Analysis II Lecture 13 Part 3 familiar theorems for manifolds
Channel: Arthur Parzygnat
Date: 2018-05-19

By using charts, one can prove many familiar theorems about differentiable functions that were true in Euclidean space for manifolds. This includes the chain rule and the inverse function theorem. In addition, the level sets of regular values for differentiable functions between manifolds are still submanifolds.

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.