An Introduction to Difference Equations (Undergraduate Texts in Mathematics) - Hardcover

Elaydi, Saber N.; Elaydi, Saber

Hardcover

ISBN 10: 0387945822 ISBN 13: 9780387945828

Publisher: Springer Verlag, 1996

Synopsis

This book combines both analytic and geometric (topological) approaches to studying difference equations. It integrates both classical and modern treatment of the subject. The book has the most updated and comprehensive material in stability, z-transform, discrete control theory, and asymptotic theory. Yet the presentation is simple enough so that the book can be used for advanced undergraduate and beginning graduate students in mathematics, engineering, science, and economics. Moreover, scientists and engineers who are interested in discrete mathematical models will find it useful as a reference. The book contains a large set of applications in a variety of disciplines including neural networks, feedback control, Markov chains, trade models, heat transfer, propagation of plants, etc. Each section of the book ends with an extensive and highly selected set of exercises.

About this title

From the Back Cover

The book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, along with recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model.

Saber Elaydi is Professor of Mathematics at Trinity University. He is also the author of Discrete Chaos (1999), and the Editor-In-Chief of the Journal of Difference Equations and Applications.

About the Second Edition:

The book is a valuable reference for anyone who models discrete systems. Dynamicists have the long-awaited discrete counterpart to standard textbooks such as Hirsch and Smale ('Differential Equations, Dynamical Systems, and Linear Algebra'). It is so well written and well designed, and the contents are so interesting to me, that I had a difficult time putting it down.

- Shandelle Henson, Journal of Difference Equations and Applications

Among the few introductory texts to difference equations this book is one of the very best ones. It has many features that the other texts don't have, e.g., stability theory, the Z-transform method (including a study of Volterra systems), and asymptotic behavior of solutions of difference equations (including Levinson's lemma) are studied extensively. It also contains very nice examples that primarily arise in applications in a variety of disciplines, including neural networks, feedback control, biology, Markov chains, economics, and heat transfer...

-Martin Bohner, University of Missouri, Rolla

Review

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)

Edition details

• Publisher: Springer Verlag
• Publication date: 1996
• ISBN 10: 0387945822
• ISBN 13: 9780387945828
• Binding: Hardcover
• Language: English
• Number of pages: 389