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An Introduction to Difference Equations by Saber Elaydi Overview
This book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material on stability, Z-transform, discrete control theory, and asymptotic theory, continued fractions and orthogonal polynomials. Yet the presentation is simple enough for the book to be used by 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, epidemic models and host-parasitoid systems. Each section ends with an extensive and highly selected set of exercises.
An Introduction to Difference Equations by Saber Elaydi Review
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. Unfortunately, among differential and difference equations, students usually only learn about differential equations, although many problems they encounter later can be solved using difference equations. Hence it is very useful for students to study difference equations (or even, dynamic equations, which can accomodate differential and difference equations at the same time), and for such an undergraduate or beginning graduate course, Saber's book can be used as a textbook. It is particularly useful for such a purpose since it contains many exercises and also many programs for the calculator TI-85. Although the first edition did contain several misprints, the second edition has eliminated most of them. Saber's superb writing style makes reading this book very enjoyable.
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