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!
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
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
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
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