**MTH 542/URI**

**Global Character of Difference Equations I**

**Course Information, Fall 2014**

**Text**:
M. R. S. Kulenovic and O. Merino, Advanced Topics in
Difference Equations (manuscript in progress) and handouts * *

Supporting literature:

M. R. S. Kulenovic and O. Merino, *Discrete
Dynamical Systems and Difference Equations with
Mathematica, *

Chapman&Hall/CRC Press, 2002.

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

**Prerequisites**:
Graduate standing , exposure to advanced calculus and
linear algebra.

**Exams and Grading**:

Course grade will be determined based on
homework (40%) and mid-term exam (40%) and final project (20%).

The topics that will be covered are:

elements of stability theory

invariant manifolds

global attractivity results

fixed point theorems

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. Comprehensive *MATHEMATICA* packages will be provided through SAKAI.

**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: 11-12, 3-4, W: 11 - 12** **and by appointment.

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

**Room: **Lippitt Hall room 201