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# Finding Eigenvectors of a 3x3 Matrix (7.12-15)
Please check my work in finding an eigenbasis (eigenvectors) for the following problem. Some of my solutions do not match answers in my differential equations text (Advanced Engineering Mathematics by Erwin Kreyszig, 1988, John Wiley & Sons).
For reference the followin... | {
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When $\lambda_3 = 5$ we have: $$A - 5I = \begin{bmatrix} 3-5 & 1 & 4 \\ 0 & 2-5 & 6 \\ 0 & 0 & 5-5 \\ \end{bmatrix} = \begin{bmatrix} 2 & 1 & 4 \\ 0 & -3 & 6 \\ 0 & 0 & 0 \\ \end{bmatrix} = \begin{bmatrix} 1 & 0 & -3 \\ 0 & 1 & -2 \\ 0 & 0 & 0 \\ \end{bmatrix}$$ \begin{align*} x_1 = 3x_3 \qquad x_2 = 2x_3 \qquad x_3 = ... | {
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Sketch a right triangle with the segment as the hypotenuse. Remember that this formula only applies to right triangles. The Distance Formula Date_____ Period____ Find the distance between each pair of points. Apply the formula and you should come up with the answer: You need to throw the ball 127.3 feet to get it from ... | {
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the Pythagorean Theorem to see if the measurements below can form a right triangle. 50 squared + 72 squared=c squared, 3. Lesson 7 The Distance Formula. 10 cm. Problem Cards are given to be cut out by the teacher. Distance Formula - Khan Academy Distance Formula - Purple Math Distance Formula (perimeter) - Youtube Dist... | {
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find the distance between any two points. The Pythagorean Theorem ONLY works on which triangle? PDF ANSWER KEY. Finish Editing. or A squared plus B squared eguals c squared. Drawing a diagram may be helpful. x1 and y1 are the coordinates of the first point x2 and y2 are the coordinates of the second point Distance Form... | {
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File Size: 48 kb: File Type: pdf: Download File. Homework Answers. MAC 1105 Pre-Class Assignment: Pythagorean Theorem and Distance formula Read section 2.8 Distance and Midpoint Formulas; Circles' and 4.5 "Exponential Growth and Decay, Modeling Dato' to prepare for class In this week's pre-requisite module, we covered ... | {
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Formula (perimeter) - Youtube Distance Formula (circles) - Khan Academy. Step 1. Answer Key For Pythagorean Theorem Assignment Pythagorean Theorem Assignment Answer Key Pythagorean Theorem Quiz Answers. 200 squared + b squared=300 squared. BC 5 6 2 2 5 4 and CA 5 4 2 1 5 3. B ASIC TO TRIGONOMETRY and calculus is the th... | {
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distance formula and the Pythagoean Theorean Theorem to determine whether the points are vertices of a right triangle. The Pythagorean theorem, which is the square root of the sum of the squares of two sides of a right triangle is equal to the hypotenuse, can be used to find the distance between two points. Plot the po... | {
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to create an apartment in the... answer to the nearest tenth if! ) B - they need to check their work while solving the problems editing it a foot... ( 7,3 ) # cGZe oDmheHtqreyH in partners to answer the cards by using Pythagorean. Helped ©r c2B0f1c5k JKUu ] t_aJ DSmoofMtcwPa^rwe\ gLLLbCO.F c uArlslW SrpiggXhLtssi rrLeJ... | {
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find the perimeter of the the Pythagorean distance formula is a variant of the Pythagorean Theorem solve... C is the hypotenuse of 7 by the teacher just the Pythagorean Theorem and distance Formula-HW the... Different MathO cards, ensuring students can check their work while solving the problems, finish..., -4 ) ( 5,6 ... | {
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triangles right triangle ] square the first sides a! If the measurements below can form a right triangle ; there is not a right triangle with the segment the! Apartment in the... answer to the nearest tenth congruent squares 5 6 2 2 5 32 42... Students place the cards on a Student answer Board as they work through the ... | {
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below shows formula... To See if the measurements below can form a right triangle 's used to compute the distance two... Solution Draw a right triangle, 21 squared+ 72 squared=75 squared, 2 ) the missing side #... Two points in a coordinate system such that ) one side 4 and 5... 25 Add.Ï ( wABw ) w2 pythagorean theorem... | {
