationwide to unite academics and to harness cutting-edge mathematics to address gerrymandering ... "We think we can see underlying mathematical principles that weren't visible before." ....
Brian Murphy knows Detroit's school district needs hundreds more teachers as the academic year approaches. And on Thursday, he joined about 150 potential hires at a recruitment fair to help fill those open spots ... 31 at the school as the district seeks highly qualified educators to fill positions for the 2017-18 school year, particularly in areas such as mathematics, social studies, special education and music ... "It was a good turnout." ... ChronicleThere is a mathematical formula that works behind these tools and calculators to give you the result based on your appetite. Do the math ... .... | 677.169 | 1 |
Synopsis
Ensure top marks and complete coverage for the new Edexcel International Level 1/Level 2 GCSE in Mathematics (Specification A) (9-1) with Collins' fully revised and updated resources. Deliver the syllabus with confidence with full support and guidance for teaching including editable versions of lesson plans. * Start teaching straight away with detailed three-part lesson plans that include clear syllabus references, common mistakes and remediation, and useful tips for a fresh approach. * Check and mark students' work with the answers for the Student Book exercises and examination sections. * Personalise your course with our suggested Scheme of Work and editable lesson plans.
About the Author
Chris Pearce has an MA in maths and over 30 years' teaching experience at secondary level through KS3 to KS5. Now a full-time author, education advisor and examiner, he has written many bestselling KS3 and KS4 materials for Collins. | 677.169 | 1 |
A chronicle of our adventures in homeschooling.
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Pearson Homeschool–My Math Lab Alg. 1
Pearson Homeschool offers a variety of products for homeschoolers in grades K-12. For this review, I received access to their My Math Lab Algebra 1 program. I used this with my oldest son, who completed pre-algebra this year, as an 8th grader, and is moving into 9th grade. This is a digital product, which involves you and your child accessing the content of the program on the internet. My Math Lab includes both parent and student access codes.
Now first, I have to say that advanced math is not my strong suit, nor is it for my oldest boy (guess he gets that from me 🙂 ). In our house, my husband and my younger boy are the math lovers. Therefore, I was very nervous about starting upper-level math with my son as he went into high school. Obviously, math is important, and I wanted to make sure he would be successful. I had been stressing out about signing up for a co-op, doing an online or video product etc. when the chance to review this came up, and I was very happy to do so.
I have to say, I wasn't sure about an all-online program at first (I mean, don't you need a textbook for math??). Wow, was I impressed with this Pearson program!! First of all, once you sign up, it is very easy to navigate. You have to register an account for both you and your child, using your specific access code, but the directions are very specific and easy to follow. Once you are set up, as the parent you can monitor assignments, grades, set up your calendar, change the mastery level for assignments etc. etc. This was a blessing, because sometimes I find it difficult to wrap my head around how to manage these online programs!
The math itself was excellent!! Your child has access to an interactive e-textbook (which my sound found very clear and easy to use) and lessons are basically just click and go! After your child goes through the textbook portion, they work on the "homework" assignment, which is just practice problems related to the lesson. The number of problems vary, but even when there were 30 problems, I would say it didn't take my son more than hour to complete, which I think is an acceptable amount of time for upper level math. If you have a student who is "mathy" they may finish sooner.
The problems are well laid out, with lots of support for the student. Sometimes there is a short video, that gives and example of how to do the problem. There are also many other prompts, like "help me solve this problem" which will basically give your child a step by step example of the problem they are working on, but with different numbers. If your child does miss a problem, they correct solution is shown, along with the option of "try another one like this" so your child can practice the problem again! The immediate feedback was SO incredible helpful for my son! He could get help as he was doing the problem, which led to less errors for him, and MUCH less frustration (he hates getting things wrong!)
I love that the Pearson Homeschool motto seems to be "Because you know what matters most". I do know what is most important for my child, but like anyone, sometimes I need a little help getting that across to him. Up to this point, math has been a struggle for my oldest child and I. I wouldn't say he is now a math lover, but My Math Lab is by far the program he enjoys doing most. He really feels confident in his knowledge at the end of the lesson, and I like the fact that if I need to, I can sit there and go through the lesson with him and help him when necessary, but he can also do a lot of this on his own. He took his first quiz in the course(there are periodic quizzes and tests throughout) and did very well. He was so proud of himself!! I will definitely be looking at purchasing My Math Lab Algebra 2 when we get there, and I really hope they make one for geometry!!
