Handbook of Integral Equations

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CRC Press, 31 мар. 1998 г. - Всего страниц: 816
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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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    Содержание

    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
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