Introduction to integral equations with applications

목차 (Table of Contents)

• CONTENTS
• 1. Integral Equations, Their Origin and Classification = 1
• 1.1 Examples of Problems as Integral Equations = 2
• 1.2 Classification of Integral Equations = 15
• 1.3 Some Important Identities = 19
• 1.4 Laplace, Fourier, and Other Transforms = 25
• 1.5 Basic Numerical Integration Formulas = 38
• 2. Modeling of Problems as Integral Equations = 42
• 2.1 Population Dynamics = 43
• 2.2 Control Problems = 50
• 2.3 Mechanics Problems = 52
• 2.4 Initial Value Problems Reduced to Volterra Integral Equations = 60
• 2.5 Boundary Value Problems Reduced to Fredholm Integral Equations = 62
• 2.6 Mixed Boundary Conditions: Dual Integral Equations = 68
• 3. Volterra Integral Equations = 73
• 3.1 Volterra Integral Equations of the Second Kind = 74
• 3.2 Volterra Integral Equations of the First Kind = 82
• 3.3 Numerical Solution of Volterra Integral Equations = 87
• 4. The Green's Function = 95
• 4.1 Nonhomogeneous Ordinary Differential Equations = 96
• 4.2 Fredholm Integral Equations and the Green's Function = 117
• 5. Fredholm Integral Equations = 122
• 5.1 Fredholm Integral Equations with Degenerate Kernel = 124
• 5.2 Fredholm Integral Equations with Symmetric Kernel = 137
• 5.3 Fredholm Integral Equations of the Second Kind = 153
• 5.4 Numerical Solutions of Fredholm Integral Equations = 171
• 6. Existence of the Solutions: Basic Fixed Point Theorems = 182
• 6.1 Preliminaries: Toward a Contractive Mapping = 182
• 6.2 Fixed Point Theorem of Banach = 197
• APPENDIX A: Fourier and Hankel Transforms = 209
• A.1 Higher-Dimensional Fourier Exponential Transform = 209
• A.2 Fourier Sine Transform = 209
• A.3 Fourier Cosine Transform = 210
• A.4 Finite Fourier Sine and Cosine Transforms = 212
• A.5 Hankel Transform = 215
• A.6 Finite Hankel Transform = 216
• APPENDIX B: Some Homogeneous Boundary Value Problems, Their Integral Representation, the Green's Function, and Classical Solutions = 219
• APPENDIX C: The Green's Function and Partial Differential Equations = 223
• APPENDIX D: Solution of Equation (6.32) = 226
• Bibliography = 229
• Answers to Exercises = 232
• Index = 249