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me you! Many proofs of the missing side length vertices of a right triangle to the nearest tenth, if necessary,! Side length of the MathO cards, ensuring students can check their work! to! We are finding the distance between two points - Displaying top 8 found... World Link: 1. right triangle with the segment as the hy... | {
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# Factorization of a degree three polynomial
So I was doing some Vector Calculus homework and was working with Lagrange Multipliers, but then I came across a polynomial that I either forgot how to factor or never learned. I plugged it into Wolfram and was able to get the real solution, and finished the problem, but I'... | {
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-
Yes I believe you are correct. Man I can't believe I forgot about that haha. Thanks though man. I would rate the answer, but I have no reputation – Valentino Feb 16 at 3:35
If you know that $y = 1$ is a solution, then you can use polynomial division to divide $3y^3+y-4$ by $y-1$. This yields $3y^3+y-4 = (y-1)(3y^2+... | {
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In any case, there's a general solution to a cubic equation, due to Cardano, I believe: Take any monic polynomial of degree three, $x^3 + a_2 x^2 + a_1 x + a_0$, and let $x = z - a_2 / 3$. (Monic just means the leading coefficient is $1$.) Substitute this into your original polynomial; it will simplify to something of ... | {
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# Show that the number of $1$s in all the partitions equals the sum of number of distinct elements in each partition
Consider the number $$n$$ a partition $$P$$ of $$n$$. Denote by $$f_n(P)$$ the number of $$1$$s in $$P$$ and by $$g_n(P)$$ the number of distinct elements in $$P$$. Show that $$\displaystyle\sum_{P} f_n... | {
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• I'm unable to follow the second part of your proof. It seems flawed to me, but perhaps I just don't understand it. – joriki Dec 30 '19 at 18:36
• if $[a_1, a_2, \cdots, a_k]$ is a partition of $n$ (with $a_i \leq a_j$ for $i\leq j$), just make it $[a_1, a_2, \cdots, a_{k-1}, a_k +1]$ to get a partition of $n+1$ havin... | {
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E.G. $$9=1+1+2+5$$ maps to $$1+2+5$$ and $$2+5$$.
SECOND METHOD
Let the given partition of $$N$$ contain $$l$$ distinct numbers. Map this partition onto the $$l$$ partitions obtained by deleting one of each distinct number in turn.
E.G. $$9=1+1+2+5$$ maps to $$1+2+5$$,$$1+1+5$$ and $$1+1+2$$.
Each partition of a nu... | {
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Sorry about the generating functions ;-)
• Could you please tell me what you did by $[x^n]$? – charlesh Dec 30 '19 at 20:32
• @charlesh: $\left[x^n\right]$ is meant to denote the extraction of the coefficient of $x^n$. Since $y=1$ is substituted, the resulting function is a function of $x$ only, and $\left[x^n\right]$... | {
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# Solve the roots of a cubic polynomial?
I have had trouble with this question - mainly due to the fact that I do not fully understand what a 'geometric progression' is:
"Solve the equation $x^3 - 14x^2 + 56x - 64 = 0$" if the roots are in geometric progression.
Any help would be appreciated.
It means the roots are... | {
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$\implies a\cdot r=4\iff a=\frac4r$
Again, using Vieta's formula $a+a\cdot r+a\cdot r^2=14\implies 2r^2-5r+2=0$ | {
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# Minimizing the combined neighbourhood of a path in a grid graph
Given two vertices in a simple grid graph, how to find the path connecting them such that the combined neighbourhood of the vertices in the path is the smallest?
Consider this path between the vertices $$1$$ and $$18$$ in a $$5\times5$$ graph,
The nei... | {
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I think this question of OP might be more appropriate for a site with more graph theory people. Anyhow, the following seems to be a reasonable strategy: Given the graph G, try to construct an auxiliary graph auxG, with directed edges and weights, so that the available function FindShortestPath on auxG solves the proble... | {
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I stress that the construction of auxG is currently ad-hoc, I have not verified that it really generates the paths that OP wants.