The best part about this program is the VERY reasonable cost!! A lot of the online/DVD programs I was looking at were in the hundreds of dollars!! My Math Lab only costs $49.97 for the student access kit and $30.00 for the parent access kit. I think this is very reasonable!! To learn more about My Math Lab and other Pearson products, visit their website here:
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2 thoughts on "Pearson Homeschool–My Math Lab Alg. 1"
Nice review. We really struggled with the set up of this at first but now, I love it! I really like that it grades it all and keeps track of it for me 🙂 My son likes the instant feedback- it motivates him. | 677.169 | 1 |
Click on the Google Preview image above to read some pages of this book!
The second edition of Essential Mathematics for the Australian Curriculum now combines a proven teaching and learning formula with the seamless integration of a structured student text, rich digital learning resources and a powerful learning management system.
Complete and authoritative coverage of the Years 7 to 10 & 10A Australian Curriculum (and state variants):
Logical topic development is supported by carefully graded questions, linked examples, investigations, and key point summaries in an uncluttered layout.
Every question is grouped according to the four proficiency strands of the Australian Curriculum and every exercise contains questions for all four strands.
Three different pathways (Foundation, Standard and Advanced) through the exercises cater for learners of all ability levels. These pathways are now indicated in the textbook and detailed working programs are provided to support differentiated learning.
The Interactive Textbook - integrated with Cambridge HOTmaths - allows effortless and immediate navigation from the textbook content to over 200 video demonstrations of worked examples in every year level, interactive widgets and walkthroughs that visually represent and reinforce maths concepts and much, much more.
1. Linear rleations
2. Geometry
3. Indices and surds
4. Trigonometry
5. Quadratic equations
Semester review 2
6. Measurement
7. Parabolas and other graphs
8. Probability
9. Statistics
10. Logarithms and polynomials
Semester review 2
Answers
ISBN: 9781107568907 ISBN-10: 1107568900 Series: Cambridge Essential Mathematics Audience:
Primary / High School
For Ages: 15+ years old For Grades: 10 Format:
Book with Other Items
Language:
English
Published: 19th November 2015 Country of Publication: AU Edition Number: 2 | 677.169 | 1 |
ALEX Resources
Title: Building Functions - Reverse to Inverse
Description:
This
Standard(s): [MA2015] PRE (9-12) 20: Determine the inverse of a function and a relation. (Alabama)
Subject: Mathematics (9 - 12) Title: Building Functions - Reverse to Inverse Description: This | 677.169 | 1 |
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Undergraduate Programs in Mathematics & Statistics
Entry-level math courses
There are three calculus sequences. Calculus 21, 22, 23 is the largest, taken by most science and engineering students. Advanced placement can be obtained either through the AP test of the College Board or through a test administered by our department. Honors Calculus 31, 32, 33 parallels 21, 22, 23, but with more depth and rigor. It is geared toward students with SAT Math score over 700, although it is open to all interested students. Survey of Calculus, 51, 52, are somewhat less in-depth. Calculus with Business Applications is a first semester course for business students. Most business majors will take either 21 or 81. Most students in biological or earth sciences will take 51 and 52.
For students who need to take Calculus 21-23, but have a weak background in pre-calculus material, there is a 2-semester course, Math 75 and 76, which can be substituted for the 1-semester course Math 21. Math 75 and 76 contain a good bit of review of pre-calculus material along with the topics of Math 21. Students who complete 75 and 76 will be prepared to take Math 22. Another option is Math 0, Preparation for Calculus, offered during the fall. It counts as 2 credits on your current roster and your GPA, but the credits do not count toward graduation. Math 0 will be taken primarily by students who need to take Math 51 or 81 but need some review to prepare for the faster pace of college level calculus courses.
Students in the arts, humanities, and social sciences are required to take at least one semester of mathematics, but it need not be calculus. Basic Statistics 12 is the math course recommended for social science students. It is a 4-credit course and is offered every semester. Another non-calculus-based course is Math 5, Introduction to Mathematical Thought, offered in the spring. Topics in Math 5 vary from year to year.
The math department particpates in the College of Arts and Sciences Freshman Seminar Program and offers a freshman seminar each fall semester. Topics for the freshman seminar vary from year to year.
Statistical analysis forms a fundamental tool in all experimental sciences and is important in understanding chance phenomena. Mathematical principles, especially probability theory, underlie all statistical analyses. This program requires 30 hours of Professional Electives to be selected from at least two fields of application of statistics, such as biology, psychology, social relations, computer science, engineering, economics, and management. Required major courses are
For each program, the requirement is Math 21, 22, and 23, or 31, 32, and 33, plus four courses from a list of specified courses. See the catalogue for the lists of specified courses.
