Includes bibliographical references (pages [257]-261) and index.

1. Introduction -- 2. Some elementary methods of solution of singular integral equations -- 3. Riemann-Hilbert problems and their uses in singular integral equations -- 4. Special methods of solution of singular integral equations -- 5. Hypersingular integral equations -- 6. Singular integro-differential equations -- 7. Galerkin method and its application -- 8. Numerical methods -- 9. Some special types of coupled singular integral equations of Carleman type and their solutions.

Integral equations occur in a natural way in the course of obtaining mathematical solutions to mixed boundary value problems of mathematical physics. Of the many possible approaches to the reduction of a given mixed boundary value problem to an integral equation, Green's function technique appears to be the most useful one, and Green's functions involving elliptic operators (e.g., Laplace's equation) in two variables, are known to possess logarithmic singularities. The existence of singularities in the Green's function associated with a given boundary value problem, thus, brings in singularities in the kernels of the resulting integral equations to be analyzed in order to obtain useful solutions of the boundary value problems under consideration. The present book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution and helps in introducing the subject of singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics. -- Provided by publisher.