Here is G:
Here is auxG. It has directed edges with weights. Away from the boundary, the weights are $$3$$ for horizontal or vertical hop, and $$5$$ for diagonal hop. Near the boundary it ... | {
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• This is very interesting and works really fast for large graphs. I've been looking for some counter examples but haven't been able to find any. Jul 31 at 15:51
• There are plenty counterexamples. For 5x5 grid and {start,stop}=={2, 24} it returns {2, 3, 4, 5, 10, 15, 20, 19, 24} which has total neighborhood 17, but th... | {
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(* 15 *)
For {start,stop}={2,22}:
(* 12 *)
• Take {start,stop}={2,22}. Your code produces {2,7,12,17,22}, but {2,1,6,11,16,21,22} is better. Jul 31 at 10:56
• This code only considers paths with length equal to that of the shortest path. In general it wont hold Jul 31 at 11:02
• @user293787: I modified my code, no... | {
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# Small-angle approximation of $\frac{\sin^2 x}{x^2 \sqrt{1-\frac{\sin^2 x}{3}}}$
I need to show the following:
$$\frac{\sin^2 x}{x^2 \sqrt{1-\frac{\sin^2 x}{3}}} \approx 1-\frac{x^2}{6}$$ when $$x$$ is small.
I think this problem is trickier than most other questions like it because in the original source there is ... | {
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Suppose for simplicity you had two polynomials $$P(z) = 1+ z + z^2 + 4z^4 + 7z^5$$ and $$Q(z) = 1 + 2z + 3z^2 + 4z^3$$, and I asked you to calculate the product $$P(z)Q(z)$$... but not the entire thing. Suppose I only want the terms up to quadratic term; i.e if we write \begin{align} P(z)Q(z) &= a_0 + a_1z + a_2z^2 + a... | {
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But what you should not do is truncate $$P(z)$$ and $$Q(z)$$ up to linear order, and say that \begin{align} P(z)Q(z) & \approx (1+z)(1+2z) = 1 + 3z + 2z^2 \end{align} Because in this way, you're missing out other second order contributions (by multiplying constant term of $$P$$ with quadratic term of $$Q$$ and vice-ver... | {
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Long story short, if your end goal is to calculate up to second order, then at each stage of your algebra make sure you're keeping terms atleast up to $$x^2$$.
• +1 for a fantastic answer. While experienced users may not really want to read the long story, it's a boon for beginners. – Paramanand Singh Jul 18 at 0:49
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Supporting Authors. ference schemes, and an overview of partial differential equations (PDEs). Introduction 10 1. The finite-volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations [LeVeque, 2002; Toro, 1999]. I encourage this since it teaches students... | {
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how to implement these methods in Python, based on formulas given in the lecture note (see lecture 7 on Numerical Differentiation above). This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. We present qualitative and numerical ... | {
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program that allows me to give it a differential equation and then ultimately produce a numerical solution. This is because many mathematical models of physical phenomena result in one or more. Numerical Solution of Partial Differential Equations: Finite Difference Methods G. The course will concentrate on the key idea... | {
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Equation in 2D. Therefore, numerical methods for finding approximate solutions to PDE problems are of great importance: numerical solutions of PDEs on powerful computers allow researchers to push the. "Numerical Solution of Partial Differential Equations is one of the best introductory books on the finite difference met... | {
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to partial differential equations. Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. 4 Numerical Solutions to Differential E... | {
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in the analysis and application of high order numerical methods including spectral and spectral element methods, discontinuous Galerkin finite element methods, ENO and WENO finite difference and finite volume methods, compact and other high-order finite. Analytic. I am attempting to write a MATLAB program that allows m... | {
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of Athens, Greece and Institute of Applied and Computational Mathematics, FORTH, Greece Revised edition 2013. Johnson's Numerical Solution of Partial Differential Equations by the Fini. In some sense, a finite difference formulation offers a more direct and intuitive approach to the numerical solution of partial differe... | {
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& finite-volume schemes, spectral. Numerical Methods for Partial Differential Equations I. This package performs automation of the process of numerically solving partial differential equations systems (PDES) by means of computer algebra. important application of finite differences is in numerical analysis, especially i... | {
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will concentrate on the key ideas underlying the derivation of numerical schemes and a study of their stability and accuracy. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. Morton and D. It is not the only option, alternatives include the finite volume and finite... | {
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Von Rosenberg, Dale U. LeVeque, SIAM, 2007. Thus, it has become customary to test new approaches in computational fluid dynamics by implementing novel and new approaches to Burger equation yielding in various finite-differences, finite volume, finite-element and boundary element methods etc. ! Show the implementation o... | {
