**MTH 545/URI**

**Ordinary Differential Equations I**

**Course Information, Fall 2012**

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

Supporting literature:

W.
Kelley and A. Peterson, The
theory of Differential Equations, Classical and Qualitative, Springer, 2010.

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 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

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,W: 1 – 2, F: 11-12 and by appointment.

**Time**: M,W: 3:00PM - 4:15

**Room: **Lippitt Hall room 201