Computational Mathematics - Worked Examples and Problems With Elements of Theory

✍ Scribed by N.V. Kopchenova; I. A. Maron

• Publisher: MIR Publishers
• Year: 1981
• Tongue: English
• Leaves: 408
• Category: Library

✦ Synopsis

Reasonable utilization of modern computer techniques is out
of the question without skillful application of approximate and
numerical analysis, which explains the remarkable growth of interest
in the methods of approximate calculation.
Computational mathematics as a teaching discipline has an
increasing place in the syllabuses of engineering and economics
faculties and colleges and with it the demand for textbooks in
this discipline has grown. A particularly acute need for manuals
on solving problems in computational mathematics is felt.
The present book is an attempt to provide such a manual.
The book has the following structure: each section begins with
a brief theoretical introduction on setting the problem, giving
working formulas, computational schemes, estimates of error, and
a comparison of different methods from the angle of their laboriousness,
their attainable degree of accuracy, and the convenience
of solving them on a computer. There follows a detailed solution
of model problems illustrating the appropriate algorithms. At the
end of the section problems for independent practice are suggested.
Answers are given for most of these problems.
For better understanding of the essence of the matter, most
of the problems for which solutions are provided have been selected
so that the computations will not be especially, cumbersome. It is
suggested that desk computers should be used in the initial stage
of instruction, and for group study.
The book is intended primarily for engineering students but
mav also prove useful for economics students, for graduate engineers,
and for post graduate students and scientific workers in
the applied sciences. The material, we would emphasize, does not
go beyond the limits of the syllabus in computational mathematics.
The authors take this opportunity to express their deep gratitude
to Kh.L. Smolitsky and I.M. Stesin for reading the
manuscript. Their advice and remarks helped to improve the book.
We also sincerely thank L.Z. Rumshisky for editing the whole
work and for his part in the writing of chapters one and six. We are aware that the work as it stands is not free of error, the
more so that it is the first teaching manual of this kind published
in our country. We shall therefore, be grateful for the advice and
criticism of readers, which should be addressed to 117071, Moscow
V-71, Leninsky Prospect, 15, “Nauka” Publishers Main Editorial
Office for Physico-Mathematical Literature.

Translated from the Russian by V. Shiffer
First published 1975
Second printing 1981
Revised from the 1972 Russian edition

✦ Table of Contents

Front Cover
Title
PREFACE
CONTENTS
1. APPROXIMATE COMPUTATIONS AND ERROR ESTIMATION IN PERFORMING COMPUTATIONS
2. COMPUTING THE VALUES OF FUNCTIONS
3. NUMERICAL SOLUTION OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS
4. NUMERICAL SOLUTION OF SYSTEMS OF NONLINEAR EQUATIONS
5. THE INTERPOLATION OF FUNCTIONS
6. NUMERICAL DIFFERENTIATION
7. APPROXIMATE COMPUTATIONOF INTEGRALS
8. APPROXIMATE SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
9. BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
10. NUMERICAL SOLUTION OF EQUATIONS WITH PARTIAL DERIVATIVES AND OF INTEGRAL EQUATIONS
APPENDICES
ANSWERS
REFERENCES