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Now why does this matter? And I'm going to tell you an example of why this matters. I'm talking about delocalization to stabilize. And I'm talking about how the actual structure of a molecule isn't this rigid two bonds here, one bond there, that's not what that says, but it was in ozone. But it's this shared equivalent bonds where the electron is shared and the whole system is lowered. Now, there is one molecule where this is very much important and dictates all of its chemical behavior. And that's benzene. And back in the day, in the 1930s, oh, by the way, Pauling, electronegativity scale. we talked about him on Wednesday. But back in the day, they didn't know what benzene was. They could kind of measure some things. But none of it worked. And Pauling wrote a number of structural formulae have been proposed for benzene, but none of them is free from very serious objections. The way they wrote stuff. Look at these shapes for benzene. If we ...

PROFESSOR: OK, why don't we you get started again? I can understand why there is an air of excitement in the room since tomorrow's a holiday. But we still got two hours before the day is over. Any questions on what we have done up to this point? No, that's good. Let me erase some of this art work then and ask why one would indulge in this rather bizarre exercise of taking the elements of something that represents a physical property and constructing a surface out of them. Well, the name suggests that maybe these surfaces, be they hyperboloids of one or two sheets or imaginary ellipsoids, have something to say about the property that the tensor that formed the coefficient of these functions is doing. So let me take the case of an ellipsoid. That would be the case where all the coefficients are positive. And let's let this be x1 and this x2. And let me ask a first question. If this is to be a well deserved function, does the surface transform in exactly the ...

PROFESSOR: Why don't we get started. Good afternoon-- to stretch the literal meaning of the word considerably. What a miserable day out there. I get to and from the boonies via the commuter rail. And this morning, we sat there for an hour part way in because a tree had fallen across the railroad track. I don't know who went out to do it, but somebody had to get a saw and saw the tree up and take it off the tracks before we could proceed into Boston. Even with that, I was sort of reluctant to get off the train. I saw how it was pouring outside. So I am highly flattered that you decided to trudge through the puddles and show up this afternoon. All right, this is a momentous occasion because we are exactly at this point, halfway through the term. And this is when we are about to change gears from our discussion of symmetry theory and switch over to physical properties of crystals and the way in which symmetry impacts on those properties. What I wanted to do primarily...

[SQUEAKING] [RUSTLING] [CLICKING] PROFESSOR: Why don't we get started. So before going back to talking about more kinds of power electronic circuits, I wanted to spend one lecture talking about heat transfer and how you model and design thermal systems. And this is principles of power electronics, chapter 25. Now, to be clear, you can spend an entire course-- or for that matter, multiple entire courses studying heat transfer and the ways to do that. And clearly, we don't have time to do that here, so what I'm going to attempt to do in this lecture is give you just enough information to be dangerous. In that a lot of the things we need to do as a power electronics designer, let us offset some of the detailed computational or deep analytical modeling onto heat sink designers and other people. And what we need to know is enough information about how to model these things so that we can predict, things like temperature rises and select the kind of correct componen...