Problems and Exercises in Integral Equations

✍ Scribed by G. Krasnov, M., Kiselev, A., Makarenko

Publisher: Mir Publishers
Year: 1971
Tongue: English
Leaves: 224
Edition: Revised
Category: Library

No coin nor oath required. For personal study only.

✦ Table of Contents

Front Cover
Title Page
CONTENTS
PRELIMINARY REMARKS
1 VOLTERRA INTEGRAL EQUATIONS
1. Basic Concepts
2. Relationship Between Linear Differential Equations and Volterra Integral Equations
3. Resolvent Kernel of Volterra Integral Equation. Solution of Integral Equation by Resolvent Kernel
4. The Method of Successive Approximations
5. Convolution-Type Equations
6. Solution of lntegro-Differential Equations with the Aid of the Laplace Transformation
7. Volterra Integral Equations with Limits (X, + oo)
8. Volterra Integral Equations of the First Kind
9. Euler Integrals
10. Abel's Problem. Abel's Integral Equation and Its Generalizations
11. Volterra Integral Equations of the First Kind of the Convolution Type
2 FREDHOLM INTEGRAL EQUATIONS
12. Fredholm Equations of the Second Kind. Fundamentals
13. The Method of Fredholm Determinants
14. Iterated Kernels. Constructing the Resolvent Kernel with the Aid of Iterated Kernels
15. Integral Equations with Degenerate Kernels. Hammerstein Type Equation
16. Characteristic Numbers and Eigenfunctions
17. Solution of Homogeneous Integral Equations with Degenerate Kernel
18. Nonhomogeneous Symmetric Equations
19. Fredholm Alternative
20. Construction of Green's Function for Ordinary Differential Equations
21. Using Green's Function in the Solution of Boundary-Value Problems ·
22. Boundary-Value Problems Containing a Parameter; Reducing Them to Integral Equations
23. Singular Integral Equations
3 APPROXIMATE METHODS
24. Approximate Methods of Solving Integral Equations
25. Approximate Methods for Finding Characteristic Numbers
ANSWERS
APPENDIX: SURVEY OF BASIC METHODS FOR SOLVING
BIBLIOGRAPHY
INDEX

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