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:
EXACT SOLUTIONS OF INTEGRAL EQUATIONS
Linear Equations of the First Kind with Variable Limit of Integration
Linear Equations of the Second Kind with Variable Limit of Integration
Linear Equations of the First Kind with Constant Limits of Integration
Linear Equations of the Second Kind with Constant Limits of Integration
Nonlinear Equations with Variable Limit of Integration
Nonlinear Equations with Constant Limits of Integration
METHODS FOR SOLVING INTEGRAL EQUATIONS
Main Definitions and Formulas. Integral Transforms
Methods for Solving Linear Equations of the Form (note: insert scanned forumula 8)
Methods for Solving Linear Equations of the Form (note: insert scanned forumula 9)
Methods for Solving Linear Equations of the Form (note: insert scanned formula 10)
Methods for Solving Linear Equations of the Form (note: insert scanned forumula 11)
Methods for Solving Singular Integral Equations of the First Kind
Methods for Solving Complete Singular Integral Equations
Methods for Solving Nonlinear Integral Equations
Elementary Functions and Their Properties
Tables of Indefinite Integrals
Tables of Definite Integrals
Tables of Laplace Transforms
Tables of Inverse Laplace Transforms
Tables of Fourier Cosine Transforms
Tables of Fourier Sine Transforms
Tables of Mellin Transforms
Tables of Inverse Mellin Transforms
Special Functions and Their Properties
"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."
-Buchbesprechungen - Book Reviews
"The number of equations described in this book is of a magnitude greater than in other available books."
--European Mathematical Society