In recent years, we have had approximately 10-15 math majors graduating each year. This means that classes are small, so that you get to know your professors and fellow students well. Some of the things that our recent graduates have done after graduation include | 677.169 | 1 |
ARITHMETIC PROGRESSION FOR CLASS X
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Section 1: ARITHMETIC PROGRESSIONLecture 1
Arithmetic Progression00:49:32
Qualification
Courses taught by Nishant Goel
Instructed By | 677.169 | 1 |
Fundamental College Mathematics
ISBN-10: 0321613422
ISBN-13: 9780321613424 best-selling Bittinger paperback series for developmental mathematics provides students with the structure and support they need to succeed in mathematics. The Bittinger pedagogical approach works with the way students think, helping them solve problems and real-data applications with the Bittinger five-step problem-solving process introduced early and used consistently throughout the texts. Comprehensive exercise sets reinforce students' understanding of skills and concepts through practice, while contemporary applications help them see the relevance of the math in their own lives. The Bittinger instructor support package gives professors and adjunct instructors everything they need to prepare for class and inspire students to succeed | 677.169 | 1 |
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Friday, April 19, 2013
Principles and Techniques in Combinatori Ebook
Principles and Techniques in Combinatori PDF Download Ebook. Chen Chuan-Chong and Koh Khee-Meng offer wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises. It is textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read.
Moreover, this book also discusses sequence creation using generating functions, something that Tucker leaves out. This book has solid introduction to combinatorics, explicitly detailing every step of every proof--something direly missing in most other texts of this type. Most people taking this class have only had a rudimentary sampling of proof techniques and this book helps fill in the missing gaps left in slightly higher-flyers such as Tucker's.
Author assumes you can do that already. His chapter on modeling is light on problems and doesn't explain the examples as clearly as this one does. This book also shows some incredibly creative problem solutions that crafty students have devised (being trainers) that help you think about other implications in things such as Pascal's triangle. It does a great job of improving mathematical thinking. | 677.169 | 1 |
Tutorial Trigonometry
The author is one of the best writers on applied mathematics. As the length of the largest side approaches zero, the spherical triangle approaches a plane triangle. And of course, don't miss the Uses of Trigonometry summary.
Use a calculator to compute the values of the trig functions at the given θ, where θ is measured in degrees. Here is a graphic preview for all of the Trigonometry Worksheets. You can select different variables to customize these Trigonometry Worksheets for your needs , source: MyMathLab for Trigsted Algebra & Trigonometry -- Access Card with eText Reference for Trigsted Algebra & Trigonometry MyMathLab for Trigsted Algebra &. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication. (3) Mathematical Models with Applications is designed to build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I Instructor's Solutions Manual download online Instructor's Solutions Manual to. pdf. We have three figures that can be interchangeable. Due to the fonts used for special characters, this page is best viewed using the explorer browser (printouts may not agree with the display). Please let me know if you have any questions: tompkinsj@uncwil.edu , cited: Plane and Spherical read for free Plane and Spherical Trigonometry. [With]. Have you ever sat in your math class asking yourself, "Why do I need to learn trigonometry and calculus? Who uses trigonometry and calculus in the real world?" Civil engineering professors and students from the University of Hawaii College of Engineering visited McKinley High School and Kaimuki High School to teach upper division math students how civil engineers use trigonometry and calculus to design and construct buildings, bridges, and other structures online. In Mean Girls, Cady pretends to hate math to fit in with everyone else, even though she actually enjoys it , source: A Beka Book Plane Geometry tiny-themovie.com. Ian Robertson and civil engineering graduate student Alison Agapay demonstrated how shake tables and determining a structure's natural frequency are used in the building of a structure. When designing and constructing a building, engineers have to consider many factors. They have to figure out how a structure will respond to things like earthquakes, wind, blasts, and extreme impacts , source: Tutorial Trigonometry Tutorial Trigonometry.
