Handbook of Integral Equations Second Edition by Andrei Polyanin, Alexander Manzhirov ISBN 9781584885078 1584885078

Handbook of Integral Equations Second Edition by Andrei D. Polyanin,  Alexander V. Manzhirov – Ebook PDF Instant Download/Delivery: 9781584885078, 1584885078
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Product details: 

ISBN 10: 1584885078

ISBN 13:  9781584885078

Author: Andrei D. Polyanin,  Alexander V. Manzhirov

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.

Table of contents: 

1. Linear Equations of the First Kind with Variable Limit of Integration

2. Linear Equations of the Second Kind with Variable Limit of Integration

3. Linear Equations of the First Kind with Constant Limits of Integration

4. Linear Equations of the Second Kind with Constant Limits of Integration

5. Nonlinear Equations of the First Kind with Variable Limit of Integration

6. Nonlinear Equations of the Second Kind with Variable Limit of Integration

7. Nonlinear Equations of the First Kind with Constant Limits of Integration

8. Nonlinear Equations of the Second Kind with Constant Limits of Integration

9. Application of Integral Equations for the Investigation of Differential Equations

10. Supplements
     10.1 Elementary Functions and Their Properties
     10.2 Finite Sums and Infinite Series
     10.3 Tables of Indefinite Integrals
     10.4 Tables of Definite Integrals
     10.5 Tables of Laplace Transforms
     10.6 Tables of Inverse Laplace Transforms

11. Methods for Solving Integral Equations
     11.1 Main Definitions and Formulas: Integral Transforms
     11.2 Methods for Solving Linear Equations of the Form (multiple chapters)
     11.3 Methods for Solving Singular Integral Equations of the First Kind
     11.4 Methods for Solving Complete Singular Integral Equations
     11.5 Methods for Solving Nonlinear Integral Equations
     11.6 Methods for Solving Multidimensional Mixed Integral Equations

12. Tables of Fourier Cosine Transforms

13. Tables of Fourier Sine Transforms

14. Tables of Mellin Transforms

15. Tables of Inverse Mellin Transforms

16. Special Functions and Their Properties

17. Some Notions of Functional Analysis

18. References

19. Index

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Tags: Andrei Polyanin, Alexander Manzhirov, Handbook of Integral