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PROFESSOR: We've talked a lot about de Broglie saying that the wavelength is given by h over p. But we have not said much yet about the frequency of the waves. So what is the frequency of those matter waves? So what is the frequency-- frequency-- of the matter waves. So de Broglie did answer that same question. And the answer was obtained by analogy. We have p equal h bar k. And he said, well, just like the wavelength is determined by the momentum, we'll have e equal h bar omega. So the frequency-- so this equation is the one that now completes the story. Omega is equal to e over h bar. Fixes omega in terms of the energy. And we're going to say a few things. In fact, this will be an interesting digression into an important subject about waves that illustrates why this answer makes a lot of sense. And that's, really, all you can do at this moment. This is a postulate of quantum mechanics. That you do this thing, and with this, you get quantum mechanics. So ...

PROFESSOR: Last time, we talked about the representation of linear time-invariant systems through the convolution sum in the discrete-time case and the convolution integral in the continuous-time case. Now, although the derivation was relatively straightforward, in fact, the result is really kind of amazing because what it tells us is that for linear time-invariant systems, if we know the response of the system to a single impulse at t = 0, or in fact, at any other time, then we can determine from that its response to an arbitrary input through the use of convolution. Furthermore, what we'll see as the course develops is that, in fact, the class of linear time-invariant systems is a very rich class. There are lots of systems that have that property. And in addition, there are lots of very interesting things that you can do with linear time-invariant systems. In today's lecture, what I'd like to begin with is focusing on convolution as an algebraic operation. A...

GERALD SCHNEIDER: OK, we talked about spinal reflexes last time. This is class 20, the second session on the motor system. And we're going to continue talking about spinal reflexes. Last time, the slide that I just mentioned is this one. Right here, you can see I had crossed it out. It says lateral horn. It made sense to them that when the spinal cord looks like that, that looks like it's the lateral horn. But this is actually an enlargement, and this is all ventral horn. The lateral horn is a tiny, little protrusion in the gray matter right at that location where I'm putting the cursor. Or it would be there, OK? So these were our slides from last time. And today, we'll talk about the stretch reflex and talk about its function. Then we'll say a little bit about intersegmental organization in the cord and then plasticity in the cord. And I don't if we'll get to descending pathways, but we need to cover that in order to introduce the film that we...

What we've talked about in recombinant DNA so far is how to get a piece of DNA from somewhere and make a whole lot of copies of it. So, instead of working with DNA extracted from my cells, which there's 3 billion different base pairs of sequence, we can find a little stretch of DNA. But simply being able to clone it, it was a long way from him being able to get a lot of a fragment of DNA to be able to figure out what that sequence is. That sequence of that gene is actually from the [zero derma? gene, the gene that's broken and the zero derma pigmentosa variant patience, missing one of these translesion DNA polymerases that can copy over a thymine, thymine, [permadine?], [dymer?], this induced by UV light. So the reason they have that problem with their skin after sunlight is because they are missing a polymerase that can't copy over accurately over this very common lesion caused by DNA damage. But how do you get from having a piece of DNA and having the se...

PROFESSOR: Last time we talked about particle on a circle. Today the whole lecture is going to be developed to solving Schrodinger's equation. This is very important, has lots of applications, and begins to give you the insight that you need to the solutions. So we're going to be solving this equation all through this lecture. And let me remind you what with had with a particle on a circle. The circle is segment 0 to L, with L and 0 identified. More properly we actually think of the whole x-axis with the identification that two points related in this way that differ by L, or therefore for 2L, 3L, are the same point. As a result, we want wave functions that have this periodicity. And that implies the same periodicity for the derivatives as well. We looked at the Schrodinger equation and we proved that the energy of any solution has to be positive or 0. And therefore the differential equation, the Schrodinger differential equation, can be read then as minus k square...

Having talked about the storage resources provided by the Beta ISA, let's design the Beta instructions themselves. This might be a good time to print a copy of the handout called the "Summary of Beta Instruction Formats" so you'll have it for handy reference. The Beta has three types of instructions: compute instructions that perform arithmetic and logic operations on register values, load and store instructions that access values in main memory, and branch instructions that change the value of the program counter. We'll discuss each class of instructions in turn. In the Beta ISA, all the instruction encodings are the same size: each instruction is encoded in 32 bits and hence occupies exactly one 32-bit word in main memory. This instruction encoding leads to simpler control-unit logic for decoding instructions. And computing the next value of the program counter is very simple: for most instructions, the next instruction can be found in the followin...