# Linear Difference Equations with Discrete Transform Methods

• Abdul J. Jerri
Book

Part of the Mathematics and Its Applications book series (MAIA, volume 363)

1. Front Matter
Pages i-xxi
2. Abdul J. Jerri
Pages 1-40
3. Abdul J. Jerri
Pages 41-137
4. Abdul J. Jerri
Pages 139-280
5. Abdul J. Jerri
Pages 281-328
6. Abdul J. Jerri
Pages 329-353
7. Abdul J. Jerri
Pages 355-383
8. Abdul J. Jerri
Pages 385-404
9. Back Matter
Pages 405-442

### Introduction

This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv­ ing, primarily, ordinary linear difference equations. Examples from various fields are presented clearly in the first chapter, then discussed along with their detailed solutions in Chapters 2-7. The book is in­ tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the di­ rect use of the discrete Fourier transforms for solving boundary value problems associated with difference equations represents an added new feature compared to other existing books on the subject at this introductory level. This means that in addition to the familiar meth­ ods of solving difference equations that are covered in Chapter 3, this book emphasizes the use of discrete transforms. It is an attempt to introduce the methods and mechanics of discrete transforms for solv­ ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the opera­ tional (integral) calculus of Laplace and Fourier transforms to solve differential equations. As in the continuous case, discrete operational methods may not solve problems that are intractable by other meth­ ods, but they can facilitate the solution of a large class of discrete initial and boundary value problems. Such operational methods, or what we shall term "operational sum calculus," may be extended eas­ ily to solve partial difference equations associated with initial and/or boundary value problems.

### Keywords

Boundary value problem Fourier transform calculus difference equation discrete Fourier transform modeling operator

#### Authors and affiliations

• Abdul J. Jerri
• 1
1. 1.Clarkson UniversityUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-5657-9
• Copyright Information Springer-Verlag US 1996
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-1-4419-4755-0
• Online ISBN 978-1-4757-5657-9
• Buy this book on publisher's site