Open course ware

Mujtaba: Today, we're going to learn about Ohm's Law. Mujtaba: I'm curious how many of you have heard of or know about Ohm's Law? Student: I know. Student: I do. Student: I've yeah, yeah. I've heard about it. Yeah. Mujtaba: So the simplest way it is represented is V equals IR. That is, the voltage drop, or the potential drop across a resistor in this case is just the current that passes through the resistor times its current. So if we were to draw a resistor right here with a value R, and this is the current, then the voltage drop across this resistor, this V is equal to the current times that resistor value that the resistor has so the resistance value of the resistor and the current path that passes through it. Current is the flow of electrons and V is the potential. So think of it as a force essentially, that allows or enables these electrons to move from an area of higher potential to low lower potential. So if you guys have drunk boba bubble t...

This week we're going to take a look at exactly what you DO with the photographs after you've made them. And, once again, frankly we could devote a full six week course to just this idea alone--presenting your work. But we'll try to cover this topic as best we can in just a couple of tutorials for you for this week. So let's start with a few figures just to dissect them and get you to think more about how you create figures with your images. Let's first take a look at a figure that the researchers made for a grant submission. And here we see a host of the pieces of devices, and the full devices, all labeled. They wanted to show what they were capable of creating--of course which is important. But there's so much going on, the question is whether we want to bother looking anywhere. By the way, just a note, I didn't make any of these images of the research, but I knew that a few of the original images were in color. So first of all, why not use t...

We're going to take a look at how point of view and composition are very clearly connected. But, before we show the connections, we have to sort of define, visually define, what I mean by point of view, for example. So, take a look at these four images. Now, it doesn't look it, but these images are of the identical sample, just simply taken with four different points of view. There, it's true that I also changed the background on them, but, generally, what I did was I moved the sample around or the camera, and we get four really completely different-looking visual ideas of what this stuff was about. Which one is right, I'm not sure there is a right in any of this. That's one of the fun things about this kind of work: There are no hard, fast rules that we have to follow. But I wanted, to give you, this example to show you that just by simply changing the angle or-of your camera, or moving your material around, you see different things. Again, we're ...

STUDENT: Today we're going to look at Hooke's Law in Cubic Solids. Hooke's law describes behavior of springs. What we're going to do is we're going to model the solid as a collection of springs connecting a whole bunch of atoms in a cubic lattice. Now, disclaimer-- I'm probably going to do this all wrong. But what's science if we don't make a few mistakes, right? Let's get started. The potential that describes fairly well the behavior of the interaction between two atoms is the Lennard-Jones potential. It describes the van der Waals interaction, and it looks something like this. It's a potential with a term which goes 1 over r to the 12th, and one term which goes 1 over r to the 6th. And as you can see, as the atoms get very close, they repel greatly, and then they have a sweet spot here, which is the distance they prefer to be at. As they get farther away, they start to repel more again. The atom like to sit right there in that lit...

PROFESSOR: OK. Finally, I'm going to solve this first order linear differential equation with a formula that works for any source term. So we've solved it for specific, nice, special source terms I'll remember later. But now we want a formula for the solution to that equation, period. And we want to understand the formula. So now, write the formula down, and then let's see why it's right. And then of course, we could put it into the equation and confirm that it's right. OK the formula is going to be-- this is the big formula you could say, for first order linear equations. So y of t. First we have the result of the amount-- I'm thinking of this as balance. The money in the bank is why it's increasing at this rate, because of interest being added. And it's increasing at this rate because of new deposits being added. And oh, maybe I should say about those deposits, I'm not thinking of like deposit once a year, or once a month, or once...

In this video, we're going to take a look at how the social contract issues have been addressed around the world. It turns out there's quite a bit of experience with this, sometimes with success for a limited period of time and sometimes without as much success. So let's see how other countries address these issues. Let's start with Australia. Australia has a long history. In the 1980s, a new prime minister came along by the name of Bob Hawke. And he came into office negotiating a new labor agreement called the accord, with the labor movement, where he was saying to labor, if you limit your wage increases to the price increases that are happening in the country, we will then find some offsetting things that we can do in social welfare. So they negotiated a national health insurance. They negotiated a national pension program. They put in place a variety of other worker adjustment programs. And for business, they allowed over time much more flexibility in p...

PROFESSOR: So today we're going to take a look at sinusoidal functions. And specifically, we're going to use complex numbers to get a handle on sinusoidal functions. The reason is complex numbers provide a robust way of analyzing sinusoidal functions. So specifically, we're interested in this function, e to the i*omega*t divided by 2 plus 3i. And we're asked to write the real part of this function using polar form and then rectangular form. And then secondly, we're asked several properties of this function, the real part of this function. What's the circular frequency? What's the amplitude? And what's the phase lag? And then lastly, we're asked to sketch the real part of this function versus time. So I'll let you take a look at this and try it for yourself. And I'll come back in a moment. Hi everyone. Welcome back. OK. So let's take a look at this problem. So we're asked to write e to i*omega*t divided by 2 plus 3i. We...

SRINI DEVADAS: We're going to do something quite different in terms of a puzzle. And while it's a recursive puzzle, it's going to play out to be a recursive solution. It looks quite different from the N-queens puzzle. And so this is going to be a tiling puzzle. And so I set up the puzzle, and then we're going to take a little segue off into a canonical recursive algorithm called merge sort because I think it's good for you to see that algorithm before you dive into solving this particular puzzle because it kind of shows you the way. All right, and but I'll set up the puzzle. I guess I didn't have to erase this square. It's a courtyard that has a bunch-- of tiles. You're supposed to tile it, and it's all square tiles. And I'll just make it eight by eight like a chessboard. And in general, we are going to say that this is a 2 raised to n by 2 raised to n courtyard. And I want to tile this courtyard. So this is a three tile-- some ...

PROFESSOR: Resume by going back to our one-dimensional body that has undergone some elastic deformation. And what I would like to do now is to distinguish between displacement of an object and fractional change of length, which turned out to be measured by the same thing, that thing that we're going to name strain when properly defined. OK, here is our one-dimensional case. And we said that originally some point, P, at a location x gets mapped to a point P prime that is at x plus some displacement U. So this is the displacement vector U. Our point Q, which is originally at some location x plus delta x, where delta x is the original separation between P and Q, gets mapped to a point Q prime, which is going to be equal to a whole collection of terms. It's going to be equal to x plus delta x, the original location, plus the linear variation of U with x that has to go U times x plus delta x. And if we simplify this a little bit, Q prime is going to be at a location, f...