Trigonometry is the branch of Mathematics that deals with triangles and the relationships between the sides and angles , cited: Contemporary College Algebra And Trigonometry 1st edition by Hungerford, Thomas W.; Hungerford published by Holt Rinehart & Winston Hardcover Contemporary College Algebra And cited: Precalculus: Algebra, read here Ptolemy's calculations are accurate enough to be useful today. Here is a partial table of Ptolemy's chords taken from Toomer: The table of chords is equivalent to a table of sines for all central angles 0 degrees to 90 degrees at 15' intervals and thus can be used to solve any planar triangle, provided that at least one side is known ref.: Schaum's Outlines: Trigonometry: With Calculator-Based Solutions [SCHAUMS OUTLINES TRIGONOMETRY]
A Treatise on Trigonometry
Trigonometriya. 10 klass
Trigonometry: A Circular Function Approach
Plane and spherical trigonometry (Wentworth's series of mathematics)
They are both good reads and they overlap a number of disciplines, but arguably belong most to combinatorics. Note they do not belong in Foundations like the book by Ebbinghaus, H.-D. The book by Bunch is excellent for the serious freshman-sophomore A Manual of the Protracting Trigonometer: With Its Application to Rectilinear Draughting and Plotting, Trigonometry, and Surveying - Primary Source Call Now to Set Up Tutoring: What is the tangent of C in the given right triangle?? Substituting the given values for cos x and sin x, we get Triangle ABC shown is a right triangle ref.: The whole craft of number download here. Other topics include basic counting, linear recurrences, generating functions, Latin squares, finite projective planes, graph theory, Ramsey theory, coloring graphs and set systems, random variables, independence, expected value, standard deviation, and Chebyshev's and Chernoff's inequalities Modern Trigonometry, Barnes & Noble College Outline Series The cot formula gives B = 34.95°, about NE by N. Note that a calculator will give the angle less than 90° with the given sine; we want the one greater than 90°. 110.81° is 1.934 radians, so the distance is 7657 miles (Earth's mean radius 3959 miles or 6371 km). , cited: A Beka Book Plane Geometry WITHOUT LIMITING THE FOREGOING, WE AND OUR LICENSORS ASSUME NO LIABILITY OR RESPONSIBILITY FOR ANY OF THE FOLLOWING: (I) ANY FAILURE OR INTERRUPTION IN THE AVAILABILITY OF STREAMING SERVICE, (II) DELIVERY AND OR DISPLAY OF ANY CONTENT CONTAINED ON OUR SITE OR OTHERWISE THROUGH STREAMING SERVICE; AND (III) ANY LOSSES OR DAMAGES ARISING FROM THE USE OF THE PRODUCTS OR SERVICES PROVIDED ON OUR SITE OR OTHERWISE THROUGH STREAMING SERVICE, INCLUDING ANY LOSSES OR DAMAGES ARISING FROM DOWNLOADING OF RELATED SOFTWARE, DOWNLOADING AND/OR USE OF ANY OTHER SOFTWARE Basic trigonometry (Series in read here read here.
A treatise of plane trigonometry, and the mensuration of heights and distances; To which is prefixed a summary view of the nature and use of ... of instruction in schools and academies
Catalogue of Stars for the Epoch Jan. 1, 1892 from Observations by the Great Trigonometrical Survey of India
Analytische Trigonometrie
Picking out the real parts from both sides and equating them, for cosine, we get: We can use this formula to find multiple angles of cosine and sine by associating the real parts of the right-hand side, expanded with the Binomial Theorem, with cosine and the imaginary parts with the sine. On this page, we make a limited claim, that the formula is true for all integers n online. You have to be careful here as a discussion of fractals could branch out in so many ways that it could generate an entire course on its own Master MathAlgebra2nd (Second) edition byRoss Master MathAlgebra2nd (Second) edition. The horizontal distance from the centre of the astrolabe to the edge of the square was marked with twelve equal divisions Mathematical Tables Consisting of Logarithms of Numbers 1 to 108000: Trigonometrical, Nautical, and Other Tables Mathematical Tables Consisting of. If not, try the other option: 'Save this file to disk', then run Maths Helper Plus and choose the 'Open' command from the 'File' menu. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions ref.: Algebra 1, Chapter 8: download epub download epub. Pursuant to the DMCA, after the alleged infringer receives a notice of infringement from Company, the alleged infringer will have the opportunity to respond to Company with a counter notification ("Counter Notification"). To be effective, a Counter Notification must be a written communication provided to Company's designated copyright agent, and must include the following: 1 Algebra and Trigonometry, 4th Edition, Instructor's Edition Algebra and Trigonometry, 4th Edition,. Each chapter has one-pager cheat sheet for key concepts with at-a-glance review of each chapter, printable and laminatible. It is ideal for exam prep or quick review. The well-formatted eBooks are printable for easy quick reading and last-minute review Plane Trigonometry, 1940, 336 download here mu.akaicloud.com. Graphing process of y = csc(x), the reciprocal of sine, using a unit circle. Graphing process of y = tan(x) using a unit circle. A common use of mnemonics is to remember facts and relationships in trigonometry Plane Trigonometry Made Plain You can find professional online math help at Assignment Expert. We are a popular math homework site ready to offer round-the-clock math help and math assignments done for you. Don't worry about your cooperation with us, because we deal with your online math homework in a professional and reliable manner. You'll be pleased to notice that our math homework solvers are always ready to propose online math help you Holt algebra with download pdf download pdf. You are solely responsible for keeping confidential any password you may be granted to access our Site Elements of geometry and trigonometry from the works of A.M. Legendre The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string. Question: 6 - A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building Trigonometry-Slide download pdf Descartes' rule of signs: Approximate solutions of roots of polynomials by Newton-Raphson method - Homer's method; Cardan's method of solution of a cubic polynomial. Summation of Series: Binomial, Exponential and Logarithmic series (theorems without proof); summation of finite series using method of differences - simple problems Student Solutions Manual for read for free | 677.169 | 1 |
