Analysis II Lecture 05 Part 2 continuously differentiable functions
Channel: Arthur Parzygnat
Date: 2018-05-19

Continuously differentiable functions (aka C1 functions) are functions whose partial derivatives exist and are continuous. Continuously differentiable functions are differentiable, but the converse need not be true.

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.