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MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 6_Charge_Separation_Part_II_Diode_Under_Illumination.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So we have an int... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 7_Toward_a_1D_Device_Model_Part_I_Device_Fundamentals.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: What we're going ... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 9_Charge_Extraction.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. TONIO BUONASSISI: Why don't ... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | Tutorial_Doping.txt | [MUSIC PLAYING] PROFESSOR: Hello, everyone. Today we'll talk about doping, which is the process of intentionally adding impurities to a semiconductor in order to change its electrical properties. Doping is a critical process in the tech world. It's used in manufacturing almost all semiconductor technologies today. With... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 16_Solar_Cell_Characterization.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So I'm going to d... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | Tutorial_Solar_Cell_Operation.txt | [MUSIC PLAYING] PROFESSOR: Hello everyone, today we're going to learn how a Solar Cell is able to turn light generated mobile charges into electricity. Today's lesson will use everything we've learned in the past videos to understand this effect. So, make sure you understand the material from the previous videos before... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 8_Toward_a_1D_Device_Model_Part_II_Material_Fundamentals.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: All right, so let... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 4_Charge_Excitation.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from 100's of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Why don't we go ahea... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 12_Thin_Films_Material_Choices_Manufacturing_Part_I.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So folks, we're g... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 1_Introduction_2627_Fundamentals_of_Photovoltaics.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Ladies and gentle... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 5_Charge_Separation_Part_I_Diode.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: We'll be talking ... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 10_Wafer_SiliconBased_Solar_Cells_Part_I.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: But today we're g... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 11_Wafer_SiliconBased_Solar_Cells_Part_II.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: All right. Why do... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 3_Light_Absorption_and_Optical_Losses.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. TONIO BUONASSISI: Today we'r... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | Student_Project_Presentations_Part_2.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. STUDENT 1: We would like to ... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 17_Modules_Systems_and_Reliability.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: So modules, syste... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 13_Thin_Films_Material_Choices_Manufacturing_Part_II.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Last class, we in... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 15_Advanced_Concepts.txt | The following content is provided under a creative commons license. Your support will help MIT OpenCourseWare continue to offer high-quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Welcome everyone,... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 19_Cost_Price_Markets_Support_Mechanisms_Part_II.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: The equivalent co... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 2_The_Solar_Resource.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: And I think we're... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | Tutorial_Texturing.txt | [MUSIC PLAYING] PROFESSOR: Hello, everyone. Today we'll be taking a look at how light interacts with the surface of a solar cell. Right now I'm standing next to a solar module made up of individual silicon solar cells. If you look closely, these cells actually appear black. And they appear black for a very important re... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | Student_Project_Presentations_Part_1.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Final presentatio... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 14_PV_Efficiency_Measurement_and_Theoretical_Limits.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Good. Well, why d... |
MIT_2627_Fundamentals_of_Photovoltaics_Fall_2011 | 18_Cost_Price_Markets_Support_Mechanisms_Part_I.txt | The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Today we're going... |
