2nd Edition

# Handbook of Integral Equations Second Edition

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.

**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

Index

### Biography

Polyanin Polyanin, Alexander V. Manzhirov

"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