The course is a self contained introduction to ordinary differential equations at the graduate level.
Topics include:
- Existence, uniqueness, and continuous dependence of solutions on parameters.
- Linear theory of differential equations.
- Stability, Lyapunov functions, invariant manifolds, local hyperbolic theory.
- Periodic orbits, Poincare-Bendixon theory.
- Normal forms, averaging method. Applications to bifurcations.
- Homoclinic orbits, Melnikov method, chaotic solutions.
Not offered in 2016-2017
credits:
3 (N-A)
semester:
Irregular
prereqs:
Linear Algebra and Real Analysis (Math 521 and 522) and basic knowledge of Ordinary Differential Equations (Math 319 or 320).