An Introduction to Difference Equations

- Preface

- List of Symbols

- 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

- Answers and Hints to Selected Problems

- Appendix A: Stability of Nonhyperbolic Fixed Points of Maps on the Real Line

- Vandermonde Matrix

- Stability of Nondifferentiable Maps

- Stable Manifold and Hartman-Grobman-Cushing Theorems

- Levin-May Theorem

- Classical Orthogonal Polynomials

- Identities and Formulas

- References

- Index

Second EditionS.N. ElaydiAn 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 SOCIETYFrom 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)