Difference between revisions of "Math 634: Theory of Ordinary Differential Equations"
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+ | # Solutions to ordinary differential equations | ||
+ | #* Existence of solutions | ||
+ | #* Uniqueness of solutions | ||
+ | #* Continuation of solutions | ||
+ | #* Gronwall’s inequality | ||
+ | #* Dependence on parameters | ||
+ | #* Contraction mapping principle | ||
+ | # Linear differential equations | ||
+ | #* Linear systems with constant coefficients | ||
+ | #* Jordan Normal Form | ||
+ | #* Fundamental solutions | ||
+ | #* Variation of constants formula | ||
+ | #* Floquet Theory for periodic solutions | ||
+ | # Stability and instability | ||
+ | #* Stability and asymptotic stability | ||
+ | #* Lyapunov functions | ||
+ | #* Bifurcations | ||
+ | # Poincare-Bendixson Theory | ||
+ | #* Invariant sets | ||
+ | #* Omega limit sets | ||
+ | #* Limit cycles | ||
=== Additional topics === | === Additional topics === |
Revision as of 16:07, 12 August 2008
Contents
Catalog Information
Title
Theory of Ordinary Differential Equations.
Credit Hours
3
Prerequisite
Description
This course is designed to provide students with a rigorous treatment of the theory of differential equations. The topics include the existence, uniqueness, and continuation of solutions to differential equations, linear differential equations, and stability of solutions for differential equations.
Desired Learning Outcomes
Prerequisites
Minimal learning outcomes
- Solutions to ordinary differential equations
- Existence of solutions
- Uniqueness of solutions
- Continuation of solutions
- Gronwall’s inequality
- Dependence on parameters
- Contraction mapping principle
- Linear differential equations
- Linear systems with constant coefficients
- Jordan Normal Form
- Fundamental solutions
- Variation of constants formula
- Floquet Theory for periodic solutions
- Stability and instability
- Stability and asymptotic stability
- Lyapunov functions
- Bifurcations
- 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