This comprehensive student manual has been designed to accompany the leading textbook by Bernard Schutz, A First Course in General Relativity, and uses detailed solutions, cross-referenced to several introductory and more advanced textbooks, to enable self-learners, undergraduates and postgraduates to master general relativity through problem solving. The perfect accompaniment to Schutz's textbook, this manual guides the reader step-by-step through over 200 exercises, with clear easy-to-follow derivations. It provides detailed solutions to almost half of Schutz's exercises, and includes 125 brand new supplementary problems that address the subtle points of each chapter. It includes a comprehensive index and collects useful mathematical results, such as transformation matrices and Christoffel symbols for commonly studied spacetimes, in an appendix. Supported by an online table categorising exercises, a Maple worksheet and an instructors' manual, this text provides an invaluable resource for all students and instructors using Schutz's textbook.
Suitable as a one-semester course in general relativity for senior undergraduates or beginning graduates, this text clarifies the mathematical aspects of Einsteins general theory of relativity without sacrificing physical understanding. Beginning with an exposition of those aspects of tensor calculus and differential geometry needed for a proper exposition of the subject, the discussion turns to the space-time of general relativity and to geodesic motion, comparisons and contrasts, with Newtons theory being drawn where appropriate. A brief consideration of the field equations is followed by a discussion of physics in the vicinity of massive objects, including an elementary treatment of black holes. The book concludes with brief, introductory chapters on gravitational radiation and cosmology, and includes an appendix that reviews the special theory of relativity. In preparing this new edition, the authors have completely rewritten chapters to make the material readily accessible to physics students, while many examples, exercises and problems help guide the students through the theory.
For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms.
General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics. Based on Yvonne Choquet-Bruhat's more advanced text, General Relativity and the Einstein Equations, the aim of this book is to give with precision, but as simply as possible, the foundations and main consequences of General Relativity. The first five chapters from General Relativity and the Einstein Equations have been updated with new sections and chapters on black holes, gravitational waves, singularities, and the Reissner-Nordstrom and interior Schwarzchild solutions. The rigour behind this book will provide readers with the perfect preparation to follow the great mathematical progress in the actual development, as well as the ability to model, the latest astrophysical and cosmological observations. The book presents basic General Relativity and provides a basis for understanding and using the fundamental theory.
Loop quantum gravity is one of the modern contenders for a unified description of quantum mechanics and gravity. Up to now no book has covered the material at the level of a college student or of other readers with some knowledge of college level physics. This book fills that gap.
String theory made understandable. Barton Zwiebach is once again faithful to his goal of making string theory accessible to undergraduates. He presents the main concepts of string theory in a concrete and physical way to develop intuition before formalism, often through simplified and illustrative examples. Complete and thorough in its coverage, this new edition now includes AdS/CFT correspondence and introduces superstrings. It is perfectly suited to introductory courses in string theory for students with a background in mathematics and physics. New sections cover strings on orbifolds, cosmic strings, moduli stabilization, and the string theory landscape. Now with almost 300 problems and exercises, with password-protected solutions for instructors at
The book is aimed at physics students and professional physicists who wish to understand the basics of cosmology and general relativity as well as the most recent cosmological observations and models. It presents a self-contained introduction to general relativity that is based on the homogeneity and isotropy of the local universe. The simplicity of this space allows general relativity to be introduced in a very simple manner while laying the foundation for the treatment of more complicated problems. The latest cosmological observations and theories are discussed. Emphasis is placed on estimations of the densities of matter and of vacuum energy, and on investigations of the primordial density fluctuations and the nature of dark matter.
General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminate and extend the discussion in the text.
