This is an introduction to the theory of ordinary differential equations. We will cover classical results including: existence and uniqueness theorems; linear theory, 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.
Ordinary Differential Equations: A Constructive Approach by J.-B. van den Berg, M. Gameiro, J.-P. Lessard, J. Mireles-James, and K. Mischaikow.
An undergraduate course on ordinary differential equations, linear algebra, advanced calculus and undergraduate analysis.