An Introduction to Difference Equations

In contemplating the third edition, I have had multiple objectives to achieve. The ?rst and foremost important objective is to maintain the - cessibility and readability of the book to a broad readership with varying mathematical backgrounds and sophistication. More proofs, more graphs, more explanations, and more applications are provided in this edition. The second objective is to update the contents of the book so that the reader stays abreast of new developments in this vital area of mathematics. Recent results on local and global stability of one-dimensional maps are included in Chapters 1, 4, and Appendices A and C. An extension of the Hartman-Grobman Theorem to noninvertible maps is stated in Appendix D. A whole new section on various notions of the asymptoticity of solutions and a recent extension of Perron's Second Theorem are added to Chapter 8. In Appendix E a detailed proof of the Levin-May Theorem is presented. In Chapters 4 and 5, the reader will ?nd the latest results on the larval- pupal-adult ?our beetle model. The third and ?nal objective is to better serve the broad readership of this book by including most, but certainly not all, of the research areas in di?erence equations. As more work is being published in the Journal of Di?erence Equations and Applications and elsewhere, it became apparent that a whole chapter needed to be dedicated to this enterprise. With the prodding and encouragement of Gerry Ladas, the new Chapter 5 was born.

List of contents

Dynamics of First-Order Difference Equations.- Linear Difference Equations of Higher Order.- Systems of Linear Difference Equations.- Stability Theory.- Higher-Order Scalar Difference Equations.- The Z-Transform Method and Volterra Difference Equations.- Oscillation Theory.- Asymptotic Behavior of Difference Equations.- Applications to Continued Fractions and Orthogonal Polynomials.- Control Theory.

Summary

In contemplating the third edition, I have had multiple objectives to achieve. The ?rst and foremost important objective is to maintain the - cessibility and readability of the book to a broad readership with varying mathematical backgrounds and sophistication. More proofs, more graphs, more explanations, and more applications are provided in this edition. The second objective is to update the contents of the book so that the reader stays abreast of new developments in this vital area of mathematics. Recent results on local and global stability of one-dimensional maps are included in Chapters 1, 4, and Appendices A and C. An extension of the Hartman–Grobman Theorem to noninvertible maps is stated in Appendix D. A whole new section on various notions of the asymptoticity of solutions and a recent extension of Perron’s Second Theorem are added to Chapter 8. In Appendix E a detailed proof of the Levin–May Theorem is presented. In Chapters 4 and 5, the reader will ?nd the latest results on the larval– pupal–adult ?our beetle model. The third and ?nal objective is to better serve the broad readership of this book by including most, but certainly not all, of the research areas in di?erence equations. As more work is being published in the Journal of Di?erence Equations and Applications and elsewhere, it became apparent that a whole chapter needed to be dedicated to this enterprise. With the prodding and encouragement of Gerry Ladas, the new Chapter 5 was born.

Additional text

Second Edition

S.N. Elaydi

An Introduction to Difference Equations

"The presentation is clear. The book provides numerous interesting applications in various domains (life science, neural networks, feedback control, trade models, heat transfers, etc.) and well-selected exercises with solutions."—AMERICAN MATHEMATICAL SOCIETY

From the reviews of the third edition:

"This is the third edition of a well-established textbook which gives a solid introduction to difference equations suitable for undergraduate students. It covers most aspects from classical results to modern topics. In comparison to the previous edition, more proofs, more detailed explanations, and more applications were added. … Thanks to the many additions, the book stays recent and valuable resource for students and teachers." (G. Teschl, Internationale Mathematische Nachrichten, Issue 202, 2006)

“This book … introduces the concept of difference equations along with several tools, as well as many example applications. … The book … is very enjoyable and smooth to read. … This is an excellent book to keep. It is very good for undergraduate students … . For fresh graduate students, it is good to read … and to keep for future reference. … The book in general is very well written, well organized, contains tons of examples, exercises (with brief solutions) and various applications.” (Adel El-Atawy, SIGACT News, Vol. 40 (3), 2009)

Report

Second Edition
S.N. Elaydi
An Introduction to Difference Equations
"The presentation is clear. The book provides numerous interesting applications in various domains (life science, neural networks, feedback control, trade models, heat transfers, etc.) and well-selected exercises with solutions."-AMERICAN MATHEMATICAL SOCIETY
From the reviews of the third edition:
"This is the third edition of a well-established textbook which gives a solid introduction to difference equations suitable for undergraduate students. It covers most aspects from classical results to modern topics. In comparison to the previous edition, more proofs, more detailed explanations, and more applications were added. ... Thanks to the many additions, the book stays recent and valuable resource for students and teachers." (G. Teschl, Internationale Mathematische Nachrichten, Issue 202, 2006)
"This book ... introduces the concept of difference equations along with several tools, as well as many example applications. ... The book ... is very enjoyable and smooth to read. ... This is an excellent book to keep. It is very good for undergraduate students ... . For fresh graduate students, it is good to read ... and to keep for future reference. ... The book in general is very well written, well organized, contains tons of examples, exercises (with brief solutions) and various applications." (Adel El-Atawy, SIGACT News, Vol. 40 (3), 2009)

Product details

• Authors: Elaydi, Saber Elaydi
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 26.10.2010
• EAN: 9781441920010
• ISBN: 978-1-4419-2001-0
• No. of pages: 540
• Dimensions: 159 mm x 234 mm x 28 mm
• Weight: 873 g
• Illustrations: XXII, 540 p.
• Series: Undergraduate Texts in Mathematics; Undergraduate Texts in Mathema; Undergraduate Texts in Mathematics; Undergraduate Texts in Mathema
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, A, Mathematics and Statistics, Difference equations, Functional equations, Calculus & mathematical analysis, Difference and Functional Equations, Analysis (Mathematics), Mathematical analysis