Power Series/Euler's Great Formula | MIT Highlights of Calculus
Power Series/Euler's Great Formula Instructor: Gilbert Strang http://ocw.mit.edu/highlights-of-calculus License: Creative Commons BY-NC-SA More information ...
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GILBERT STRANG: OK, I thought I would talk today about power series. These are powers of x. I'm going to keep going. All powers, all those x to the fourth, x to the fifth, they'll all come in too. And my idea is combine them, add them up to get a function of x. So we're doing calculus, but a new part of it, with these infinite series. So what do I mean by combine them? I mean I'll multiply those powers by some numbers. Let me call those numbers a0. So this first guy will be an a0, and then I'll add on an a1 x. I'm out of x. I'll add on some a2 x squared, some a3 x cubed and onwards. So now I have a function. And that function, let me call it f of x. So here's my starting plan here. Well, we've seen this for e to the x. Let me remember how ...
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GILBERT STRANG: OK, I thought I would talk today about power series. These are powers of x. I'm going to keep going. All powers, all those x to the fourth, x to the fifth, they'll all come in too. And my idea is combine them, add them up to get a function of x. So we're doing calculus, but a new part of it, with these infinite series. So what do I mean by combine them? I mean I'll multiply those powers by some numbers. Let me call those numbers a0. So this first guy will be an a0, and then I'll add on an a1 x. I'm out of x. I'll add on some a2 x squared, some a3 x cubed and onwards. So now I have a function. And that function, let me call it f of x. So here's my starting plan here. Well, we've seen this for e to the x. Let me remember how ...
