In contemplating the third edition, I have had multiple objectives to achieve. 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.

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.

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

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)

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 Includes supplementary material: sn.pub/extras Request lecturer material: sn.pub/lecturer-material

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