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

**Prerequisites**:
Graduate standing , exposure to basic ordinary differential equations
and
linear algebra; Mth 545 is not a prerequirement

**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:

Invariant manifolds -
center manifold

Normal form theory

Gradient and Hamiltonian systems

The Poincare map

Periodic solutions and Floquet theory

The Stable manifold theorem for periodic orbits

Poincare-Bendixson theory

Structural stability

Bifurcations at nonhyperbolic equilibrium points

Hopf bifurcations

**Computer Requirements**

The use of computer algebra systems such as
MATHEMATICA,
MAPLE, and Scientific Notebook is encouraged. 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**:

**Time**: M,W: 4:30 - 5:45

**Room: **