Analysis II Lecture 06 Part 4 continuously differentiable versus differentiable
Channel: Arthur Parzygnat
Date: 2018-05-19

There is a subtle difference between k-times continuously differentiable functions and k-times differentiable functions. Both kinds are defined in this video. An approach useful for functions as manifolds is given in terms of vector fields.

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.