Difference equations appear naturally in many fields of science and engineering. This book presents, in a systematic way, some general tools for handling difference equations.

The authors start with the classical Fibonacci sequence (chapter 1). They then proceed with a presentation of both theoretical results and computational techniques for linear difference equations (chapters 2 through 4). Difference equations with nonnegative coefficients are discussed in chapters 5 and 6. Matrix difference equations are discussed in chapter 7. Difference equations over other rings are addressed in chapter 8. Different computational aspects (including the divide-and-conquer algorithm, applications of the Newton method, and the fast Fourier transform) are presented in chapter 9. The last chapter, chapter 10, is devoted to nonlinear difference equations, and discusses local and global stability, convergence issues, and chaotic systems. There are four appendices, where some concepts and results used in the book, which are not directly related to the theory of difference equations, are presented. In nearly every chapter of the book, the authors have added different applications related to the specific theorems and results discussed. Exercises are also included at the end of each chapter and appendix. Several working examples are presented in Appendix A.

The authors have succeeded in preparing a book that is accessible to undergraduate students. Therefore, the book can be used as a textbook in a general course on difference equations. The book will also be useful for many specialists from different fields of science and engineering who have to deal with difference equations in their research work.