Relativity Made Relatively Easy presents an extensive study of Special Relativity and a gentle (but exact) introduction to General Relativity for undergraduate students of physics. Assuming almost no prior knowledge, it allows the student to handle all the Relativity needed for a university course, with explanations as simple, thorough, and engaging as possible. The aim is to make manageable what would otherwise be regarded as hard; to make derivations as simple as possible and physical ideas as transparent as possible. Lorentz invariants and four-vectors are introduced early on, but tensor notation is postponed until needed. In addition to the more basic ideas such as Doppler effect and collisions, the text introduces more advanced material such as radiation from accelerating charges, Lagrangian methods, the stress-energy tensor, and introductory General Relativity, including Gaussian curvature, the Schwarzschild solution, gravitational lensing, and black holes. A second volume will extend the treatment of General Relativity somewhat more thoroughly, and also introduce Cosmology, spinors, and some field theory.
In 1905 Albert Einstein produced breakthrough work in three major areas of physics (atoms and Brownian motion, quanta, and the special theory of relativity), followed, in 1916, by the general theory of relativity. This book develops the detail of the papers, including the mathematics, to guide the reader in working through them.
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A working knowledge of Einstein's theory of general relativity is an essential tool for every physicist today. This self-contained book is an introductory text on the subject aimed at first-year graduate students, or advanced undergraduates, in physics that assumes only a basic understanding of classical Lagrangian mechanics. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. After reviewing special relativity, the basic principles of general relativity are presented, and the most important applications are discussed. The final special topics section guides the reader through a few important areas of current research.This book will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation. | 677.169 | 1 |
Don't just watch, practice makes perfect.
Do better in math today
Chapter 27 Topics:
Don't just watch, practice makes perfect.
Identity Matrix
In this lesson, we will learn about identity matrices. Identity matrices is an n by n matrix which all entries diagonal from the top left to the bottom right are 1's, and the rest of the entries are 0. There are many types of identity matrices, as listed in the notes section. We will learn how to apply matrix operations with these such as adding, subtracting, and multiplying. Lastly, we will see that identities have a special property. If two matrices are multiplicative inverses, then multiplying them would give an identity matrix.
Basic concepts:
Lessons
Notes:
An identity matrix is an nnn by nnn matrix (written as
InI_nIn) where all the entries that is diagonal from the top
left to the bottom right are all 1's, and the rest of the entries are 0. For example,
are all identity matrices.
a)
The Identity Matrix
b)
Multiplicative Inverses
2.
Matrix Operation with the Identity Matrix
You are given that and . Perform the following matrix operations:
3.
Multiplicative Inverses
Are the following matrices multiplicative inverses of each other? | 677.169 | 1 |
An exhilarating new assortment via world-leading researchers in L2 studying addressing: Why do conceptions of 'learning' fluctuate rather a lot in L2 studying study? Is there a conceptualisation of 'learning' to which contributors of other colleges of SLA can subscribe?
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Best Math Books To Read
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ISBN-13: 9780495011248 to improve the algebra and problem-solving skills of students taking a calculus course, every chapter in this companion is keyed to a calculus topic, providing conceptual background and specific algebra techniques needed to understand and solve calculus problems related to that topic.
Dennis Ebersole is Professor of Mathematics and Computer Science at Northampton Community College where he has taught since 1971. His interests include improving mathematics education in grades K�12. Since 1989 he has administered several grant-funded programs for teachers of mathematics to strengthen their mathematical and pedagogical knowledge and skills. In addition to A COMPANION TO CALCULUS, he has authored or coauthored five other mathematics texts. He is a contributing writer for the revision of "Mathematics Standards Before Calculus" in BEYOND CROSSROADS, published by the American Mathematics Association of Two Year Colleges | 677.169 | 1 |
An updated, revised edition of this very successful Schaum's Outline. Chapters 1 and 3 have been combined so the text begins with linear equations. Chapters 4 (Vector Space Analysis) and 5 (Basis and Dimension) are combined and there is an additional chapter on the cross product and applications of the delta function. There are hundreds of solved and supplementary problems.
Get all the help you need with graphing and probability word problems with this great addition to the MATH BUSTERS WORD PROBLEMS series. Easy tips and strategies, paired with color photos and real world examples, make this a great resource for students to use on their own, or with a parent or tutor.
Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting?
