Math
848 Class Notes
Note: These are informal notes which are to be
corrected and updatedregularly.
Math 848, Final Examination:
TBA
Prerequisite:
Advanced Calculus, Linear Algebra, Analysis, suggested course to be
taken in advance or concurrently: Math 828
Suggested additional references: J.Hale, Ordinary Differential
Equations, L. Perko, Differential Equations and Dynamical Systems,
P. Hartman, Ordinary Differential Equations
- 1. Introduction
- 2. Linear
Transformations
- 3. General
Properties of Differential Equations
- 4. Existence
Uniqueness Theorem
- 5. Dependence
of Solutions to Differential Equations onParameters
- 6. Dependence
of Solutions to Differential Equations onParameters--Continued
- 7. Autonomous
Differential Equations
- 8. Limit
Sets
- 9. Two
dimensional systems
- 9a
Differential Equations on a Two dimensional Torus
- 9b
Differential Equations on a Two dimensional Torus--alternate
- 10.
Umlaufsatz
- 10a.
Degree of Circle Maps
- 10b. Alternate
version of Umlaufsatz
- 11. Another
index formula
- 11a. Alternate
treatment of Section 11
- 12. Linear
Differential Equations
- 13. Linear
Differential Equations with Constant Coefficients
- 14. Some
examples
- 15. Jordan
Canonical Form
- 16. The
Grobman-Hartman theorems
- 17. Proofs
of the Grobman-Hartman theorems
- 18. Proofs
of the Grobman-Hartman theorems -Continued
- 19. Hyperbolic
Periodic Orbits and Lyapunov Stability
- 20. Hamiltonian
Systems in $R^{2n}$
- 21. Hamiltonian
Systems and Variational Problems
Exercises