Handbook of Integral Equations

Handbook of Integral Equations: Second Edition

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Features

  • Contains over 2,500 linear and nonlinear integral equations and their exact solutions—more than any other book currently available
  • Outlines exact, approximate analytical, and numerical methods for solving integral equations
  • Illustrates the application of the methods with numerous examples
  • Explores equations that arise in elasticity, plasticity, creep, heat and mass transfer, hydrodynamics, chemical engineering, and other areas
  • 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 ∫xa K(x, t)y(t)dt = f(x)
    Methods for Solving Linear Equations of the Form y(x)xa K(x, t)y(t)dt = f(x)
    Methods for Solving Linear Equations of the Form ∫xa K(x, t)y(t)dt = f(x)
    Methods for Solving Linear Equations of the Form y(x)xa 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

    Editorial 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