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Analysis II Lecture 11 Part 1 manifolds

The definition of a diffeomorphism is given together with what a manifold is. Several examples are drawn to provide intuition. 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.