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.
|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 anintroduction to chaotic dynamics.
This is an analysis course, however the novelty is that the proofs will be presented in a manner which allows for rigorous computer verification.
Using Julia we will apply these new techniques to rigorously extract specific solutions and explore the dynamics of explicit nonlinear systems.
|For a more detailed overview of the philosophy of the course (we will only consider ODEs as opposed to PDEs and FDEs) see|
|and the description of the AMS short course delivered at the National Meeting January 2015|
|To have a sense of the cutting edge work see|