Handbook of Integral Equations: Second Edition

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CRC Press, 12 февр. 2008 г. - Всего страниц: 1144
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.

 

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Содержание

Linear Equations of the First Kind with Variable Limit of Integration
3
Linear Equations of the Second Kind with Variable Limit of Integration
127
Linear Equations of the First Kind with Constant Limits of Integration
217
Linear Equations of the Second Kind with Constant Limits of Integration
301
Nonlinear Equations of the First Kind with Variable Limit of Integration
393
Nonlinear Equations of the Second Kind with Variable Limit of Integration
403
Nonlinear Equations of the First Kind with Constant Limits of Integration
433
Nonlinear Equations of the Second Kind with Constant Limits of Integration
453
Application of Integral Equations for the Investigation of Differential Equations
875
Supplements
903
Elementary Functions and Their Properties
905
Finite Sums and Infinite Series
919
Tables of Indefinite Integrals
933
Tables of Definite Integrals
951
Tables of Laplace Transforms
961
Tables of Inverse Laplace Transforms
969

Methods for Solving Integral Equations
499
Main Definitions and Formulas Integral Transforms
501
Methods for Solving Linear Equations of the Form
519
Methods for Solving Linear Equations of the Form
539
Methods for Solving Linear Equations of the Form
573
Methods for Solving Linear Equations of the Form
625
Methods for Solving Singular Integral Equations of the First Kind
707
Methods for Solving Complete Singular Integral Equations
757
Methods for Solving Nonlinear Integral Equations
805
Methods for Solving Multidimensional Mixed Integral Equations
839
Tables of Fourier Cosine Transforms
983
Tables of Fourier Sine Transforms
989
Tables of Mellin Transforms
997
Tables of Inverse Mellin Transforms
1001
Special Functions and Their Properties
1007
Some Notions of Functional Analysis
1055
References
1071
Index
1081
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