Math 231: Ordinary differential equations
Instructor: S. Venakides

Topics: Theory for existence, uniqueness, continuation, and
dependence on parameters for solutions of ODE's. Linear systems with
constant or periodic coefficients. Stability of equilibria and periodic
orbits. Qualitative behavior, bifurcations of steady and periodic solutions,
examples of chaos.

Ordinary differential equations (those with unknown functions of one
variable, usually time), or more generally dynamical systems, model many
processes in science and economics. The understanding of their behavior is
one of the strongest links between mathematics and science. Subtleties
include complex large-time behavior and the effect of combining fast and
slow time scales.

This course is aimed at beginning mathematics graduate students. Others are
welcome if they have the background
of a math major, especially linear algebra and real analysis For math grad
students, the subject uses and applies concepts of these subjects.
Qualitative properties and key examples exhibit phenomena which are more
involved for partial differential equations and serve as a step toward
deeper understanding of mathematical physics.