Demidovich, Maron - Computational Mathematics torrent

Computational Mathematics
by B. P. Demidovich, I. A. Maron.

The basic aim of this book is to give as far as possible a
systematic and modern presentation of the most important methods and
techniques of computational mathematics on the basis of the general
course of higher mathematics taught in higher technical schools. The
book has been arranged so that the basic portion constitutes a
manual for the first cycle of studies in approximate computations
for higher technical colleges. The text contains supplementary
material which goes beyond the scope of the ordinary college course,
but the reader can select those sections which interest him and omit
any extra material without loss of continuity. The chapters and
sections which may be dropped out in a first reading are marked with
an asterisk.

For a full comprehension of the contents of this book, the reader
should have a background of linear algebra and the theory of linear
vector spaces. With the aim of making the text as self-contained as
possible, the authors have included all the necessary starting
material in these subjects. The appropriate chapter are completely
independent of the basic text and can be omitted by readers who have
already studied these sections.

A few words about the contents of the book. In the main it is
devoted to the following problems: operations involving approximate
numbers, computation of functions by means of series and iterative
processes, approximate and numerical solution of algebraic and
transcendental equations, computational methods of linear algebra,
interpolation of functions, numerical differentiation and
integration of functions, and the Monte Carlo method.

This book was translated from the Russian by George Yankovsky. The book was
published by first Mir Publishers in 1973, with reprints in 1976,
and 1981. The book below is from the 1981 reprint.

All credits to the original uploader.

DJVU | OCR | 17.1 MB | Pages: 688 |

Table of Contents
PREFACE

INTRODUCTION.

GENERAL RULES OF COMPUTATIONAL WORK

CHAPTER 1
APPROXIMATE NUMBERS 19

CHAPTER 2
SOME FACTS FROM THE THEORY OF CONTINUOUS FRACTIONS 55

CHAPTER 3
COMPUTING THE VALUES OF FUNCTIONS 77

CHAPTER 4
APPROXIMATE SOLUTIONS OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS 115

CHAPTER 5
SPECIAL TECHNIQUES FOR APPROXIMATE SOLUTION OF EQUATIONS 162

CHAPTER 6
ACCELERATING THE CONVERGENCE OF SERIES 203

CHAPTER 7
MATRIX ALGEBRA 229

CHAPTER 8
SOLVING SYSTEMS OF LINEAR EQUATIONS 273

CHAPTER 9
THE CONVERGENCE OF ITERATION PROCESSES FOR SYSTEMS OF LINEAR EQUATIONS 322

CHAPTER 10
ESSENTIALS OF THEORY OF LINEAR VECTOR SPACES 336

CHAPTER 11
ADDITIONAL FACTS ABOUT THE CONVERGENCE OF ITERATION PROCESSES FOR
SYSTEMS OF LINEAR EQUATIONS 394

CHAPTER 12
FINDING THE EIGENVALUES AND EIGENVECTORS OF A MATRIX 410

CHAPTER 13
APPROXIMATE SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS 459

CHAPTER 14
THE INTERPOLATION OF FUNCTIONS 507

CHAPTER 15
APPROXIMATE DIFFERENTIATION 574

CHAPTER 16
APPROXIMATE INTEGRATION OF FUNCTIONS 590

CHAPTER 17
THE MONTE CARLO METHOD 649

COMPLETE LIST OF REFERENCES 675

INDEX 679