Linear Difference Equations with Discrete Transform Methods: 363 (Mathematics and Its Applications) - Softcover

Jerri, A.J. J.

 
9781441947550: Linear Difference Equations with Discrete Transform Methods: 363 (Mathematics and Its Applications)
Softcover
ISBN 10: 1441947558 ISBN 13: 9781441947550
Verlag: Springer, 2010

Inhaltsangabe

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.

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Reseña del editor

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.

Reseña del editor

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. It is lucidly written and carefully motivated with examples from various fields of applications. These examples are presented in the first chapter and then discussed with their detailed solutions in Chapters 2-7. A particular feature is the use of the discrete Fourier transforms for solving difference equations associated with, generally nonhomogeneous, boundary conditions. Emphasis is placed on illustrating this new method by means of applications. The primary goal of the book is to serve as a primer for a first course in linear difference equations but, with the addition of more theory and applications, the book is suitable for more advanced courses. Audience: In addition to students from mathematics and applied fields the book will be of value to academic and industrial researchers who are interested in applications.

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Verlag
Springer
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
1441947558
ISBN 13 
9781441947550
Einband
Tapa blanda
Anzahl der Seiten
468
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Hamburg
Deutschland

Weitere beliebte Ausgaben desselben Titels

9780792339403: Linear Difference Equations with Discrete Transform Methods: 363 (Mathematics and Its Applications)

Vorgestellte Ausgabe

ISBN 10:  0792339401 ISBN 13:  9780792339403
Verlag: Springer, 1996
Hardcover