World_History_TED_Talks | The_incredible_history_of_Chinas_terracotta_warriors_Megan_Campisi_and_PenPen_Chen.txt | What happens after death? Is there a restful paradise? An eternal torment? A rebirth? Or maybe just nothingness? Well, one Chinese emperor thought that whatever the hereafter was, he better bring an army. We know that because in 1974, farmers digging a well near their small village stumbled upon one of the most import... |
World_History_TED_Talks | 히틀러는_어떻게_힘을_얻을_수_있었을까_알렉스_겐들러_안토니_하자드Alex_Gendler_Anthony_Hazard.txt | How did Adolf Hitler, a tyrant who orchestrated one of the largest genocides in human history, rise to power in a democratic country? The story begins at the end of World War I. With the successful Allied advance in 1918, Germany realized the war was unwinnable and signed an armistice ending the fighting. As its impe... |
World_History_TED_Talks | 책의_진화ㅣ쥴리_드레이프스Julie_Dreyfuss.txt | What makes a book a book? Is it just anything that stores and communicates information? Or does it have to do with paper, binding, font, ink, its weight in your hands, the smell of the pages? Is this a book? Probably not. But is this? To answer these questions, we need to go back to the start of the book as we know it ... |
World_History_TED_Talks | 북아메리카_탄생_배경_피터_J_하프로프_Peter_J_Haproff.txt | The geography of our planet is in flux. Each continent has ricocheted around the globe on one or more tectonic plates, changing quite dramatically with time. Today, we'll focus on North America and how its familiar landscape and features emerged over hundreds of millions of years. Our story begins about 750 million y... |
World_History_TED_Talks | 알리야_부터_제이지_까지_힙합_역사에서_잡혀진_순간들_조나산_매니언_Jonathan_Mannion.txt | This is The Notorious B.I.G., 1995, the Palladium nightclub, New York City. What really I want to talk about is my dedication, my 100% focus, and finding something that I love, my passion point. I fought to be on this stage, to be able to stand next to Lil' Kim and take all these pictures to create one definitive photo... |
World_History_TED_Talks | 비단길_역사_최초의_세계교역망_샤논_헤리스_카스텔로Shannon_Harris_Castelo.txt | A banker in London sends the latest stock info to his colleagues in Hong Kong in less than a second. With a single click, a customer in New York orders electronics made in Beijing, transported across the ocean within days by cargo plane or container ship. The speed and volume at which goods and information move across ... |
World_History_TED_Talks | How_inventions_change_history_for_better_and_for_worse_Kenneth_C_Davis.txt | Transcriber: tom carter Reviewer: Bedirhan Cinar This is the story of an invention that changed the world. Imagine a machine that could cut 10 hours of work down to one. A machine so efficient that it would free up people to do other things, kind of like the personal computer. But the machine I'm going to tell you abou... |
World_History_TED_Talks | The_history_of_our_world_in_18_minutes_David_Christian_TED.txt | First, a video. Yes, it is a scrambled egg. But as you look at it, I hope you'll begin to feel just slightly uneasy. Because you may notice that what's actually happening is that the egg is unscrambling itself. And you'll now see the yolk and the white have separated. And now they're going to be poured back into the eg... |
World_History_TED_Talks | Where_did_English_come_from_Claire_Bowern.txt | When we talk about English, we often think of it as a single language but what do the dialects spoken in dozens of countries around the world have in common with each other, or with the writings of Chaucer? And how are any of them related to the strange words in Beowulf? The answer is that like most languages, English ... |
World_History_TED_Talks | When_will_the_next_mass_extinction_occur_Borths_DEmic_and_Pritchard.txt | About 66 million years ago, something terrible happened to life on our planet. Ecosystems were hit with a double blow as massive volcanic eruptions filled the atmosphere with carbon dioxide and an asteroid roughly the size of Manhattan struck the Earth. The dust from the impact reduced or stopped photosynthesis from ma... |
World_History_TED_Talks | A_brief_history_of_rhyme_Baba_Brinkman_TEDxNavesink.txt | Translator: Tanya Cushman Reviewer: Peter van de Ven Yes, indeed, I am a rap artist, but I release records with subject matters that are a little bit different. One of my albums is a hip-hop adaptation of Chaucer's "Canterbury Tales." (Laughter) Another one is a hip-hop interpretation of Charles Darwin's "Theory of Evo... |
World_History_TED_Talks | 만사_무사_가장_부유하게_살았던_사람들_중_한_사람_제시카_스미스.txt | If someone asked you who the richest people in history were, who would you name? Perhaps a billionaire banker or corporate mogul, like Bill Gates or John D. Rockefeller. How about African King Musa Keita I? Ruling the Mali Empire in the 14th century CE, Mansa Musa, or the King of Kings, amassed a fortune that possibly... |
