Analysis II Lecture 07 Part 2 dynamical systems
Channel: Arthur Parzygnat
Date: 2018-05-19

A linear n-th order ordinary differential equation (ODE) is turned into a linear system of n 1st order differential equations in terms of vector fields. There is a typo at the beginning on the second line as there should be no ``=0'' for the ODE. Hamiltonian systems from classical physics provide many examples including a hanging pendulum.

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.