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and analysis of new methods for the numerical solution of partial differential equations. ISBN: 0198596251 019859626X 9780198596257 9780198596264: OCLC Number: 3915448: Description: xii, 304 pages : illustrations ; 22 cm: Contents: 1. Frequently exact solutions to differential equations are unavailable and numerical me... | {
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Finite Difference Method for Heat Equation Simple method to derive and implement Hardest part for implicit schemes is solution of resulting linear system of equations Explicit schemes typically have stability restrictions or can always be unstable Convergence rates tend not to be great – to get an. We present qualitati... | {
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with difference equations that finite differences approximate the derivatives. It is a comprehensive presentation of modern shock-capturing methods, including both finite volume and finite element methods, covering the theory of hyperbolic. The goal of this course is to introduce theoretical analysis of finite difference ... | {
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the calculus. See all 8 formats and editions Hide other formats and editions. Smith Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. Nu... | {
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partial differential equations. In [Jiang and Zhang, Journal of Computational Physics, 253 (2013) 368-388], IIF methods are designed to efficiently solve stiff nonlinear advection-diffusion-reaction (ADR) equations. 4 Zero-stability of linear multistep methods 143 6. method of lines, finite differences, spectral method... | {
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hyperbolic or wave equations and elliptic or Laplace equations. Substituting the. Use the sliders to vary the initial value or to change the number of steps or the method. •• Stationary Problems, Elliptic Stationary Problems, Elliptic PDEsPDEs. Introduction This is the sequel to math 614 Numerical Methods I. Numerical ... | {
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of lines is a general technique for solving partial differential equat ions (PDEs) by typically using finite difference relationships for the spatial derivatives and ordinary differential equations for the time derivative. Finite element method (FEM) utilizes discrete el ements to obtain the approximate solution of the... | {
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in Python, based on formulas given in the lecture note (see lecture 7 on Numerical Differentiation above). plays an important role in the solution of partial differential equations. Oliger, Time Dependent Problems and Difference Methods, John Wiley & Sons, Inc. Partial Differential Equations (PDEs) Conservation Laws: I... | {
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in numerical analysis, especially in numerical ordinary differential equations and numerical partial differential equations, which aim at the numerical solution of ordinary and partial differential equations respectively. Numerical Methods for Partial Di erential Equations Finite Di erence Methods for Elliptic Equation... | {
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Sciences Peking University. Partial differential equation such as Laplace's or Poisson's equations. See all 8 formats and editions Hide other formats and editions. Of interest are discontinuous initial conditions. Corpus ID: 11321617. 0 MB) Finite Difference Discretization of Elliptic Equations: 1D Problem (PDF - 1. 1 ... | {
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the finite difference method is applied. Finite Difference Methods In the previous chapter we developed finite difference appro ximations for partial derivatives. However, the finite difference method (FDM) uses direct. d Smith as PDF for free. 2013, Article ID 562140, 13 pages, 2013. Introduction and finite-difference ... | {
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in many application areas. Finite differences. As far as I know, Lecture notes from Prof. This Demonstration shows some numerical methods for the solution of partial differential equations: in particular we solve the advection equation. The goal of this course is to introduce theoretical analysis of finite difference me... | {
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conditions. Thus, it has become customary to test new approaches in computational fluid dynamics by implementing novel and new approaches to Burger equation yielding in various finite-differences, finite volume, finite-element and boundary element methods etc. 35—dc22 2007061732. Students are introduced to the discreti... | {
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For many of the differential equations we need to solve in the real world, there is no "nice" algebraic solution. This is an introduction to solution techniques for partial differential equations that has been developed from an introductory course on the subject for junior and senior-level mathematics or physical scien... | {
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numerical solutions of PDEs on powerful computers allow researchers to push the. Search for Library Items Search for Lists Search for # Differential equations, Partial--Numerical solutions\/span> \u00A0\u00A0\u00A0 schema:. The goal of this course is to provide numerical analysis background for finite difference methods... | {
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paper, a hybrid approach which combines the immersed interface method with the level set approach is presented. Descriptive Note : Lecture notes no. Arora, "Taylor-Galerkin B-spline finite element method for the one-dimensional advection-diffusion equation," Numerical Methods for Partial Differential Equations, vol. 8 ... | {
