Undergraduate Texts in Mathematics

An Introduction to Difference Equations

Authors: Elaydi, Saber N.

  • A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics
  • Contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations
  • Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems
  • Includes chapters on continued fractions, orthogonal polynomials and asymptotics
  • Lucid and transparent writing style
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eBook $69.99
price for USA (gross)
  • ISBN 978-1-4757-3110-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
About this Textbook

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.

Reviews

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)


Table of contents (9 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4757-3110-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Difference Equations
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
1999
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-3110-1
DOI
10.1007/978-1-4757-3110-1
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XVIII, 429
Number of Illustrations and Tables
8 b/w illustrations
Topics