**Text**:
L. Perko, Differential Equations and Dynamical Systems * *

**Prerequisites**:
Graduate standing , exposure to basic ordinary differential equations and
linear algebra

**Exams and Grading**:

Course grade will be determined based on homework and
mid-term and final exams. The exams will be of the take home variety.

The topics that will be covered are:

existence and uniqueness theorems

continuous dependence on parameters and initial conditions

oscillation and comparison theorems

elements of stability theory

invariant manifolds

Lyapunov's second method and first integrals

introduction to delay and difference equations

group transformation methods for solving ordinary differential
equations.

**Computer Requirements**

The use of computer algebra systems such as MATHEMATICA,
MAPLE, and Scientific Notebook is encouraged. Some computer lectures in
some of these systems will be presented, and provided. Some MATHEMATICA
and/or MAPLE notebooks will be provided and demonstrated in the class.
Most of the exams may require the substantial use of MAPLE or MATHEMATICA.

**Instructor**: M. Kulenovic

e-mail: kulenm@math.uri.edu

**Online information**: www.math.uri.edu/courses
or www.math.uri.edu/~kulenm

**Office hours**: M, W: 9-10 Th: 1-2, and by appointment.

**Time**: T,Th: 3:30 -4:45

**Room: **