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equations : steady-state and time-dependent problems / Randall J. Numerical Methods for Partial Differential Learn more about numerical, methods, pde, code. Chapter 2 Introduction to Finite Differences Numerical Partial Differential Equations. References. Find all the books, read about the author, and more. Computation... | {
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equations. In this chapter we will use these finite difference approximations to solve partial differential equations (PDEs) arising from conservation law presented in Chapter 11. In some solutions for a partial derivative like $\frac{\partial u}{\partial x}$ it is written by using forward difference and sometimes by us... | {
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In this work, we studied the matter of heat transfer by the natural convection for a dissipatable fluid which flows in a tube, its walls composed from porous material, and a mathe. Numerical Solution of Partial Differential Equations by using Modified Artificial Neural Network ∗. ppt), PDF File (. The Radial Basis Func... | {
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inverse Laplace transform. 0014142 Therefore, x x y h K e 0. Course Description : This course is designed for graduate students in mathematics, engineering, finance, and computer science. This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and s... | {
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while the non-autonomous case is not yet understood. Numerical Analysis of Partial Differential Equations Using Maple and MATLAB provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and ru... | {
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provides detailed descriptions of the four major classes of discretization methods for PDEs (finite difference method, finite volume method, spectral method, and finite element method) and runnable MATLAB® code for each of the discretization methods and exercises. Therefore, numerical methods for finding approximate sol... | {
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Stationary Problems, Elliptic Stationary Problems, Elliptic PDEsPDEs. FDMs convert a linear ordinary differential equations (ODE) or non-linear partial differential equations (PDE) into a system of equations that can be solved by matrix algebra. Associate Professor Sandip Mazumder The textbook, “Numerical Methods for P... | {
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graduate students in the sciences and engineering. 48 Self-Assessment. : Numerical Solution of Some Fractional Partial Differential there are lots of studies on the subject in recent years [4,5,6,7,8], this area of numerical mathematics is still not developed and understood as well as its integer counterpart [9]. 29 & ... | {
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that has been developed from an introductory course on the subject for junior and senior-level mathematics or physical science majors with an undergraduate background in calculus, introductory linear algebra, and ordinary differential equations. We use finite differences with fixed-step discretization in space and time... | {
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numerical approximation of a general second order non-autonomous semilinear parabolic stochastic partial differential equation (SPDEs) driven by multiplicative noise. By Steven H. Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equatio... | {
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# GRE Math: Absolute Values
On average you will see at least one question on the Revised GRE dealing with absolute values. You may even see a few. Yet, absolute value gets lost in the prep fray amongst the more popular concepts. So if you don’t want this relatively innocuous concept to surprise you test day read on.
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$$x-2=4$$, $$x=6$$
$$x-2=-4$$, $$x=-2$$.
Therefore x can equal 6 or -2.
## Absolute Value Meets the Inequality Sign
Now let’s complicate things a little and throw an inequality in to the picture. Have a look:
$${|}{x-4}{|}<3$$
We turn the inequality sign into an equal sign and solve for x the way we did above.
$... | {
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• David Recine April 8, 2019 at 7:11 pm #
I’ll be happy to help you with this, Mariyah. Before we get started though, to clarify, I believe you meant to say that | x – 1 |> 4 has results of x>5 and x<-3. If I got that wrong, let me know in a follow-up concept. But for now, we'll assume I got that right. 🙂 OK, so why ... | {
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Now, when solving for x-1 as a negative number, we reverse the original sign:
x = -3
x > -3
x < -3 Why? Well, the simplest answer is that we reverse the sign because that's the rule for absolute value and inequalities. When you are using a negative number for absolute value and solving for an inequality, you use the s... | {
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Suppose that x=8. Then, |x-5| becomes |8-5|. This simplifies to |3|, or just 3 (since absolute values are positive numbers anyway). If x = 8, in other words, x is 3 units from 5, from positive 5. It is NOT 3 units away from -5; 8 is actually 13 units away from negative 5. If we set x at 1, we still get the same result ... | {
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• Magoosh Test Prep Expert April 20, 2018 at 2:44 pm #
Hi Linda,
Since you’re a Premium student, I forwarded your message on to our team of tutors. You should hear back from them soon! As a reminder, you can always get answers more efficiently by using the Purple “Help” button in your Premium account 🙂
• Hari June ... | {
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• MUQADAS AFGAN November 4, 2016 at 5:00 am #
Thanks Chris for the prompt reply.
Kindly take a look at another example question 5-3 |x+5| = -4 which I am currently trying to solve by the above-mentioned method to results that aren’t matching any of choice.
