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**About this book :- **
**Linear Difference Equations with Discrete Transform Methods** written by
** Abdul J. Jerri **.

This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solving, 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 intended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the direct 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 methods 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 solving ordinary difference equations. The treatment closely parallels what many students have already learned about using the operational (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 methods, 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 easily to solve partial difference equations associated with initial and/or boundary value problems.

Difference equations are often used to model "an approximation of differential equations, an approach which underlies the development of many numerical methods. However, there are many situaxvtions, for example, recurrence relations and the modeling of discrete processes such as traffic flow with finite number of entrances and exits in which difference equations arise naturally, as we shall illustrate

(Abdul J. Jerri)

**Book Detail :- **
** Title: ** Linear Difference Equations with Discrete Transform Methods
** Edition: **
** Author(s): ** Abdul J. Jerri
** Publisher: ** Springer US
** Series: ** Mathematics and Its Applications 363
** Year: ** 1996
** Pages: ** 455
** Type: ** PDF
** Language: ** English
** ISBN: ** 978-1-4419-4755-0,978-1-4757-5657-9
** Country: ** US
**Download Similar Books from Amazon **

**About Author :- **

The author **Abdul Jabbar Hassoon Jerri** is an Iraqi American mathematician, most recognized for his contributions to Shannon Sampling Theory, It's Generalizations, Error Analysis, and Historical Reviews, and in particular his establishment in 2002 of the journal Sampling Theory in Signal and Image Processing (STSIP-ISSN 1530-6429) with over thirty top international experts as its editors, besides establishing its Sampling Publishing, also his contribution to the general understanding of the Gibbs Phenomenon, where he wrote the first book ever on the subject, published by Springer - Verlag, then he followed it by editing another book on Advances in Gibbs Phenomenon published by Sampling Publishing.

Abdul Jerri earned a B.Sc. in Physics with honors at the University of Baghdad (1955) and M.S. in Physics from Illinois Institute of Technology (1960) in Chicago where he continued to work within the research group (1960–63) in Reactor Physics and Radiation streaming in Shelter Entrance ways. He also earned a Ph.D. in Mathematics from Oregon State University in 1967 with the dissertation title On Extensions of the Generalized Sampling Theorem.

Abdul Jerri commenced his tenure with the faculty of the Department of Mathematics and Computer Science at Clarkson University in Potsdam, NY (1967), where he worked from 1967 until his retirement as Professor Emeritus in 2002.

Abdul Jerri's career includes visiting positions at the American University in Cairo, where he established the Study Programs in Mathematics and Computer Science (1972–74). He was also the Director of the Graduate Mathematics Study Program at Kuwait University (1978–80).

He is the author of several other popular books: Introduction to Integral Equations with Applications, accompanied by a Students Solution Manual: Sampling Publishing,Introduction to Wavelets accompanied by a Students Solution Manual( The latter Manual was co-authored with Prof Masaru Kamada); Sampling Publishing. Other books include Integral and Discrete Transforms with Applications and Error Analysis: Marcel Dekker, and Linear Difference Equations with Discrete Transform Methods:Sp ringer-Verlag.

He had published over forty papers, with numerous lectures on his areas of research interest nationally and internationally. Jerri's main research interests include the areas of Integral and Discrete Transforms, Sampling Expansion and its Applications,History and Error Analysis, the Gibbs Phenomenon, Transform-Iterative Methods for Nonlinear Problems, and Operational Sum Methods for Difference Equations.

In his first workshop, he introduced the subject of Shannon Sampling Theory in four-one hour lectures. In 1997 workshop in Aveiro, Portugal, the Proceedings of the workshop was dedicated to jerri 65th birthday. Presently, he is working on writing a Tutorial review paper on the subject "Multidimensional sampling in Signal Processing. He is dedicating this paper for the occasion of the CENTENNIAL of the American Scientist of the century, the father of Information Theory, Claude Elwood Shannon.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions, solution manuals or solved notes avaliable of this author, We recomended you to download all.

** • Read Online Introduction to Integral Equations with Applications by Abdul Jerri **

** • Download PDF Integral & Discrete Transforms with Applications & Error Analysis by Abdul Jerri **

** • Download PDF Linear Difference Equations with Discrete Transform Methods by Abdul J. Jerri **

** • Download PDF The Gibbs Phenomenon in Fourier Analysis, Splines & Wavelet Approximations by Abdul J. Jerri **

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**Book Contents :- **
**Linear Difference Equations with Discrete Transform Methods ** written by
** Abdul J. Jerri **
cover the following topics.

PREFACE

Acknowledgements

COURSE ADOPTION

1. SEQUENCES AND DIFFERENCE OPERATORS

2. SUM CALCULUS AND THE DISCRETE TRANSFORMS METHODS

3. BASIC METHODS OF SOLVING LINEAR DIFFERENCE EQUATIONS

4. DISCRETE FOURIER TRANSFORMS

5. THE DISCRETE SINE (DST) AND COSINE (DCT) TRANSFORMS FOR BOUNDARY VALUE PROBLEMS

6. THE z-TRANSFORM FOR INITIAL VALUE PROBLEMS

7. MODELING WITH DIFFERENCE EQUATIONS

REFERENCES

ANSWERS TO EXERCISES

INDEX OF NOTATIONS

SUBJECT INDEX

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