Analysis II Lecture 10 Part 4 statement and example of implicit function theorem
Channel: Arthur Parzygnat
Date: 2018-05-19

The statement of the implicit function theorem is given in its general form. Rather than giving a proof, an explicit example is provided. Note: In the statement of the theorem, I accidentally wrote g(A_1) several times instead of g(B). The domain of g is B so g(A_1) does not make sense: I mean g(B). 

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.