Analysis II Lecture 18 Part 3 non-autonomous linear ordinary differential equations
Channel: Arthur Parzygnat
Date: 2018-05-19

Non-autonomous linear ODEs can be solved by using the time-ordered exponential of a matrix. This is a generalization of the usual matrix exponential. This is an example of the iterative technique and its existence and uniqueness is a consequence of the contraction mapping theorem. 

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.