**MTH 545/URI**

**Ordinary
Differential Equations I**

**Course
Information, Fall 2010**

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

Supporting literature:

Carmen Chicone, Ordinary Differential
Equations with Aplications

S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos

**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 exam and final project. The exam 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

group transformation methods for solving
ordinary differential equations

applications to population dynamics

**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,F: 10 – 11, W: 1-2 and by appointment.

**Time**: M,W,F: 2:00PM - 2:50

**Room: **Lippitt Hall room 201