Handbook of Integral Equations: Second Edition

Summary

Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, Wiener–Hopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. With 300 additional pages, this edition covers much more material than its predecessor.

New to the Second Edition

•          New material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions

•          More than 400 new equations with exact solutions

•          New chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs

•          Additional examples for illustrative purposes

To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity. The book can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations.

Table of Contents

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 of the First Kind with Variable Limit of Integration
Nonlinear Equations of the Second Kind with Variable Limit of Integration
Nonlinear Equations of the First Kind with Constant Limits of Integration
Nonlinear Equations of the Second Kind with Constant Limits of Integration
METHODS FOR SOLVING INTEGRAL EQUATIONS
Main Definitions and Formulas: Integral Transforms
Methods for Solving Linear Equations of the Form ∫^x_a K(x, t)y(t)dt = f(x)
Methods for Solving Linear Equations of the Form y(x) – ∫^x_a K(x, t)y(t)dt = f(x)
Methods for Solving Linear Equations of the Form ∫^x_a K(x, t)y(t)dt = f(x)
Methods for Solving Linear Equations of the Form y(x) – ∫^x_a K(x, t)y(t)dt = f(x)
Methods for Solving Singular Integral Equations of the First Kind
Methods for Solving Complete Singular Integral Equations
Methods for Solving Nonlinear Integral Equations
Methods for Solving Multidimensional Mixed Integral Equations
Application of Integral Equations for the Investigation of Differential Equations


SUPPLEMENTS
Elementary Functions and Their Properties
Finite Sums and Infinite Series
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
Some Notions of Functional Analysis


References
Index

Reviews

"This well-known handbook is now a standard reference. It contains over 2,500 integral equations with solutions, as well as analytical numerical methods for solving linear and non-linear equations . . . the number of equations described in an order of magnitude greater than in any other book available."

– Jürgen Appell, in Zentralblatt Math, 2009