This work combines both analytic and geometric (topological) approaches to studying difference equations. It integrates both classical and modern treatments of the subject, offering material stability, z-transform, discrete control theory and symptotic theory. The book contains a set of applications in a variety of disciplines including neural networks, feedback control, Markov chains, trade models, heat transfer, propagation of plants, and so forth. Each section of the text end with a set of selected exercises.
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)