Analysis II Lecture 11 Part 2 alternative definition of manifold and non-examples
Channel: Arthur Parzygnat
Date: 2018-05-19

An alternative (seemingly weaker) definition of a differentiable/C^r manifold is given. With this definition, it is easier to see why certain subsets of Euclidean space fail to be manifolds. 

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.