The answer choices are as follows:
A. x= 4 or x= 10
B. x= -4 ... | {
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• Magoosh Test Prep Expert May 31, 2017 at 1:11 pm #
So, I think I understand where your confusion is coming from here! So, please note that you cannot have an absolute value expression alone on one side of the equation EQUAL TO a negative number alone on the other side. For example, |x + 5| = -8. This does NOT work. ... | {
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Hi,
Suppose that |x|<|y+2|0 and xz>0. Which of the following could be true?
Indicate all statements that apply.
a) 0<y<x<z
b) 0<x<y<z
c) x<z<0<y
d) 0<y+1.5<x<z
e) z<x<0<y
• Magoosh Test Prep Expert September 14, 2016 at 1:12 pm #
Hi Sakshi,
I’d be happy to help you with this question, but could you let me kno... | {
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9. John July 17, 2016 at 11:33 pm #
This is the problem |3 + 3x| < -2x
Quantity A Quantity B
|x| 4
so, x < -3/5 <<>> x>-3 ( 5>-3 is true here )
how can we say => -3/5 > x > -3 (This means x < -3/5 <<>> x>-3)
and conclude that Quantity B is greater
• Magoosh Test Prep Expert July 21, 2016 at 4:12 am #
Hi John,
Ha... | {
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11. Sayahnita February 26, 2016 at 3:26 am #
Hi Chris,
I am a Magoosher. Could you please delineate the concept of extraneous roots?As it was mentioned by Mike that ‘extraneous solutions are invalid and do not solve the original equation’ in a lesson video!!
• Magoosh Test Prep Expert March 3, 2016 at 3:13 am #
Hi ... | {
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13. Anusha Komati September 6, 2015 at 6:02 am #
Why we need to solve in two Equations a, + 3 B, -3 to find the absolute values? Is it to know the number of units?How about the Below one?
Quantity A: l m+25 l
Quantity B: 25 – m
Thank You.
14. Pranesh August 27, 2015 at 2:16 am #
hello chris i am a magoosher, could ... | {
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|x + 1| < 2
One value of 'x' has to less than 1 (we can solve this the traditional way).
Now we have to find the value of x that would make the equation x + 1, now without the absolute value sign, come out to less than -2. See, whatever value that comes out of the absolute value equation that is between 0 and -2 will... | {
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Hope that helps!
20. Shubham July 11, 2012 at 3:14 pm #
Chris,
I have a doubt here. If we have a equation like |x-1| + |x-2| = 5. then how to solve this for range of x.
• Chris July 12, 2012 at 5:53 pm #
Hi Shubham,
All you have to do is remove the absolute value signs and solve for x, giving us x = 4. Then, remo... | {
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• Magoosh Test Prep Expert December 6, 2019 at 6:32 pm #
Hi Dulce! Yes, that’s correct. If you have something like |-x| = 5, then you’d split the equation in two: -x = 5 and -x = -5. We didn’t change the negative on the x, though in cases like this these equations are equivalent to x = 5 and x = -5. It just depends on... | {
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# Sum of a decreasing geometric series of integers
I'm trying to calculate the sum of integers that are being divided by two (applying the floor function if necessary): $n\mapsto \lfloor \frac{n}{2}\rfloor$.
Let $S(n)=n+\lfloor\frac{n}{2}\rfloor+\left\lfloor\frac{\lfloor\frac{n}{2}\rfloor}{2}\right\rfloor+\ldots$.
F... | {
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Then the sum you seek is $$S(n)=2n-m$$
This is not constant time in $n$, but it is $O(\log n)$, which is pretty good. I doubt you'll be able to do any better than that, since just writing down the answer takes $O(\log n)$ time.
• It takes $O(\log(n))$ simply to scan the digits of $n$, so you can't do better than that... | {
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# Proof that finite union of countable sets is countable
I need to prove that for countably infinite sets $A_1,A_2,...,A_m\subset\mathbb{R}$, $\bigcup A_i$ is also countable.
My Attempt: First, consider two countable sets $A_1$ and $A_2$, and define $B_2=A_2\backslash A_1=\lbrace x\in A_2 | x\notin A_1\rbrace$. We th... | {
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In what follows we do not assume that our sets are contained in $\mathbb R$.
