Cornell Math - MATH 717, Spring 2000

MATH 717 — Spring 2000
Applied Dynamical Systems

Nonlinear dynamical systems are used as models in every field of science and engineering. Universal patterns of behavior, including "chaos," have been observed in large sets of examples. Mathematical theories describing geometrically the qualitative behavior of "generic" systems explain many of these patterns. This course will discuss dynamical systems theory and its application to examples. Several representative examples from different disciplines, including the life sciences, will be described at the beginning of the course and used throughout the semester to illustrate theoretical ideas. Emphasis will be placed upon bifurcation, the qualitative changes in solutions that occur as system parameters are varied. Computational methods for the analysis of dynamical systems will also be discussed. Both the performance of algorithms and their mathematical foundations will be considered. Further development of these computational methods is an active research area, and the course lectures will repeatedly deal with this frontier. Computer laboratory sessions will be held in addition to lectures.

Prerequisites:

Good courses in undergraduate analysis, multivariable calculus and linear algebra. Some exposure to ordinary differential equations or dynamical systems will be helpful.

Requirements:

Homework and a student selected project.