World_History_TED_Talks | Hunting_for_Perus_lost_civilizations_with_satellites_Sarah_Parcak.txt | In July of 1911, a 35-year-old Yale graduate and professor set out from his rainforest camp with his team. After climbing a steep hill and wiping the sweat from his brow, he described what he saw beneath him. He saw rising from the dense rainforest foliage this incredible interlocking maze of structures built of granit... |
World_History_TED_Talks | 역사_대_블리디미르_레닌알렉스_젠들러_Alex_Gendler.txt | He was one of the most influential figures of the 20th century, forever changing the course of one of the world's largest countries. But was he a hero who toppled an oppressive tyranny or a villain who replaced it with another? It's time to put Lenin on the stand in History vs. Lenin. "Order, order, hmm. Now, wasn't it... |
World_History_TED_Talks | History_vs_Napoleon_Bonaparte_Alex_Gendler.txt | After the French Revolution erupted in 1789, Europe was thrown into chaos. Neighboring countries' monarchs feared they would share the fate of Louis XVI, and attacked the New Republic, while at home, extremism and mistrust between factions lead to bloodshed. In the midst of all this conflict, a powerful figure emerged... |
World_History_TED_Talks | Is_graffiti_art_Or_vandalism_Kelly_Wall.txt | Spray-painted subway cars, tagged bridges, mural-covered walls. Graffiti pops up boldly throughout our cities. It can make statements about identity, art, empowerment, and politics, while simultaneously being associated with destruction. And, it turns out, it's nothing new. Graffiti, or the act of writing or scribbli... |
World_History_TED_Talks | 역사_대_크리스토퍼_콜롬버스_알렉스_젠들러.txt | Many people in the United States and Latin America have grown up celebrating the anniversary of Christopher Columbus's voyage, but was he an intrepid explorer who brought two worlds together or a ruthless exploiter who brought colonialism and slavery? And did he even discover America at all? It's time to put Columbus o... |
World_History_TED_Talks | 징기스칸_대_역사_알렉스_젠들러.txt | He was one of the most fearsome warlords who ever lived, waging an unstoppable conquest across the Eurasian continent. But was Genghis Khan a vicious barbarian or a unifier who paved the way for the modern world? We'll see in "History vs. Genghis Khan." "Order, order. Now who's the defendant today? Khan!" "I see Your... |
World_History_TED_Talks | 흑사병의_과거_현재_그리고_미래.txt | Imagine if half the people in your neighborhood, your city, or even your whole country were wiped out. It might sound like something out of an apocalyptic horror film, but it actually happened in the 14th century during a disease outbreak known as the Black Death. Spreading from China through Asia, the Middle East, Af... |
World_History_TED_Talks | 타투의_역사_애디슨_앤더슨Addison_Anderson.txt | Thinking of getting a tattoo? Decorating your birthday suit would add another personal story to a history of tattoos stretching back at least 8000 years. Tattooed mummies from around the world attest to the universality of body modification across the millennia, and to the fact that you really were stuck with it foreve... |
World_History_TED_Talks | 아테네에서_민주주의의_진실한_의미는_무엇인가_Melissa_Schwartzberg.txt | Hey, congratulations! You've just won the lottery, only the prize isn't cash or a luxury cruise. It's a position in your country's national legislature. And you aren't the only lucky winner. All of your fellow lawmakers were chosen in the same way. This might strike you as a strange way to run a government, let alone ... |
World_History_TED_Talks | 화약의_치명적인_역설_에릭_로사도_Eric_Rosado.txt | Everybody loves fireworks -- the lights, the colors, and, of course, the big boom. But the history of fireworks isn't all hugs and celebrations. Long before epic fireworks displays, chemists in China invented the key ingredient that propels those bright lights into the sky. That invention was what we now call gunpowder... |
World_History_TED_Talks | 햇빛은_당신의_생각보다_나이가_많습니다_스텐_오덴왈드.txt | You may know that it takes light a zippy eight minutes to reach us from the surface of the Sun, so how long do you think it takes light to travel from the Sun's core to its surface? A few seconds or a minute at most? Well, oddly enough, the answer is many thousands of years. Here's why. Photons are produced by the nucl... |
World_History_TED_Talks | 고대_로마의_4자매_레이_로렌스_Ray_Laurence.txt | Translator: Andrea McDonough Reviewer: Jessica Ruby Today, we're going to look at the world of Rome through the eyes of a young girl. Here she is, drawing a picture of herself in the atrium of her father's enormous house. Her name is Domitia, and she is just 5 years old. She has an older brother who is fourteen, Lucius... |
World_History_TED_Talks | 예술에서의_종교의_짧은_역사_TEDEd.txt | It's only been the last few hundreds years or so that Western civilization has been putting art in museums, at least museums resembling the public institutions we know today. Before this, for most, art served other purposes. What we call fine art today was, in fact, primarily how people experienced an aesthetic dimensi... |
