Open course ware

GILBERT STRANG: I would like you to see the big picture of linear algebra. We're not doing, in this set of videos, a full course on linear algebra. That's already on OpenCourseWare 1806. And now I'm concentrating on differential equations, but you got to see linear algebra this way. And this way means subspaces. And there are four of them in the big picture. And we-- previous video described the column space and the null space. Now, we've got two more, making four. And let me look at this matrix-- it's for subspaces-- and put them into the big picture. So the first space I'll look at is the row space. Now, the row space has these rows-- has the vector 1, 2, 3 and the vector 4, 5, 6, two vectors there, and all their combinations. That's the key idea in linear algebra, linear combinations. So 1, 2, 3 is a vector in three dimensional space. 4, 5, 6 is another one. Now, if I take all their combinations, do you visualize that if I have two vectors, ...

SPEAKER: I'd like to move now to a special announcement and bring back President Susan Hockfield, who will describe the next chapter, I would say, in the unfolding of the OpenCourseWare movement. SUSAN HOCKFIELD: Yes. [CHUCKLES] You don't have to sit here. You may move back to-- [LAUGHTER] Thank you all. That was a great panel. Thank you. Thank you, audience participants also. This is open sourcing of information. You all participate. So I get the great fun of today, which is announcing the next chapter in OpenCourseWare. Now as you have probably gathered of the [INAUDIBLE] today, if you all weren't there at the very beginning, that OpenCourseWare was designed really for university and college faculty and their students. And the idea was to share what we do on this campus with what happens on other campuses. And it has been successful, I would say, probably beyond almost anyone's wildest, wildest dreams, depending on how you count visits to the OpenCourseW...

GERALD SCHNEIDER: OK, I'd like to introduce neuroscience to you by going through a bit of history that I use to describe three kinds of goals that recur in this field since the 19th century-- three different kinds of goals, and then what modern people are doing, sort of a synthesis, the subsystems approach we'll describe in the fourth lecture. But these are the goals, and we're going to start today talking about this one, OK. Number one, coming up with specific narrow circuits which could explain behavior. And if we could do that adequately, we would be able to come up with a machine that would behave just like a person. So I'll talk about how that goal originated with the discovery of the reflex arc, which was not in the 19th century. It was long before, at least the concept of reflexes, discovered a long time ago. That led to a philosophical view called reflexology. I'll explain that to you. I'll talk a little bit about the machines that have ins...

I usually like to start a lecture with something new, but this time I'm going to make an exception, and start with the finishing up on Friday because it involves a little more practice with complex numbers. I think that's what a large number of you are still fairly weak in. So, to briefly remind you, it will be sort of self-contained, but still, it will use complex numbers. And, I think it's a good way to start today. So, remember, the basic problem was to solve something with, where the input was sinusoidal in particular. The k was on both sides, and the input looked like cosine omega t. And, the plan of the solution consisted of transporting the problem to the complex domain. So, you look for a complex solution, and you complexify the right hand side of the equation, as well. So, cosine omega t becomes the real part of this complex function. The reason for doing that, remember, was because it's easier to handle when you solve linear equations. It's m...

I actually would like to take this occasion to praise and thank the TAs. We've been teaching this course for about a dozen years and we've had some really excellent groups of TAs, but this year's crop is really off scale, really outstanding. And we're all very grateful. [APPLAUSE] You know their names. I won't go through them all. But the fact of the matter is these TAs teach this course because they're told to teach the course, and at the same time they're doing all their thesis research, so they end spending about 168 hours a week on various kinds of work. So it's not a natural thing for them to spend an enormous amount of time, as they have been this year, really just off scale extraordinarily good. Here they are, Winston, Susan, Michelle, Sara, Divia, Jim, Sydney, Yasmine and Cha. So thank you all. At the same time, I'd also like to thank Claudette Gardel who runs this thing. This is a l...