**MTH 545/URI**

**Ordinary
Differential Equations I**

**Course
Information, **

**Fall 2016**

**Text**:
J. Hale and H. Kocak, Dynamics
and Bifurcation, Springer, 1996

Supplementary texts:

L. Perko, Differential
Equations and Dynamical Systems * *
,Springer 2006

Linda Allen, An Introduction to Mathematical Biology, Pearson, 2006

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

**Exams and Grading**:

Course grade will be determined based on homework
(40%) and mid-term exam and final project or final exam (60%). The exams
will be of the take home variety.

The topics that will be covered are:

Existence and Uniqueness theorems

Stability Theory of ODE

Basic topics for delay DE

Oscillation Theory of ODE

The Poincare map

Periodic solutions and Floquet theory

Bifurcations for first and second order ODE

Applications to Mathematical Biology

**Computer Requirements**

The use of computer algebra systems such as *MATHEMATICA *and
Scientific Notebook is encouraged. Some *MATHEMATICA*
notebooks will be provided and
demonstrated in the class. Most of the exams may require the substantial use of *MATHEMATICA*.

Interesting links:

**Instructor**: M. Kulenovic

Office: Lippitt 202D; Ph. 44436

e-mail: mkulenovic@mail.uri.edu

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

**Office hours**: MWF: 11-12 and by appointment.

**Time**: M,W: 5 - 6:15

**Room: **Lippitt
201