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.|
|The novelty of the course is that the proofs will be presented in a manner which allows one to apply the results to specific systems of ODEs and obtain rigorous computer verification of the theorems.|
|This is not numerical analysis course, however, we will use Julia and Matlab to demonstrate these new techniques and to 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|