Handbook of Integral Equations

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 ∫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 EquationsSUPPLEMENTS 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 AnalysisReferences Index