**MTH 545/URI**

**Ordinary
Differential Equations I**

**Course
Information, **

**Spring 2019**

**Text**:
F. Verhulst, Nonlinear
Differential Equations and Dynamical Systems, Springer, 2006

Supplementary texts:

J. Hale and H. Kocak,
Dynamics
and Bifurcation, Springer, 1996

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

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**: TuWTh: 11-12 and by appointment.

**Time**: TTh: 2 - 3:15

**Room: **Lippitt
201