Difference Equations An Introduction with Applications

PDF | English | 13MB

This book uses elementary analysis and linear algebra to investigate solutions to difference
equations. The reader likely will have encountered difference equations in
one or more of the following contexts: the approximation of solutions of equations
by Newton's Method, the discretization of differential equations, the computation of
special functions, the counting of elements in a defined set (combinatorics), and the
discrete modeling of economic or biological phenomena. In this book, we give examples
of how difference equations arise in each of these areas, as well as examples
of numerous applications to other subjects.
Our goal is to present an overview of the various facets of difference equations
that can be studied by elementary mathematical methods. We hope to convince the
reader that the subject is a rich one, both interesting and useful. The reader will not
find here a text on numerical analysis (plenty of good ones already exist). Although
much of the contents of this book is closely related to the techniques of numerical
analysis, we have, except in a few places, omitted discussion of computation by
computer.

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