Analysis II Lecture 15 Part 1 vector fields on manifolds
Channel: Arthur Parzygnat
Date: 2018-05-19

Tangent vector fields on smooth manifolds are defined. A smooth homotopy of smooth functions is defined between manifolds. Examples are given. A smooth homotopy interpolating between diffeomorphisms and which is also a diffeomorphism for all values of the varying parameter is a smooth isotopy.

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.