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