Analysis II Lecture 12 Part 4 Hadamard's Lemma
Channel: Arthur Parzygnat
Date: 2018-05-19

Hadamard's Lemma expands a differentiable function in terms of its value at a point plus a linear combination of functions satisfying certain convenient conditions. This Lemma is incredibly useful in many contexts. For instance, it is used to prove the one-to-one correspondence between derivations and vectors.

This is part of a series of lectures on Mathematical Analysis II. Topics covered include continuous and differentiable multi-variable functions on Euclidean space, the chain rule, the implicit function theorem, manifolds, tangent spaces, vector fields, the degree and index of a smooth map, the Euler characteristic, metric spaces, the contraction mapping theorem, existence and uniqueness of solutions to ordinary differential equations, and integral equations.

I speak rather slowly, so you may wish to increase the speed of this video.

These videos were created during the 2017 Spring semester at the UConn CETL Lightboard Room.