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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...

In this case study, we're going to see how we can create a photo illustration of your work. The idea here is to show how a liquid battery works for a final illustration. So first, create photographic bits and pieces and put them all together. Think of it just as if you were drawing the pieces and putting those sketches together. After I met with the researchers for a brainstorming meeting, I got all this material from them, including a diagram that described my idea to create a model of how a liquid battery works. This is the way I imagined the shoot to go. OK first, I would take an optical quality cuvette and would then pour the mercury and the water into the cuvette and somehow suspending with a clamp, a strip of metal foam, which is an important part of the science. And because I was imagining a full container of this material after making the image, I would then crop out the right side-- we don't need to see the clamping device-- and then flip the left side, o...

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 ...

Hi. In this problem, we're going to get a bunch of practice working with multiple random variables together. And so we'll look at joint PDFs, marginal PDFs, conditional PDFs, and also get some practice calculating expectations as well. So the problem gives us a pair of random variables-- x and y. And we're told that the joint distribution is uniformly distributed on this triangle here, with the vertices being 0, 0 1, 0, and 0, 1. So it's uniform in this triangle. And the first part of the problem is just to figure out what exactly is disjoint PDF of the two random variables. So in this case, it's pretty easy to calculate, because we have a uniform distribution. And remember, when you have a uniform distribution, you can just imagine it being a sort of plateau coming out of the board. And it's flat. And so the height of the plateau, in order to calculate it, you just need to figure out what the area of this thing is, of this triangle is. So rememb...

GILBERT STRANG: OK. We're still solving systems of differential equations with a matrix A in them. And now I want to create the exponential. It's just natural to produce e to the A, or e to the A t. The exponential of a matrix. So if we have one equation, small a, then we know the solution is an e to the A t, times the starting value. Now we have n equations with a matrix A and a vector y. And the solution should be, at time t, e to the A t, times the starting value. It should be a perfect match with this one, where this had a number in the exponent and this has a matrix in the exponent. OK. No problem. We just use the series for e to the A t. We plug in a matrix instead of a number. So the identity, plus A t, plus 1/2 A t squared, plus 1/6 of A t cubed, forever. It's the same. It's the exponential series. The most important series in mathematics, I think. And it gives us an answer. And that answer is a matrix. Everything here, every term, is a matrix. OK....

[MUSIC PLAYING] ANNE WHITE: We're hurtling through space on our planet, and we're just bombarded by high-energy particles from the universe all the time. SARAH HANSEN: Today, on Chalk Radio, we're delving into the fascinating world of nuclear physics. I'm Sarah Hansen. For this episode, I sat down with Professor Anne White, physicist and professor in the Department of Nuclear Science and Engineering at MIT. ANNE WHITE: My research is on fusion energy, so I'm a plasma physicist hiding out in an engineering department. SARAH HANSEN: I so enjoyed this conversation with Anne. The information she shared in this interview changed the way I experienced the air around me. I mean, how often can you say that? The topics that she explains are complex, but she makes them so approachable, even showing us that we can learn about nuclear science using objects that we find in our own kitchens. So for this episode, we're going to do something a little differently f...