In the Little Mathematics Library we now come to *Method of Successive Approximations* by *N. Ya. Vilenkin*. As the title suggests the book has to do with approximation methods, but what kind of approximations and for what kind of use one may ask?

The preface of the book reads:

The main purpose of this book is to present various methods of approximate solution of equations. Their practical value is beyond doubt, but still little attention is paid to them either at school or a college and so someone who has passed a college level higher mathematics course usually has difficulty in solving a transcendental equation of the simplest type. Not only engineers need to solve equations, but also technicians, production technologists and people in other professions as well. It is also good for high-school students to become acquainted with the methods of approximate solution of equations. Since most approximate solution methods involve the idea of the derivative we were forced to introduce this concept. We did this intuitively, making use of a geometric interpretation. Hence, a knowledge of secondary school mathematics will be sufficient for anyone wanting to read this book.

The book was translated from the Russian by *Mark Samokhvalov* and was first published by Mir in 1979. You can get the book here. All credits to the original uploader.

Contents of the book are as under:

1. Introduction 9

2. Successive Approximations 12

3- Achilles and the Tortoise 14

4 Division On Electronic Computers 16

5 Extraction of Square Roots by Method of Successive Approximations 19

6. Extraction of Roots with Positive Integer Indices Using Method of Successive Approximations 25

7 Method of Iteration 27

8. Geometrical Meaning of Method of Iterations 30

9 Contraction Mappings (Contractions) 32

10 Contraction Mappings and Method of Iteration 36

11. Method of Chords 43

12. Improved Method of Chords 47

13 Derivative of Polynomial 49

14 Newton’s Method for Approximate Solution of Algebraic Equations 51

15. Geometrical Meaning of Derivative 54

16. Geometrical Meaning of Newton’s Method 57

17 Derivatives of Arbitrary Functions 59

18 Computation of Derivatives 61

19. Finding the First Approximations 63

20 Combined Method of Solving Equations 66

21 Convergence Test for Method of Iterations 68

22. Rate of Convergence of Iteration Process 71

23. Solving Systems of Linear Equations by Method of Successive Approximations 74

24. Solving Systems of Non-linear Equations Using Method of Successive Approximations 79

25. Modified Distance 82

26. Convergence Tests for Process of Successive Approximations for Systems of Linear Equations 85

27. Successive Approximations in Geometry 91

28 Conclusion 94

Exercises 96

Solutions 98

Password, if needed: *mirtitles*

4-shared link here

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happy new year damitr and to everyone .This book seems to be great ,many many thanx.can anyone post link to GROUPS AND THEIR GRAPHS by grossman not by mir publisher but new mathematical library.

I am uploading the LML books uploaded by damitr in jumbofiles .You can download the files from here

http://jumbofiles.com/user/desperadomar/174503/Little%20Mathematics%20Library%20%28LML%29

no password required and Damitr please let me whether I am missing any files.

Biju