Handbook of Integral Equations

Integral equations are encountered in various fields of science and in numerous applications, including elasticity, plasticity, heat and mass transfer, oscillation theory, fluid dynamics, filtration theory, electrostatics, electrodynamics, biomechanics, game theory, control, queuing theory, electrical engineering, economics, and medicine.

Exact (closed-form) solutions of integral equations play an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of natural science. Equations of physics, chemistry, and biology contain functions or parameters obtained from experiments - hence, they are not strictly fixed. Therefore, it is expedient to choose the structure of these functions for more easily analyzing and solving the equation. As a possible selection criterion, one may adopt the requirement that the model integral equation admit a solution in a closed form. Exact solutions can be used to verify the consistency and estimate errors of various numerical, asymptotic, and approximate methods.

The first part of Handbook of Integral Equations:

Contains more than 2,100 integral equations and their solutions

Includes many new exact solutions to linear and nonlinear equations

Addresses equations of general form, which depend on arbitrary functions

Other equations contain one or more free parameters (the book actually deals with families of integral equations); the reader has the option to fix these parameters.

The second part of the book - chapters 7 through 14 - presents exact, approximate analytical, and numerical methods for solving linear and nonlinear integral equations. Apart from the classical methods, the text also describes some new methods. When selecting the material, the authors emphasize practical aspects of the matter, specifically for methods that allow an effective "constructing" of the solution. Each section provides examples of applicatio

When compiling this handbook, the author had not just mathematicians in mind, but physicists, engineers, etc. as well. This group in particular will be able to use profitably the extensive first part of the book which collects the solutions of over 2100 integral equation arranged in an intelligible order...the handbook provides a wealth of useful material.
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The number of equations described in this book is of a magnitude greater than in other available books.
--European Mathematical Society