MTH 442
Introduction to Difference Equations
Course
Information and Syllabus, Spring 2016
Text: M. R. S. Kulenovic
and Orlando Merino, Discrete Dynamical Systems and
Difference Equations with Mathematica,
Chapman&Hall/CRC Press, 2002. www.amazon.com
Lecture Notes by M. R. S. Kulenovic and O. Merino
Prerequisites: MTH 142, 243
About the Course: This course is an introduction to the basic concepts and
techniques of difference equations for advanced undergraduates and beginning
graduate students. Difference equations appear in situations where the (n + 1)st generation (or
state) of a system depends upon some previous generations (or states). Such
equations also appear naturally as discrete analogues of differential
equations, and as numerical solutions of differential equations that model
various diverse phenomena in biology, ecology, physiology, physics,
engineering, economics, and other areas. In addition to performing mathematical
analysis of difference equations, with the aid of a Computer Algebra System (Mathematica)
you will experiment with difference equations, and discover that such equations
possess fascinating properties with a great amount of structure. Some of these
computer observations may be cast as theorems that you discover and prove!
Topics:
1. Introduction to Difference Equations
2. First order Difference Equations
3. Linear equations with constant coefficients and variable coefficients
4. Stability in both hyperbolic and nonhyperbolic cases, bifurcations
5. Linear theory for two dimensional systems of difference equations,
6. Equilibrium solutions, stability, periodic solutions
7. Period-doubling bifurcation
8. Global dynamics for second order difference equations.
Exams and Grading:
Course grade will be determined based on homework, quizzes, mid-term and final exams, Mathematica projects and the final project.
The exams could be in part of the take home variety.
TWO TESTS: 50 percent
Mathematica
PROJECTS, QUIZZES, AND HOMEWORK: 30 percent
FINAL PROJECT: 20 percent
Computer Requirements
The use of computer algebra systems Mathematica is required. Mathematica worksheets dealing with the different problems in theory will be provided and demonstrated in the class. The textbooks comes with the simulation package Dynamica which will be used for all simulation purposes. No programming is needed.
Instructor: Dr. M. Kulenovic Office: Lippitt 202D
Phone: 874-4436
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: 11-11:50
Place: Bliss 304
Illness Due to Flu
The nation is experiencing widespread influenza-like illness.
If any of us develop flu-like symptoms, we are being advised to stay home until
the fever has subsided for 24 hours. So, if you exhibit such symptoms,
please do not come to class. Notify me at 874-xxxx or xxx@uri.edu
of your status, and we will communicate through the medium we have established for
the class. We will work together to ensure that course instruction and work is
completed for the semester.
The Centers for Disease Control and Prevention have posted simple
methods to avoid transmission of illness. These include: covering your
mouth and nose with tissue when coughing or sneezing; frequent washing or sanitizing
your hands; avoiding touching your eyes, nose, and mouth; and staying home when
you are sick. For more information please view www.cdc.gov/flu or flu.gov .
URI Health Services web page, www.health.uri.edu
, will carry advice and local updates.
Useful links:
1. Difference Equations at URI
2. The Dynamical Systems at Boston University
4. Fractint