Handbook of Integral Equations
Integral equations are encountered in various fields of science and in numerous applications, including elasticity, plasticity, heat and mass transfer, oscillation theory, fluid dynamics, filtration theory, electrostatics, electrodynamics, biomechanics, game theory, control, queuing theory, electrical engineering, economics, and medicine. Exact (closed-form) solutions of integral equations play an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of natural science. Equations of physics, chemistry, and biology contain functions or parameters obtained from experiments - hence, they are not strictly fixed. Therefore, it is expedient to choose the structure of these functions for more easily analyzing and solving the equation. As a possible selection criterion, one may adopt the requirement that the model integral equation admit a solution in a closed form. Exact solutions can be used to verify the consistency and estimate errors of various numerical, asymptotic, and approximate methods. The first part of Handbook of Integral Equations: o Contains more than 2,100 integral equations and their solutions o Includes many new exact solutions to linear and nonlinear equations o Addresses equations of general form, which depend on arbitrary functions Other equations contain one or more free parameters (the book actually deals with families of integral equations); the reader has the option to fix these parameters. The second part of the book - chapters 7 through 14 - presents exact, approximate analytical, and numerical methods for solving linear and nonlinear integral equations. Apart from the classical methods, the text also describes some new methods. When selecting the material, the authors emphasize practical aspects of the matter, specifically for methods that allow an effective "constructing" of the solution. Each section provides examples of applications to specific equations. Supplements follow the main material, presenting: o Properties of elementary and special functions o Tables of indefinite and definite integrals o Tables of Laplace, Mellin, and other transforms To accommodate different mathematical backgrounds, the authors avoid special terminology, outlining some of the methods in a schematic, simplified manner and offering references to books considering the details of these methods. Handbook of Integral Equations includes chapters, sections, and subsections - numbering equations and formulas separately in each section, arranging the equations in increasing order of complexity, and providing immediate access to the desired equations through an extensive table of contents.
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