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STEPHEN CARPENTER: Welcome, everyone. It's good to have you here. I see some familiar faces and some less familiar faces. So that's fantastic. So what I wanted to do is prepare to talk. And within the talk, I have some images, a few videos to look at, and there's also a audience participation component, because that's just how I roll. We have to practice what we're up to. So this segment, this talk, is one that is looking at pedagogy as not simply pedagogical strategies in general but to look more at the ways that I translate this idea of pedagogy through lenses or filters of disruption or of criticality. And so part of the work that I do professionally is prepare teachers of art for K12. But I also work with graduate students as they conduct their research, I also do my own research in scholarly kinds of moves about the ways in which visual imagery, visual art, visual cultural production, functions, as modes or spaces for teaching and learning. Jasper...

PROFESSOR: Hi everyone. Welcome back. So today, I'd like to tackle a problem in undetermined coefficients, specifically find a particular solution to each of the following equations using undetermined coefficients. So for part A, we have x dot plus 3x equals t squared plus t. And for B, we have x dot dot plus x dot equals t to the four. So I'll let you work this problem out. And I'll come back in a minute. Hi Everyone. Welcome back. So we're asked to solve this problem using the method of undetermined coefficients. And specifically, the observation is if we have a differential equation with constant coefficients, and we have a forcing on the right-hand side which is a polynomial, then there's always going to be a particular solution, which is a polynomial, that has the form of some constant times t to the power of r plus constant t^(r-1) plus a constant c_(r-2) t^(r-2) plus dot, dot, dot, plus c_1*t and then possibly plus c_0. And typically, the proble...

[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 reason. Solar engineers work very hard to make their solar cells as efficient as possible. Reflected light is lost energy, so good engineers will want to minimize the total amount of reflected light. To make solar cells absorb as much light as possible, and appear black, solar engineers do two things. First, they grow this very thin film of a dielectric layer on the surface. This layer is aptly called an anti-reflection coating. Second, they texture the wafer. And today we'll demonstrate how texturing is performed, and quantify its enhancement for reducing light reflection. Silicon wafers don't start out black. In fact, they appear gray. Polish...

[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. Without doping, the solar industry would not exist, but even though doping is common today, the effects of impurities confused semiconductor physicists in the 1950s, who had trouble reproducing results. Eventually, they realized that contamination levels, as low as 1 in a billion, were vastly changing the electrical properties of their samples. Today, we'll show you how this works with a very simple experiment. We'll be measuring the electrical conductivity of two silicon slabs using an ohmmeter. One is doped with impurities, phosphorus in our case, and the other is ultra-pure, or what we call intrinsic. Let's go over our experiment. We'l...

PROFESSOR: Hi, everyone. Welcome back. So today, I'd like to talk about positive definite matrices. And specifically, we're going to analyze several properties of positive definite matrices. And specifically, we're going to look at why each one of these following statements is true. So first off, why every positive definite matrix is invertible. Why the only positive definite projection matrix is the identity matrix. If D is a diagonal matrix with positive entries, show that it must also be positive definite. And then lastly, if S is a symmetric matrix where the determinant S is bigger than 0, show why this might not necessarily imply that it's positive definite. So I'll let you think about these for a moment. And I'll come back in a second. Hi, everyone. Welcome back. OK. So let's take a look at part A. So part A is asking why every positive definite matrix is invertible. Well, let's just recall that if A is a matrix and if A is invertible...

PROFESSOR: Hi, everyone. Welcome back. So today, I'd like to talk about positive definite matrices. And specifically, we're going to analyze several properties of positive definite matrices. And specifically, we're going to look at why each one of these following statements is true. So first off, why every positive definite matrix is invertible. Why the only positive definite projection matrix is the identity matrix. If D is a diagonal matrix with positive entries, show that it must also be positive definite. And then lastly, if S is a symmetric matrix where the determinant S is bigger than 0, show why this might not necessarily imply that it's positive definite. So I'll let you think about these for a moment. And I'll come back in a second. Hi, everyone. Welcome back. OK. So let's take a look at part A. So part A is asking why every positive definite matrix is invertible. Well, let's just recall that if A is a matrix and if A is invertible...

STUDENT: Hello, everyone. Today, I'm going to talk about a very important model, analyze the energy band of a crystal, that is the tight binding model. Before I talk about tight binding model, let's now take a look at free electron model. The potential energy of free electron can be considered as zero, so the Hamiltonian of the free electron system is without the potential term. And the waveform function can be simply written as a plane wave. By substituting the wave function into Schrodinger equation, we can gather energy dispersion relation, which is a parabola in one dimension case. And we usually form the parabola into the first Brillouin zone. And this is the reduced Brillouin zone. And in this figure, we can see that the first band is at the bottom of the parabola. And the second band and third band, fourth, and so on. Similar to one dimension case, the energy of three dimension case is proportional to kx squared plus ky squared plus kz squared. For a given ...

MORGAN BINGGELI: Hi, everyone. My name is Morgan Binggeli. I'm a first year masters student at EPFL in material science and engineering, and I'm going to present to you this video about heat transfer in a material. This video start with a little introduction where I will give you some definitions which will be useful for heat transfer, and where I will talk a bit about heat equations. Then I'm going to present to you some concrete examples that you can meet in your everyday life. In order to be able to see the next example in a proper way, we need to give some definitions. In this video we're going to say that heat is a form of energy. The temperature is a measurable manifestation of the stored heat Instabilities in which different temperatures are in contact-- a heat transfer occurs, transferring the heat from the warmer to the colder body. Several heat transfer modes exists. Through heat conduction, which corresponds to the heat exchanged between two poi...

SRINI DEVADAS: Good morning, everyone. Thanks for making it here through the snow and sleet. You will be, quote unquote, rewarded with a cool little puzzle that has both recreational value as well as a deep connection to the most popular sorting algorithm, or at least the most commonly used sorting algorithm, called quicksort. And so what we have up here is what I call the disorganized handyman puzzle. This is not a puzzle of my invention, but I called it this because I think at some point when I read this, it was a carpenter who had a bunch of nuts and bolts in his bag, and they were all mixed up. So rather than having these nuts attached to the bolts, he was disorganized and the nuts and bolts were separate. And then they all got mixed up together in a bag, OK? Now, obviously, all puzzles are a little bit contrived. And so we're going to assume here that there's 100 different nuts and 100 associated bolts. And these 200 objects are all mixed up into this one bag...