World_History_TED_Talks | This_is_Sparta_Fierce_warriors_of_the_ancient_world_Craig_Zimmer.txt | In ancient Greece, violent internal conflict between bordering neighbors and war with foreign invaders was a way of life, and Greeks were considered premier warriors. Most Greek city-states surrounded themselves with massive defensive walls for added protection. Sparta in its prime was a different story, finding walls ... |
World_History_TED_Talks | 고대_올림픽의_기원_아마드_디안고어_Armand_DAngour.txt | Thousands of years in the making, what began as part of a religious festival honoring the Greek god Zeus in the rural Greek town of Olympia has today become the greatest show of sporting excellence on Earth. The inception date in 776 BC became the basis for the Greek's earliest calendar, where time was marked in four... |
World_History_TED_Talks | A_TED_Talk_on_the_History_of_Everything_Big_History_Project.txt | [Music] [Music] first a video yes it is a scrambled egg but as you look at it I hope you'll begin to feel just slightly uneasy because you may notice that what's actually happening is that the egg is on scrambling itself and you'll now see the yolk and the white have separated and now they're going to be poured back in... |
World_History_TED_Talks | The_Akune_brothers_Siblings_on_opposite_sides_of_war_Wendell_Oshiro.txt | There are many stories that can be told about World War II, from the tragic to the inspring. But perhaps one of the most heartrending experiences was that of the Akune family, divided by the war against each other and against their own identities. Ichiro Akune and his wife Yukiye immigrated to America from Japan in 19... |
World_History_TED_Talks | Neil_MacGregor_2600_years_of_history_in_one_object.txt | The things we make have one supreme quality -- they live longer than us. We perish, they survive; we have one life, they have many lives, and in each life they can mean different things. Which means that, while we all have one biography, they have many. I want this morning to talk about the story, the biography -- or r... |
MIT_Learn_Differential_Equations | Impulse_Response_and_Step_Response.txt | GILBERT STRANG: OK. So this is a video in which we go for second-order equations, constant coefficients. We look for the impulse response, the key function in this whole business, and the step response, too. So those are the responses. So I'm going to call g-- that will be the impulse response, where the right-hand sid... |
MIT_Learn_Differential_Equations | Laplace_Transforms_and_Convolution.txt | PROFESSOR: OK. This is one more thing to tell you about Laplace transforms, and introducing a new word, convolution. And so we're going to find our old formula in new language, a new way. But the formula is familiar. And the problem is our basic problem, second order, linear, constant coefficient with a forcing term. A... |
MIT_Learn_Differential_Equations | Similar_Matrices.txt | GILBERT STRANG: OK, thanks. Here's a second video that involves the matrix exponential. But it has a new idea in it, a basic new idea. And that idea is two matrices being called "similar." So that word "similar" has a specific meaning, that a matrix A, is similar to another matrix B, if B comes from A this way. Notice ... |
MIT_Learn_Differential_Equations | Midpoint_Method_ODE2.txt | PROFESSOR: The cost of a numerical method for solving ordinary differential equations is measured by the number of times it evaluates the function f per step. Euler's method evaluates f once per step. Here's a new method that evaluates it twice per step. If f is evaluated once at the beginning of the step to give a slo... |
MIT_Learn_Differential_Equations | The_Tumbling_Box_in_3D.txt | PROFESSOR: OK. Here's an example that's more or less for fun. Because you'll see me try to do it. You can do it better. I call the problem the tumbling blocks. Only in this example, in my demonstration, it's going to be a tumbling book. I'm going to take a book, the sacred book, and throw it in the air. And I'll throw ... |
MIT_Learn_Differential_Equations | Boundary_Conditions_Replace_Initial_Conditions.txt | GILBERT STRANG: OK. Well my problem today is a little different. Because I don't have two initial conditions, as we normally have for a second-order differential equation. Instead, I have two boundary conditions. So let me show you the equation. So I'm changing t to x because I'm thinking of this as a problem in space ... |
MIT_Learn_Differential_Equations | Examples_of_Fourier_Series.txt | This video is to give you more examples of Fourier series. I'll start with a function that's odd. My odd function means that on the left side of 0, I get the negative of what I have on the right side of 0. F at minus x is minus f of x. And it's the sine function that's odd. The cosine function is even, and we will have... |
MIT_Learn_Differential_Equations | Lorenz_Attractor_and_Chaos.txt | CLEVE MOLER: The Lorenz strange attractor, perhaps the world's most famous and extensively studied ordinary differential equations. They were discovered in 1963 by an MIT mathematician and meteorologist, Edward Lorenz. They started the field of chaos. They're famous because they are sensitive to their initial condition... |
