Kelley, Walter G. : University of Oklahoma Norman Campus
Perterson, Allan C. : University of Nebraska - Lincoln
Summary
This book uses elementary analysis and linear algebra to investigate solutions of difference equations. Some
of the techniques
discussed are summation methods, generating functions, z-transforms, theory of linear equations, matrix methods,
stability,
chaos, asymptotic methods, Green's functions, finite Fourier analysis, variational methods, fixed point theorems,
and
connections with differential equations. Applications of difference equations to combinatorics, geometry, epidemiology,
special
functions, economics, population biology, numerical analysis, circuit analysis, differential equations, and other
fields have been
included. Many examples of the theory are given, and there are a large number of exercises, with difficulty ranging
from
elementary calculation to investigation of new ideas or applications. The new edition also includes an appendix
on the use of
computer algebra systems.
NEW TO THIS EDITION
Phase plane analysis for systems of two linear equations
Use of equations of variation to approximate solutions
Fundamental matrices and Floquet theory for periodic systems
LaSalle invariance theorem
Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
Appendix on the use of Mathematica for analyzing difference equaitons
Exponential generating functions
Many new examples and exercises
Table of Contents
Preface
Introduction
The Difference Calculus
Linear Difference Equations
Stability Theory
Asymptotic Methods
The Self-Adjoint Second Order Linear Equation
The Sturm-Liouville Problem
Discrete Calculus of Variations
Boundary Value Problems for Nonlinear Equations
Partial Difference Equations
Appendix
Answers to Selected Problems
References
Index
