Ordinary Differential Equations

Ordinary Differential Equations, Spring 2021

Instructor: Marcio Gameiro-Fuzeto

This is an introduction to the theory of ordinary differential equations. We will cover the classical results: existence and uniqueness theorems; linear theory including Floquet theory and elementary bifurcations; stable and unstable manifolds; boundary value problems; and a brief introduction to chaotic dynamics. The novelty of the course is that the proofs will be presented in a manner which allows for rigorous computer verification. Using Julia and Matlab we will apply these new techniques to rigorously extract specific solutions and explore the dynamics of explicit nonlinear systems.