North Carolina State University
Department of Mathematics
Fall Semester, 2002

MA532 --- Ordinary Differential Equations I

Text: Differential Equations and Dynamical Systems, 3rd edition,
      by Lawrence Perko

Topics: The general topics of the course in approximate order are as follows:

1. Statement of Existence-uniqueness theorem.
2. Solution of $x' = A x$, including $e^{At}$ and phase portraits. 
3. General theory of $x' = A(t)x + f(t)$. fundamental matrix solutions and
   variation of parameters.
4. Equilibria of $x' = f(x)$, linearization, stability, Hartman's theorem and
   stable manifold theorem
5. Limit sets
6. One and two dimensional autonomous systems, phase portraits
7. Liapunov theory, LaSalle invariant principle.

There will be two tests and one final exam. The grade is determined by:

1. Homework 	30%
2. Tests        40%
3. Final        30%