The study of differential equations is an important part of mathematics that involves many topics, both theoretical and practical. The precise subject matter of this course will vary from year to year. In spring 2013 the topics will be nonlinear dynamics and chaos. We will study the dynamics of one- and two-dimensional flows. The focus of the course will be on bifurcation theory: how do solutions of nonlinear differential equations change qualitatively as a control parameter is varied, and how does chaos arise? To illustrate the analysis, we will consider examples from physics, biology, chemistry, and engineering. The course will also cover basic theorems concerning existence and uniqueness of solutions and continuous dependence on parameters. Four class hours per week, one of which will be in the computer lab.
Requisite: MATH 211 or consent of the instructor. Spring semester. Professor Leise.