DIFFERENTIAL EQUATIONS
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
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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