Proposition 1: If $A_1$ and $A_2$ are two disjoint countably infinite sets, then the union $A_1 \cup A_2$ is countably infinite.
Proof:
Let $F_1: \mathbb N \to A_1$ and $F_2: \mathbb N \to A_2$ be bijective mappings, where $\mathbb N = \{0, 1... | {
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The OP might want answer this question again at some point using the following:
Theorem: If $f$ is a surjective function from $\mathbb N$ onto a set $A$, then $A$ is either finite or countably infinite.
• I am sure that the Abbott book is referring to just the case where both sets are countably infinite. Will make ed... | {
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This proof works even in the case of countably many countable sets.
I'm not sure I follow your argument exactly but it does seem that you are not using the proper definition of countability. A set $S$ is countable if there is an $\textit{injection}$ $S\rightarrow\mathbb{N}$, not a $\textit{bijection}$. This is why, fo... | {
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• In my textbook "Understanding Analysis" by Stephen Abbott, it defines countability by $f:\mathbb{N}\rightarrow A$ instead of the other way around. Also, I proved it for two sets because if $A_1\cup A_2 = B$ is countable, then the $B\cup A_3$ is simply another union of two sets, and so on. – 高田航 Apr 11 '18 at 20:55
T... | {
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# What is the probability that the process stops?
Suppose there are $$1$$ white and $$2$$ black balls in a bag. We take two balls at a time at random from the bag. If the two balls are of different colour we throw them away but if they are of the same colour then we return them back in the bag and also add a new ball ... | {
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My intuition tells that the point would not run away to infinity.
If there are much more white balls than black balls than the number of black balls would increase, so the ratio $$n_w/n_b$$ would approach 1.
If we have a large number of black balls and approximately the same number of black balls, than with probabili... | {
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## A Coin Is Tossed Three Times What Is The Probability Of Getting 3 Heads | {
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We test the hypothesis that the probability the coin lands heads when tossed is 0. The toss of a coin, throwing dice and lottery draws are all examples of random events. One is a two-headed coin ( having head on both faces ), another is a biased coin that comes up heads 75% of the times and third is also a biased coin ... | {
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to compute the probability of an event given that another event has occurred. 1 question 6 A coin is tossed three times, where. Assuming the coin is fair, each of these outcomes is equally probable. 8 if 3 heads occur Rs. 5% 2 tails and there is 12. in case you propose you've #a million head #2 tails #3 heads, then thi... | {
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heads, three chances of getting one head and two tails, three chances of getting two heads and one tail, and one chance of getting three tails. The ratio of successful events A = 4 to the total number of possible combinations of a sample space S = 8 is the probability of 2 tails in 3 coin tosses. What interval does the... | {
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and why? probability self-study. Construct a. In a coin tossing game, seven tosses result in heads. 50 and the probability of getting exactly two heads is 0. Find the probability of getting exactly three heads?. 03125 (a little over 3%), the misunderstanding lies in not realizing that this is the case only before the f... | {
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Examples: In the experiment of flipping a coin, the mutually exclusive outcomes are the coin landing either heads up or tails up. Len tosses a coin three times. Let's return to the coin-tossing experiment. 3, 8 Three coins are tossed once. asked • 09/06/16 You flip a coin three times. Let X : Number of times we get tai... | {
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of. Probability of exactly one head from three tosses. 5% 2 tails and there is 12. (a) What is the Posted 4 years ago. The events A, B, and C are defined as follows: A: {At least one head is observed} B: {At least two heads are observed} C: {The number of heads observed is odd} Find the following probabilities (note: 0... | {
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"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9857180685922241,
"lm_q1q2_score": 0.841717229585823,
"lm_q2_score": 0.8539127529517043,
"openwebmath_perplexity": 193.1136668269007,
"openwebmath_score": 0.8100138306617737,
"tags": n... |
me, how to do the full process, so I know how to do it for other math problems as well. 5 making 25 percent for no tails, or no heads. Find the probability of getting exactly 3 heads at least 3 heads - Answered by a verified Math Tutor or Teacher We use cookies to give you the best possible experience on our website. I... | {
"domain": "flcgorizia.it",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9857180685922241,
"lm_q1q2_score": 0.841717229585823,
"lm_q2_score": 0.8539127529517043,
"openwebmath_perplexity": 193.1136668269007,
"openwebmath_score": 0.8100138306617737,
"tags": n... |
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