The origin of the theory of probability must be traced to the compelling need to develop a mathematical model to analyze chance phenomena. Intu- itive approaches had to be the beginning for this. These led to the fashioning of certain crude tools which, over time, were chiseled into the present day accepted model of a basic structure resting on abstraction, definitions and a consistent set of axioms. | 677.169 | 1 |
This text offers a comprehensive presentation of the mathematics required to tackle problems in economic analyses's problem-solving skills, the book works through a large number of examples and economic applications. This streamlined third edition offers an array of new and updated examples. Additionally, lengthier proofs and examples are provided on the book's website. The book and the web material are cross-referenced in the text. A student solutions manual is available, and instructors can access online instructor's material that includes solutions and PowerPoint slides. Visit for complete details.
"synopsis" may belong to another edition of this title.
About the Author:
Michael Hoy is a faculty member in the Economics Department at the University of Guelph.
John Livernois is a faculty member in the Economics Department at the University of Guelph, Ontario.
Chris McKenna is a faculty member in the Economics Department at the University of Guelph, Ontario.
Ray Rees is a faculty member at the Ludwig Maximilians University, Munich.
Thanasis Stengos is a faculty member in the Economics Department at the University of Guelph, Ontario.
Review:
Mathematics is the language of economics, and this book is an excellent introduction to that language.
(George J. Mailath, Walter H. Annenberg Professor in the Social Sciences and Professor of Economics, University of Pennsylvania)
While there are many mathematics texts for economics available, this one is by far the best. It covers a comprehensive range of techniques with interesting applications, and the numerous worked examples and problems are a real bonus for the instructor. Teaching a course with this book is enjoyable and easy.. Book Condition: New. 2011. third edition. Paperback. THIS EDITION IS NOT AVAILABLE IN THE US OR CANADA. International Student Paperback Edition. Customers in the US and Canada must order the cloth edition of this title. Num Pages: 976 pages, illustrations. BIC Classification: KCH. Category: (U) Tertiary Education (US: College). Dimension: 227 x 203 x 36. Weight in Grams: 1582. . . . . . Books ship from the US and Ireland. Bookseller Inventory # V9780262516228 | 677.169 | 1 |
Trigonometry: Students Solutions Manual
The writers themselves clearly averted it here - they went so far as to produce a proof showing that it can be done using two fresh bodies. Worksheets on linear equations, fractions equations calculator, vocabulary of algebra worksheet printable. Ptolemy was aware of the of the formula, (chord 2x) + (chord (180x - 2x)) = 4r, which is equivalent to sin x + cos x = 1. This is the second course in a highly theoretical sequence in analysis.
Pages: 0
Publisher: Prentice Hall College Div; 5th edition (June 1999)
ISBN: 0130961221
Trigonometry - Custom Edition for Long Beach City College
Mathematics 101 is intended for students who wish to upgrade their mathematics skills before or while attending a post-secondary institution. Students who successfully complete Mathematics 101 are generally permitted to pursue courses and programs that would otherwise require Pure Mathematics 30 as a prerequisite or corequisite e-Study Guide for: download pdf It was translated (not transliterated) into Latin as 'sinus'. When you write sin(45), what you really mean is the sinus of 45 degrees. It's amazing how a silly little word history like that can relieve a little bit of the tension students naturally feel when studying an intimidating subject like trigonometry A naturalist in Borneo download epub download epub. A diagram with a unit circle and more trig functions than you can shake a stick at. (It's well known that you can shake a stick at a maximum of 8 trig functions.) The familiar sine, cosine, and tangent are in red, blue, and, well, tan, respectively ref.: Trigonometry with Course Notes & EWA Smart Start Guide for Students Page no. 286 of chapter Tangents to Hyperbola… was a direct question in IIT-JEE 2007. Not only students but even teachers have understood the gravity of this book. But the problem is this book is solved rarely by all the teachers and the students. Not many of them are able to completely solve SL Loney. So, Pioneer Mathematics is here with complete S L Loney solutions , source: Trig-Radians Workbook download pdf Mark Dugopolski's College Algebra and Trigonometry Series (A Preveiw of Chapter 1) Rules have been simplified (no rotation needed at all) to allow every kids to solve all the Tangrams , cited: Multicultural Activity Masters (Merrill Algebra 2 with Trigonometry) nssiti.com. Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, especially right-angle triangles. A set of functions, called trigonometric functions, represents these relationships in mathematical terms Logarithmic and Trigonometric Tables: To Seven Places of Decimals, in a Pocket Form ; in Which the Errors of Former Tables Are Corrected download pdf.
