Analysis II Lecture 15 Part 1 vector fields on manifolds

Автор: Arthur Parzygnat

Загружено: 2018-05-19

Просмотров: 5206

Описание:

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.

Analysis II Lecture 15 Part 1 vector fields on manifolds

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