Handbook of Integral Equations: Second Edition (Handbooks of Mathematical 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.

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.

"The Handbook of Integral Equations: contains over 2,500 linear and nonlinear integral equations and their exact solutions; outlines exact, approximate analytical, and numerical methods for solving integral equations; illustrates the application of the methods with numerous examples; considers equations that arise in elasticity, plasticity, creep, heat and mass transfer, hydrodynamics, chemical engineering, and other areas; can be used as a database of test problems for numerical and approximate methods for solving linear and nonlinear integral equations; and presents more integral equations than any other book currently available" "This Second Edition features: additional material on Volterra, Fredholm, singular, hypersingular, mixed, multidimensional, dual, and nonlinear integral equations, integral transforms, and special functions; methods of integral equations for ODEs and POEs; and over 300 added pages and more than 400 new integral equations with exact solutions."--BOOK JACKET Suitable for engineers and scientists, this title contains over 2,400 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, and the sciences For equations of the form, a x b, where the functions K(x, t) and f(x) are continuous, the right-hand side must satisfy the following conditions: 1. If K(a, a) 0, then we must have f(a) = 0 (for example, the right-hand sides of equations 1.1.1 and 1.2.1 must satisfy this condition).