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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....

this week but it's still let's see because it doesn't literally it means how does it go so it's it's general it doesn't matter if i'm talking to one person or more people at a time coming up try to say it oh what is it the festival yeah it could be it could be a party but in this case it's a celebration or a holiday women international women's day oh yeah it's wednesday once so it's celebrated well everywhere around the world it's the international international women's day and it's a day when we honor women and well we try to remind ourselves that we need to make a constant action to keep equality and to be fair in every aspect of life so i think it's really funny because in the us everybody's paying attention to equality but there isn't a big celebration for la festa de la donna well in italy it's different since about 1945 we actually celebrate women's day the conditions of women are worse in i...

PROFESSOR: Continue today. We're still in the spirit of origami. And we're going to do some origami design and foldability again. There are two main topics here on the design side we're going to talk about-- universal hinge patterns, which are the things that make underlying this robot, which I showed in lecture one. You may recall. So it's called a box pleat pattern. It's a square grid with alternating diagonal creases. And the idea with the robot is you're constrained to only-- you have to build the creases ahead of time. You can't say, you can't build one sheet that can fold anywhere at anytime. You want to build a sheet that can fold at any of the crease lines, at the built crease lines whenever you want. And so whereas with something like Origamizer, every design has a completely different crease pattern and it's difficult to control that, here we wanted to make one. It's not exactly a crease pattern, because you're not usi...

GERALD SCHNEIDER: We're still on this first topic, primitive cellular mechanisms. And we'll be on that for the entire session today, talking mainly about secretion in neurons. We started that before, when we talked about excitatory and inhibitory postsynaptic potentials and summation effects. Is action at a synapse always one way? Well, if it's a chemical synapse, the information flows always in one direction. It doesn't mean there's nothing that goes the other direction. There is some communication, but the electrical changes generally are going one direction. There are such things as electrical synapses. They're not very common in the mammalian nervous system, where the action can go in both ways. We talked about Otto Loewi. And remember, he discovered some pretty good evidence for chemical transmission at synapses. He was in the peripheral nervous system, the autonomic nervous system, working with the innervation of the frog heart. And what was ...