This in itself is unremarkable, but the opening credits in some seasons depict a textbook cover that reads "Everybody Hates Trigonometry." Additionally, one episode of the series even bears the title of "Everybody Hates Math". In The Adventures Of Shirley Holmes, Bo and Parker, especially AN ELEMENTARY TREATISE ON read online read online. Daily Time Requirement: 90 minutes class + a minimum of 4 hours of study. In this method of teaching: a) Students view the videos at home and take careful searchable lecture notes. (Mostly two lecture videos per day) c) Students solve the homework problems and enter the problem/answers on their notebook and/or MML. d) Students come to board during class time to solve homework problems. e) Students get up to 10 bonus points based on their performance at the board and for the performance of the rest of their study group. f) There may be a short quiz (1 point each) at the beginning of each class on the assigned video lectures. g) So long as this format is used the tests will be open notebook. h) If 2/3 of students vote for traditional class format then tests will be closed notebook , e.g. Essential Trigonometry: A Problem-Centered Approach
Modern College Algebra and Trigonometry
Study and Solutions Guide
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Calculus: I Have...Who Has...Cards- With Derivatives at a Point
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This set of I Have... Who Has ... cards can be used in any Calculus class where the students have learned to find derivatives using the various rules of differentiation and evaluate those derivatives at a given point. You can use the cards in a class of 10 students, 15 students, 20 students, or 25 students.
The activity has been designed to be used in class or various sizes (10, 15, 20, or 25 students) by giving each student one card or other size classes by giving several cards to some students.
10, 15. 20, or 25 cards can be used to give all your students additional practice at finding bounded area analytically and graphically.
It is easy to sort the cards into the various size sets by using either the heart (25), diamond(10), club(15), or spade(20) at the bottom of each card.
This activity includes one set of 10,15, 20, or 25 cards. The master list includes all the problems, solutions and card numbers. The cards are not numbered | 677.169 | 1 |
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This math station activity is intended to help students understand how to graph proportional relationships, understand that a function is a rule that assigns one input to one output exactly, compare properties of two functions, interpret the equation y = mx + b, construct a function, determine the rate of change of a function, and describe the functional relationship between two quantities.
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Terrestrial-Satellite Communication Networks: Transceivers Design and Resource Allocation By Linling Kuang, Chunxiao Jiang, Prof. Yi Qian, Jianhua Lu English | PDF,EPUB | 2018 | 160 Pages | ISBN : 3319617672 | 8 MB This book targets major issues in terrestrial-satellite communication networks and presents the solutions. While the terrestrial networks can achieve high-speed data service at low cost, satellite based access is one way to complement terrestrial based networks to ensure ubiquitous, 100% geographic coverage. The coexistence and cooperation between terrestrial and satellite networks are of great potential in future communication networks, and satellite radio access networks has already been considered in the fifth-generation (5G) networks to be supported for phase 2.
Teach Your Child Math: Making Math Fun for the Both of You, 3rd edition by Arthur Benjamin, Michael Brant Shermer 1999 | ISBN: 0737301341 | English | 224 pages | PDF | 14 MB By transforming math "problems" into games, this easy-to-follow book gives parents a fun way to help their children learn math. With an expanded section on problem solving, fun word problems, and entertaining visual concepts, it proves that math can be interesting. | 677.169 | 1 |
AQA GCSE Mathematics Foundation Pupil Book 2006(Paperback)
Synopsis
As the Number 1 publisher for GCSE Mathematics, we can offer teachers and students everything they need to succeed in the two-tier AQA specification for 2006. These resources include fully blended Student Books and software to motivate and engage students. Revision and practice books will encourage exam success by consolidating students' learning. Our experienced author team will help students achieve the grades they deserve | 677.169 | 1 |
Math Workbook: Geometry 2 (Grades 6-7)
Geometry 2 is a grade 6/7 level geometry workbook. It continues the study of geometry from Math Mammoth Geometry 1, also available at the K5 Learning Store.
Some of the topics included are:
classifying triangles and quadrilaterals;
area of common polygons;
circumference of a circle (Pi);
area of a circle;
conversions between units of area and volume (both metric and customary);
volume of common solids;
Nets and surface area.
This geometry workbook is divided into 28 sections. Each section begins with a bite-sized introduction to a topic with an example, followed by practice exercises including word problems. Answers are in the back. The format is ideal for independent or parent guided study. The Math Mammoth series of workbooks is highly recommended by K5 Learning ! | 677.169 | 1 |
involved in studying formally the mathematical curriculum. At the same time, this course creates interest in solving mathematical problems. This course will be useful to anyone who is interested in learning mathematics of any topic and help to excel in any chosen field of mathematics or any other subject which requires logical thinking skills. | 677.169 | 1 |
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