The second edition has greatly benefited from a sizable number of comments and suggestions I received from users of the book. I hope that I have corrected all the er rors and misprints in the book. Important revisions were made in Chapters I and 4. In Chapter I, we added two appendices (global stability and periodic solutions). In Chapter 4, we added a section on applications to mathematical biology. Influenced by a friendly and some not so friendly comments about Chapter 8 (previously Chapter 7: Asymptotic Behavior of Difference Equations), I rewrote the chapter with additional material on Birkhoff's theory. Also, due to popular demand, a new chapter (Chapter 9) under the title "Applications to Continued Fractions and Orthogonal Polynomials" has been added. This chapter gives a rather thorough presentation of continued fractions and orthogonal polynomials and their intimate connection to second-order difference equations. Chapter 8 (Oscillation Theory) has now become Chapter 7. Accordingly, the new revised suggestions for using the text are as follows. The diagram on p. viii shows the interdependence of the chapters The book may be used with considerable flexibility. For a one-semester course, one may choose one of the following options: (i) If you want a course that emphasizes stability and control, then you may select Chapters I, 2, 3, and parts of 4, 5, and 6. This is perhaps appropriate for a class populated by mathematics, physics, and engineering majors.
Rezensionen / Stimmen
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)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
8 s/w Abbildungen
XVIII, 429 p. 8 illus.
ISBN-13
978-1-4757-3110-1 (9781475731101)
DOI
10.1007/978-1-4757-3110-1
Schweitzer Klassifikation
1 Dynamics of First-Order Difference Equations.- 2 Linear Difference Equations of Higher Order.- 6 Control Theory.- 8 Asymptotic Behavior of Difference Equations.- 9 Applications to Continued Fractions and Orthogonal Polynomials.- Answers to Selected Problems.- Maple Programs.- Appendix C Classical Orthogonal Polynomials.- Appendix D Identities and Formulas.
