Wednesday, February 14, 2007

Class summaries: February 14

Calculus III: We talked about the Taylor polynomials associated to a function
f(x) and discussed Taylor's formula: f(x)= Pn(x) + Rn(x), where Rn(x) is an explicitly defined error term. This is amazing since it allows us to use a polynomial (these don't suck, remember) to approximate any function we like, and we can even put a bound on the error associated with doing this. Nice!


Topology: got two-thirds of the way through the proof of Sard's theorem: the set of critical values of a smooth function has measure zero.

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