Analysis II Lecture 06 Part 1 The derivative functor
Channel: Arthur Parzygnat
Date: 19/05/2018

The differential can be defined for any point in the domain of a differentiable function. Instead of applying the differential to a fixed vector at all points, it is natural to apply it to a varying vector field to obtain a new function. The partial derivatives are special cases.

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.