In this post we see yet another problem and solution book in mathematics titled Problems and Exercises in Integral Equations by M. Krasnov, A. Kiselev, G. Makarenko.

About the book:

As the name suggests the book is about integral equations and methods of solving them under different conditions. The book has three chapters. Chapter 1 covers Volterra Integral Equations in details. Chapter 2 covers Fredholm integral equations. Finally in Chapter 3, Approximate Methods for solving integral equations are discussed. There are plenty of solved examples in the text to illustrate the methods, along with problems to solve. This will be a useful resource book for those studying integral equations.

The book was translated from the Russian by George Yankovsky and was first published by Mir Publishers in 1971.

PDF | OCR | 600 dpi | Bookmarked | Paginated | Cover | 224 pp | 7.3 MB  (Zipped 6.7 MB)
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You can get the book here (IA) and here (filecloud).

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Contents

CONTENTS
PRELIMINARY REMARKS 7

CHAPTER I.
VOLTERRA INTEGRAL EQUATIONS 15

1. Basic Concepts 15
2. Relationship Between Linear Differential Equations and Volterra Integral Equations 18
3. Resolvent Kernel of Volterra Integral Equation. Solution
of Integral Equation by Resolvent Kernel 21
4. The Method of Successive Approximations 32
5. Convolution-Type Equations 38
6. Solution of Integro-Differential Equations with the
Aid of the Laplace Transformation 43
7. Volterra Integral Equations with Limits (x, + $\infty$) 46
8. Volterra Integral Equations of the First Kind 50
9. Euler Integrals 52
10. Abel’s Problem. Abel’s Integral Equation and Its Generalizations 56
11. Volterra Integral Equations of the First Kind of the
Convolution Type 62

CHAPTER II.
FREDHOLM INTEGRAL EQUATIONS 71

12. Fredholm Equations of the Second Kind. Fundamentals 71
13. The Method of Fredholm Determinants 73
14. Iterated Kernels. Constructing the Resolvent Kernel
with the Aid of Iterated Kernels 78
15. Integral Equations with Degenerate Kernek. Hammerstein
Type Equation 90
16. Characteristic Numbers and Eigenfunctions 99
17. Solution of Homogeneous Integral Equations with
Degenerate Kernel 118
18. Nonhomogeneous Symmetric Equations 119
19. Fredholm Alternative 127
20. Construction of Green’s Function for Ordinary
Differential Equations 134
21. Using Green’s Function in the Solution of Boundary-
Value Problems 144
22. Boundary-Value Problems Containing a Parameter;
Reducing Them to Integral Equations 148
23. Singular Integral Equations 151

CHAPTER III.
APPROXIMATE METHODS 166

24. Approximate Methods of Solving Integral Equations 166
1. Replacing the kernel by a degenerate kernel 166
2. The method of successive approximations 171
3. The Bubnov-Galerkin method 172
25. Approximate Methods for Finding Characteristic Numbers 174
1. Ritz method 174
2. The method of traces 177
3. Kellogg’s method 179

ANSWERS 182
APPENDIX. SURVEY OF BASIC METHODS FOR SOLVING
INTEGRAL EQUATIONS 198
BIBLIOGRAPHY 208
INDEX 210