MIT_Learn_Differential_Equations | Unforced_Damped_Motion.txt | GILBERT STRANG: OK. So today is unforced-- that means zero on the right-hand side, looking for null solutions-- damped-- that means there is a coefficient B in the first derivative. And what's the solution? This is really a basic, basic equation. In many applications, A would be the mass. In a spring, for example, A wo... |
MIT_Learn_Differential_Equations | Positive_Definite_Matrices.txt | GILBERT STRANG: OK. This is positive definite matrix day. Our application was the second-order equation with a symmetric matrix, S. And we solved this equation. Second derivative, plus S times y, equals 0. And you maybe remember how we solved it. We looked for an exponential solution. e to the I omega t, times a vector... |
MIT_Learn_Differential_Equations | Classical_RungeKutta_ODE4.txt | PROFESSOR: Here is the classical Runge-Kutta method. This was, by far and away, the world's most popular numerical method for over 100 years for hand computation in the first half of the 20th century, and then for computation on digital computers in the latter half of the 20th century. I suspect it's still in use today... |
MIT_Learn_Differential_Equations | Linearization_of_two_nonlinear_equations.txt | GILBERT STRANG: OK. Two equations, the question of stability for two equations, stability around a critical point. OK. So the idea will be to linearize, to look very near that critical point, that point. But now we're in two dimensions. So that's a little more to do. So here's the general picture, and then here is an e... |
MIT_Learn_Differential_Equations | The_Column_Space_of_a_Matrix.txt | GILBERT STRANG: OK. We're coming to the point where we need matrices. That's the point when we have several equations, several differential equations instead of just one. And it's a matrix that does that coupling. So can I-- this won't be a full course in linear algebra. That would be available, you may know on, open c... |
MIT_Learn_Differential_Equations | The_Stability_and_Instability_of_Steady_States.txt | GILBERT STRANG: This is a topic I think is interesting. I like this one. It's about stability or instability of a steady state. So let me show you the differential equation. It could be linear, but might be non linear. dy dt is f of y. I'm going to-- I keep it that right hand side not depending on t, so just a function... |
MIT_Learn_Differential_Equations | Eigenvalues_and_Stability_2_by_2_Matrix_A.txt | GILBERT STRANG: This is a good time to do two by two matrices, their eigenvalues, and their stability. Two by two eigenvalues are the easiest to do, easiest to understand. Good to separate out the two by two case from the later n by n eigenvalue problem. And of course, let me remember the basic dogma of eigenvalues and... |
MIT_Learn_Differential_Equations | Fourier_Series.txt | GILBERT STRANG: OK, I'm going to explain Fourier series, and that I can't do in 10 minutes. It'll take two, maybe three, sessions to see enough examples to really use the idea. Let me start with what we're looking for. We have a function. And we want to write it as a combination of cosines and sines. So those our basis... |
MIT_Learn_Differential_Equations | Incidence_Matrices_of_Graphs.txt | GILBERT STRANG: OK. I want to continue the last video, which was about incidence matrices, and graphs, and networks, and flows in the network. So that was 5.6. This is 5.6b. And I'll remember the same graph. You remember a graph is some nodes, four nodes here, and some edges, and in this case five edges. So I have a 5 ... |
MIT_Learn_Differential_Equations | Systems_of_Equations.txt | PROFESSOR: Many mathematical models involve high order derivatives. But the MATLAB ODE solvers only work with systems of first order ordinary differential equations. So we have to rewrite the models to just involve first order derivatives. Let's see how to do that with a very simple model, the harmonic oscillator. x do... |
MIT_Learn_Differential_Equations | Tumbling_Box.txt | PROFESSOR: Here are the differential equations for the angular momentum of a tumbling box. Try throwing a book, or a box, or any rectilinear object whose three dimensions are all different, into the air with a twist, to make a tumble. You could go to rotate about its longest axis, or about its shortest axis. But you ca... |
MIT_Learn_Differential_Equations | Powers_of_Matrices_and_Markov_Matrices.txt | GILBERT STRANG: OK. So this video is about using eigenvectors and eigenvalues to take powers of a matrix, and I'll show you why we want to take powers of a matrix. And then the next video would be using eigenvalues and eigenvectors to solve differential equations. The two big applications. So here's the first applicati... |
MIT_Learn_Differential_Equations | Electrical_Networks_Voltages_and_Currents.txt | GILBERT STRANG: This video is about one of the key applications of ordinary differential equations to electrical flow, flow of currents in a network. And so I drew a network, a very simple network. It's just called an RLC loop. It's only got one loop, so it's a really simple network. The R stands for resistance to the ... |
