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