Analysis II Lecture 08 Part 2 motivation for the inverse function theorem
Channel: Arthur Parzygnat
Date: 2018-05-19

The inverse function theorem states that if the determinant of the differential of a continuously differentiable function at a point is nonzero then the function is locally one-to-one and its inverse is differentiable at the image of that point. An example from analysis I is provided for comparison.

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.