Handbook of integral equations

Description

"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.  Read more... Abstract: 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.  Read more... Content: 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 a form -- 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 Laplance 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.