Handbook of Integral Equations

CRC Press, 31 ěŕđ. 1998 ă. - Âńĺăî ńňđŕíčö: 816
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:
• Contains more than 2,100 integral equations and their solutions
• Includes many new exact solutions to linear and nonlinear equations
• 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 applicatio
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Ńîäĺđćŕíčĺ

 Linear Equations of the First Kind With Variable Limit of Integration 3 Equations Whose Kernels Contain Trigonometric Functions 42 Linear Equations of the Second Kind With Variable Limit of Integration 107 Linear Equation of the First Kind With Constant Limits of Integration 197 Linear Equations of the Second Kind With Constant Limits of Integration 247 Nonlinear Equations With Variable Limit of Integration 337 Nonlinear Equations With Constant Limits of Integration 371 Main Definitions and Formulas Integral Transforms 427
 Methods for Solving Singular Integral Equations of the First Kind 597 Methods for Solving Complete Singular Integral Equations 633 Methods for Solving Nonlinear Integral Equations 659 Elementary Functions and Their Properties 679 Tables of Indefinite Integrals 687 Tables of Definite Integrals 703 Supplements Tables of Inverse Laplace Transforms 719 Tables of Fourier Cosine Transforms 733

 Methods for Solving Linear Equations of the Form J Kx tyt dt fx 441 Methods for Solving Linear Equations of the Form Kx tyt dt fx 491 Methods for Solving Linear Equations of the Form yx Kx tyt dt x 527
 Supplements Tables of Mellin Transforms 747 References 779 Ŕâňîđńęčĺ ďđŕâŕ