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The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.

Preface**Introduction**Basic Definitions

Occurrence of singular integral equations

**Some Elementary Methods of Solution of Singular Integral Equations**

Abel integral equation and its generalization

Integral equations with logarithmic type of singularities

Integral equations with Cauchy type kernels

Application to boundary value problems in elasticity and fluid mechanics

**Riemann-Hilbert Problems and Their Uses in Singular Integral Equations**

Cauchy principal value integrals

Some basic results in complex variable theory

Solution of singular integral equations involving closed contours

Riemann Hilbert problems

Generalised Abel integral equations

Singular integral equations with logarithmic kernels

Singular integral equation with logarithmic kernel in disjoint intervals

**Special Methods of Solution of Singular Integral Equations**

Integral equations with logarithmically singular kernels

Integral equations with Cauchy type kernels

Use of Poincareâ€™-Bertrand formula

Solution of singular integral equation involving two intervals

**Hypersingular Integral Equations**

Definitions

Occurrence of hypersingular integral equations

Solution of simple hypersingular integral equation

Solution of hypersingular integral equation of the second kind

**Singular Integro-differential Equations**

A class of singular integro-differential equations

A special type of singular integro-differential equation

Numerical solution of a special singular integro-differential equation

Approximate method based on polynomial approximation

Approximate method based on Bernstein polynomial basis

**Galerkin Method and its Application**

Galerkin method

Use of single-term Galerkin approximation

Galerkin method for singular integral equations

**Numerical Methods**

The general numerical procedure for Cauchy singular integral equation

A special numerical technique to solve singular integrals equations of first kind with Cauchy kernel

Numerical solution of hypersingular integral equation using simple polynomial expansion

Numerical solution of simple hypersingular integral equation using Bernstein polynomials as basis

Numerical solution of some classes of logarithmically singular integral equations using Bernstein polynomials

Numerical solution of an integral equation of some special type

Numerical solution of a system of generalized Abel integral equations

**Some Special Types of Coupled Singular Integral Equations of Carleman Type and their Solutions**

The Carleman singular integral equation

Solution of the coupled integral equations for large

*l*

Solution of the coupled integral equations for any

*l*

*Bibliography*

*Subject index*

### Biography

Mandal\, B. N.; Chakrabarti\, A.