Difference Equations, Second Edition: An Introduction with Applications

✍ Scribed by Walter G. Kelley, Allan C. Peterson

• Publisher: Academic Press
• Year: 2000
• Tongue: English
• Leaves: 415
• Edition: 2
• Category: Library

✦ Synopsis

Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.
Phase plane analysis for systems of two linear equations
Use of equations of variation to approximate solutions
Fundamental matrices and Floquet theory for periodic systems
LaSalle invariance theorem
Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
Appendix on the use of Mathematica for analyzing difference equaitons
Exponential generating functions
Many new examples and exercises

✦ Table of Contents

Cover
Title Page
Cpyright Page
Table of Contents
Preface
Chapter 1 Introduction
Chapter 2 The Difference Calculus
Section 2.1 The Difference Operator
Section 2.2 Summation
Section 2.3 Generating Functions and Approximate Summation
Chapter 3 Linear Difference Equations
Section 3.1 First Order Equations
Section 3.2 General Results for Linear Equations
Section 3.3 Solving Linear Equations
Section 3.4 Applications
Section 3.5 Equations with Variable Coefficients
Section 3.6 Nonlinear Equations That Can Be Linearized
Section 3.7 The z-Transform
Chapter 4 Stability Theory
Section 4.1 Initial Value Problems for Linear Systems
Section 4.2 Stability of Linear Systems
Section 4.3 Phase Plane Analysis for Linear Systems
Section 4.4 Fundamental Matrices and Floquet Theory
Section 4.5 Stability of Nonlinear Systems
Section 4.6 Chaotic Behavior
Chapter 5 Asymptotic Methods
Section 5.1 Introduction
Section 5.2 Asymptotic Analysis of Sums
Section 5.3 Linear Equations
Section 5.4 Nonlinear Equations
Chapter 6 The Self-Adjoint Second Order Linear Equation
Section 6.1 Introduction
Section 6.2 Sturmian Theory
Section 6.3 Green's Functions
Section 6.4 Disconjugacy
Section 6.5 The Riccati Equation
Section 6.6 Oscillation
Chapter 7 The Sturm-Liouville Problem
Section 7.1 Introduction
Section 7.2 Finite Fourier Analysis
Section 7.3 Nonhomogeneous Problem
Chapter 8 Discrete Calculus of Variations
Section 8.1 Introduction
Section 8.2 Necessary Conditions
Section 8.3 Sufficient Conditions and Disconjugacy
Chapter 9 Boundary Value Problems for Nonlinear Equations
Section 9.1 Introduction
Section 9.2 The Lipschitz Case
Section 9.3 Existence of Solutions
Section 9.4 Boundary Value Problems for Differential Equations
Chapter 10 Partial Difference Equations
Section 10.1 Discretization of Partial Differential Equations
Section 10.2 Solutions of Partial Difference Equations
Appendix
Answers to Selected Problems
References
Index