Math 634: Theory of Ordinary Differential Equations

Catalog Information

Title

Theory of Ordinary Differential Equations.

Credit Hours

3

Prerequisite

Math 316, 334.

Description

This course is designed to provide students with a rigorous treatment of the theory of differential equations.

Desired Learning Outcomes

Minimal learning outcomes

1. Solutions to ordinary differential equations
   • Existence of solutions
   • Uniqueness of solutions
   • Continuation of solutions
   • Gronwall’s inequality
   • Dependence on parameters
   • Contraction mapping principle
2. Linear differential equations
   • Linear systems with constant coefficients
   • Jordan Normal Form
   • Fundamental solutions
   • Variation of constants formula
   • Floquet Theory for periodic solutions
3. Stability and instability
   • Stability and asymptotic stability
   • Lyapunov functions
   • Bifurcations
4. Poincare-Bendixson Theory
   • Invariant sets
   • Omega limit sets
   • Limit cycles

Additional topics

These are at the instructor's discretion as time allows examples are: Stability of nonautonomous equations, Fredholm alternative, normal forms, Hamiltonian dynamics, control theory, stable manifold theorem, and center manifold theorem.

Courses for which this course is prerequisite

Math 635