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*.

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)

(Note: IA file parameters maybe different.)

You can get the book here (IA) and here (filecloud).

Password, if needed: *mirtitles*

See FAQs for password related problems.

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

I love you guys so much!!! Once you guys get Elsgolts up, then mixing this book with that & the NPTEL lectures on CoV & integral equations brings us completely back to 1950’s Russia :p

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Yes. Sorry for this and also for the earlier post on Partial Differential Equations. Both these got published accidentally when they were not ready. Check the link in some time, it should be there.

D

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