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Course Descriptions

16:640:515 - Ordinary Differential Equations

Konstantin Mischaikow

Text:

Ordinary Differential Equations: A Constructive Approach by J.-B. van den Berg, M. Gameiro, J.-P. Lessard, J. Mireles-James, and K. Mischaikow.

Prerequisites:

An undergraduate course on ordinary differential equations, linear algebra, advanced calculus and undergraduate analysis.

Description:

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
http://www.ams.org/notices/201509/rnoti-p1057.pdf
and the description of the AMS short course delivered at the National Meeting January 2015
http://www.ams.org/notices/201509/rnoti-p1106.pdf
To have a sense of the cutting edge work see
http://www.crm.math.ca/crm50/en/activities/2019-activities/topological-and-rigorous-computational-methods-for-high-dimensional-dynamics/


Schedule of Sections:

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530