MIT_Learn_Differential_Equations | Fourier_Series_Solution_of_Laplaces_Equation.txt | GILBERT STRANG: OK. So this is using Fourier series. So I had to pick an equation where we were given a function, and not just a couple of initial values. So I made the equation a partial differential equation. The most famous one, Laplace's equation. So this is the setup. And you'll see how Fourier series comes in. We... |
MIT_Learn_Differential_Equations | Pictures_of_Solutions.txt | PROFESSOR: OK. So we've moved on into Chapter 3. Chapter 1 and 2 were about equations we could solve, first order equations, chapter one; second order equations in chapter 2, often linear, constant coefficient sometimes. Now we take any equation. And I'll start with first order. First derivative is some function and no... |
MIT_Learn_Differential_Equations | Laplace_Equation.txt | Today I'm speaking about the first of the three great partial differential equations. So this one is called Laplace's equation, named after Laplace. And you see partial derivatives. So we have-- I don't have time. This equation is in steady state. I have x and y, I'm in the xy plane. And I have second derivatives in x ... |
MIT_Learn_Differential_Equations | Heat_Equation.txt | GILBERT STRANG: This is heat equation video. So this is the second of the three basic partial differential equations. We had Laplace's equation, that was-- time was not there. Now time comes into the heat equation. We have a time derivative, and two-- matching with two space derivatives. So I have my function. My solut... |
MIT_Learn_Differential_Equations | Phase_Plane_Pictures_Spirals_and_Centers.txt | GILBERT STRANG: OK. So this is the second lecture about these pictures, in the phase plane that's with axes y and y prime, for a second order constant coefficient linear, good problem. Good problem. And you remember that we study that equation by looking for special solutions y equals e to the st. When we plug that int... |
MIT_Learn_Differential_Equations | Integrating_Factor_for_Constant_Rate.txt | GILBERT STRANG: OK. This is our last look at the first order linear differential equation that you see up here. The dy dt is ay, that's the interest rate growing in the bank example. y is our total balance. And q of t is our deposits or withdrawals. Only one change. We allow the interest rate a to change with time. Thi... |
MIT_Learn_Differential_Equations | Gilbert_and_Cleve_Introduction.txt | GILBERT STRANG: Hi. I'm Gilbert Strang. I'm a math professor at MIT. CLEVE MOLER: And I'm Cleve Moler. I'm one of the founders of MathWorks, and I'm chief mathematician. Gil and I have made a video series about ordinary differential equations. GILBERT STRANG: This developed really from my experience of the linear algeb... |
MIT_Learn_Differential_Equations | Solving_Linear_Systems.txt | GILBERT STRANG: So this is the key video about solving a system of n linear constant coefficient equations. So how do I write those equations? Y is now a vector, a vector with n components. Instead of one scalar, just a single number y-- do you want me to put an arrow on y? No, I won't repeat it again. But that's to em... |
MIT_Learn_Differential_Equations | ODE45.txt | PROFESSOR: The most frequently used ODE solver in MATLAB and Simulink is ODE45. It is based on method published by British mathematicians JR Dormand and PJ Prince in 1980. The basic method is order five. The error correction uses a companion order four method. The slope of tn is, first same as last left over from the p... |
MIT_Learn_Differential_Equations | Step_Function_and_Delta_Function.txt | GILBERT STRANG: OK, this is the video about two neat functions-- the step function and its derivative the delta function. So if I can just introduce you to those functions and show you that they're very natural inputs to a differential equation. They happen all the time in real life. And so we need to understand how to... |
MIT_Learn_Differential_Equations | Singular_Value_Decomposition_the_SVD.txt | PROFESSOR: The previous video was about positive definite matrices. This video is also linear algebra, a very interesting way to break up a matrix called the singular value decomposition. And everybody says SVD for singular value decomposition. And what is that factoring? What are the three pieces of the SVD? So this i... |
MIT_Learn_Differential_Equations | Graphs.txt | PROFESSOR: OK. This video is a different direction. It will be about linear equations and not differential equations. A matrix is at the center of this video and it's called the incidence matrix. And that incidence matrix tells me everything about a graph. Now, what do I mean by the word graph? I don't mean a graph of ... |
