An Introduction to Difference Equations

✍ Scribed by Saber Elaydi

• Publisher: Springer
• Year: 2005
• Tongue: English
• Leaves: 563
• Series: Undergraduate Texts in Mathematics
• Edition: 3rd
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Cover......Page 1
Preface to the Third Edition......Page 6
Preface to the Second Edition......Page 10
Preface to the First Edition......Page 12
Contents......Page 16
List of Symbols......Page 22
1. Dynamics of First-Order Difference Equations......Page 24
2. Linear Difference Equations of Higher Order......Page 80
3. Systems of Linear Difference Equations......Page 140
4. Stability Theory......Page 196
5. Higher-Order Scalar Difference Equations......Page 268
6. The Z-Transform Method and Volterra Difference Equations......Page 296
7. Oscillation Theory......Page 336
8. Asymptotic Behavior of Difference Equations......Page 358
9. Applications to Continued Fractions and Orthogonal Polynomials......Page 420
10. Control Theory......Page 452
A. Stability of Nonhyperbolic Fixed Points of Maps on the Real Line......Page 500
B. The Vandermonde Matrix......Page 504
C. Stability of Nondifferentiable Maps......Page 506
D. Stable Manifold and the Hartman-Grobman-Cushing Theorems......Page 510
E. The Levin-May Theorem......Page 514
F. Classical Orthogonal Polynomials......Page 522
G. Identities and Formulas......Page 524
Answers and Hints to Selected Problems......Page 526
Maple Programs......Page 540
References......Page 546
Index......Page 554
Back Cover......Page 563