Difference Equations with Applications (UMAP)

In this module techniques for solving first and second order linear difference equations are presented along with illustrative applications. The relation between homogeneous and nonhomogeneous equations is discussed and the method of undetermined coefficients for nonhomogeneous equations is illustrated by examples. There are applications to problems in finance, economics, and populations.

Table of Contents:

1. INTRODUCTION

2. FIRST ORDER DIFFERENCE EQUATIONS
2.1 Homogeneous Equations
2.2 Nonhomogeneous Equations
2.3 The Equation xn+1 - bxn = a
2.4 The Method of Undetermined Coefficients

3. SECOND ORDER LINEAR DIFFERENCE EQUATIONS
3.1 Homogeneous Equations
3.2 The Auxiliary Equation
3.3 Nonhomogeneous Equations

4. ANSWERS TO EXERCISES