MIT_Learn_Differential_Equations | Response_to_Exponential_Input.txt | GILBERT STRANG: OK. We're still talking about first order differential equations with a dy dt. And there is still a gross term proportional to the balance. This might be the interest that's added on to y. And then there is input, a source term, of deposits being made all the time. So I'm looking to solve that different... |
MIT_Learn_Differential_Equations | An_Example_of_Undetermined_Coefficients.txt | GILBERT STRANG: OK. So can I begin with a few words about the big picture of solving differential equations? So if that was a nonlinear equation, we would go to computer solutions. And Cleve Moler is making a parallel video series about the Matlab suite of codes for solving differential equations. Then when that equati... |
MIT_Learn_Differential_Equations | Separable_Equations.txt | GILBERT STRANG: OK. So speaking today about separable equations. These are, in principle, the easiest to solve. They include nonlinear equations but they have a special feature that makes them easy, makes them approachable. And that special feature is that the right hand side of the equation separates into some functio... |
MIT_Learn_Differential_Equations | The_Big_Picture_of_Linear_Algebra.txt | GILBERT STRANG: I would like you to see the big picture of linear algebra. We're not doing, in this set of videos, a full course on linear algebra. That's already on OpenCourseWare 1806. And now I'm concentrating on differential equations, but you got to see linear algebra this way. And this way means subspaces. And th... |
MIT_Learn_Differential_Equations | Independence_Basis_and_Dimension.txt | PROFESSOR: So as long as I'm introducing the idea of a vector space, I better introduce the things that go with it. The idea of its dimension and, all important, the idea of a basis for that space. That space could be all of three dimensional space, the space we live in. In that, case the dimension is three, but what's... |
MIT_Learn_Differential_Equations | Integrating_Factor_for_a_Varying_Rate.txt | GILBERT STRANG: OK? I want to talk about a slightly different way to solve a linear first-order equation. And if you look at the equation-- I'll do an example. That's the best. Do you notice what's different from our favorite equation? The change is 2t. The interest rate a is increasing with time, changing with time. S... |
MIT_Learn_Differential_Equations | Second_Order_Equations_with_Damping.txt | GILBERT STRANG: I'm coming back to the number one example, but not the easiest example, of a second order equation with an oscillating forcing term, cosine omega t. We have to know the answer to this problem. And it's a little messy, but the method is not messy. The method is straightforward. So let me begin by looking... |
MIT_Learn_Differential_Equations | Forced_Harmonic_Motion.txt | GILBERT STRONG: This is the second video on second order differential equations, constant coefficients, but now we have a right hand side. And the first one was free harmonic motion with a zero, but now I'm making this motion, I'm pushing this motion, but at a frequency omega. This is my forcing term. So I think I'm ha... |
MIT_Learn_Differential_Equations | Eigenvalues_and_Eigenvectors.txt | GILBERT STRANG: So today begins eigenvalues and eigenvectors. And the reason we want those, need those is to solve systems of linear equations. Systems meaning more than one equation, n equations. n equal 2 in the examples here. So eigenvalue is a number, eigenvector is a vector. They're both hiding in the matrix. Once... |
MIT_Learn_Differential_Equations | Stiffness_ODE23s_ODE15s.txt | INSTRUCTOR: I want to illustrate the important notion of stiffness by running ode45, the primary MATLAB ODE solver, on our flame example. The differential equation is y prime is y squared minus y cubed, and I'm going to choose a fairly-- an extremely small initial condition, 10 to the minus sixth. The final value of t ... |
MIT_Learn_Differential_Equations | Exponential_Response_Possible_Resonance.txt | GILBERT STRONG: Well, you see spring has finally come to Boston. My sweater is gone and it's April the 16th, I think. It's getting late spring. So today, this video is the nice case, constant coefficient, linear equations, and the right hand side is an exponential. Those are the best. And we've seen that before. In fac... |
MIT_Learn_Differential_Equations | Linearization_at_Critical_Points.txt | GILBERT STRANG: OK. I'm concentrating now on the key question of stability. Do the solutions approach 0 in the case of linear equations? Do they approach some constant, some steady state in the case of non-linear equations? So today is the beginning of non-linear. I'll start with one equation. dy dt is some function of... |
MIT_Learn_Differential_Equations | Second_Order_Systems.txt | GILBERT STRANG: OK. Now, I'm going to have differential equations, systems of equations, so there'll be matrices and vectors, using symmetric matrix. They'll be second order. So second order, second derivative, that y is the vector. And S is the symmetric matrix. And that's the first time we've been prepared for the mo... |
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