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ISBN 10: 0634017489
ISBN 13: 9780634017483
Author: David Keif, George Lopez
1. Introduction
* 1.1 Basic Definitions of Integral Equations
* 1.2 Classification of Integral Equations
* 1.2.1 Volterra Integral Equations
* 1.2.2 Fredholm Integral Equations
* 1.2.3 Singular Integral Equations
* 1.3 Occurrence of Singular Integral Equations in various fields
* 1.3.1 Elasticity
* 1.3.2 Fluid Mechanics
* 1.3.3 Electromagnetism
* 1.3.4 Quantum Mechanics
* 1.3.5 Other Engineering and Physics Applications
* 1.4 Weakly Singular Integral Equations (Abel's Problem)
* 1.5 Cauchy Type Singular Integral Equations
* 1.6 Hypersingular Integral Equations
2. Some Elementary Methods of Solution of Singular Integral Equations
* 2.1 Abel Integral Equation and its Generalization
* 2.2 Integral Equations with Logarithmic Type of Singularities
* 2.3 Integral Equations with Cauchy Type Kernels
* 2.4 Applications to Boundary Value Problems in Engineering and Physics
3. Riemann-Hilbert Problems and Their Uses in Singular Integral Equations
* 3.1 Cauchy Principal Value Integrals
* 3.2 Basic Results in Complex Variable Theory
* 3.2.1 Cauchy's Integral Formula
* 3.2.2 Liouville's Theorem
* 3.2.3 Plemelj–Sokhotski Formulas
* 3.2.4 Other Relevant Theorems
* 3.3 Solution of Singular Integral Equations involving Closed Contours
* 3.4 General Riemann-Hilbert Problems
* 3.5 Generalized Abel Integral Equations
* 3.6 Singular Integral Equations with Logarithmic Kernels
* 3.7 Singular Integral Equations with Logarithmic Kernels in Disjoint Intervals
4. Special Methods of Solution of Singular Integral Equations
* 4.1 Integral Equations with Logarithmically Singular Kernels
* 4.2 Integral Equations with Cauchy Type Kernels
* 4.3 Use of Poincaré-Bertrand Formula
* 4.4 Solution of Singular Integral Equations involving Two Intervals
5. Hypersingular Integral Equations
* 5.1 Definitions of Hypersingular Integrals
* 5.2 Occurrence of Hypersingular Integral Equations in different contexts
* 5.3 Solution of Simple Hypersingular Integral Equations
* 5.4 Solution of Hypersingular Integral Equations of the Second Kind
6. Singular Integro-Differential Equations
* 6.1 A Class of Singular Integro-Differential Equations
* 6.2 A Special Type of Singular Integro-Differential Equation
* 6.3 Numerical Solutions for Singular Integro-Differential Equations
* 6.3.1 Polynomial Approximation Methods
* 6.3.2 Bernstein Polynomial Basis
* 6.3.3 Other Numerical Approaches
7. Galerkin Method and its Application
* 7.1 General Principles of the Galerkin Method
* 7.2 Use of Single-Term Galerkin Approximation
* 7.3 Galerkin Method for Singular Integral Equations
8. Numerical Methods for Singular Integral Equations
* 8.1 General Numerical Procedures for Cauchy Singular Integral Equations
* 8.2 Special Numerical Techniques for First Kind Singular Integral Equations with Cauchy Kernel
* 8.3 Numerical Solution of Hypersingular Integral Equations
* 8.3.1 Using Polynomial Expansion
* 8.3.2 Using Bernstein Polynomials
* 8.4 Numerical Solution of Logarithmically Singular Integral Equations
* 8.5 Numerical Solution of Systems of Generalized Abel Integral Equations
9. Some Special Types of Coupled Singular Integral Equations
* 9.1 Carleman Type Singular Integral Equations
* 9.2 Other Coupled Systems
* 9.3 Methods of Solution for Coupled Systems
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Tags: David Keif, George Lopez, Latin, Bass
