VECTOR AND TENSOR ANALYSIS WITH APPLICATIONS.
Edition. Translated and Edited by Richard A. Silverman.
Publications, Inc.- New York. - 1968
Copyright © 1968 by Richard A. Silverman.
All rights reserved under Pan American and Inter-
national Copyright Conventions
Published in Canada by General Publishing Company.
Ltd., 30 Lesmill Road, Don Mills, Toronto. Ontario.
Published in the United Kingdom by Constable and
This Dover edition, first published in 1979. is an unabridged
and corrected republication of the work
originally published in 1968 by Prentice-Hall, Inc.
International Standard Book Number. 0-486-63833-2
Library of Congress Catalog Card Number: 79-87809
Manufactured in the United States of America
Dover Publications, Inc.
180 Varick Street New York 10014
The present book is a freely revised and restyled version
of the third edition of the Russian original (Moscow,
1966). As in other volumes of this series, I have not
hesitated to introduce a number of pedagogical and
mathematical improvements that occurred to me in the
course of doing the translation. I have also added a brief
Bibliography, confined to books in English dealing with
approximately the same topics, at about the same level.
In their prefaces to the three Russian editions, the au-
thors, acknowledge the help of the following colleagues:
Professors Y. P. Blank, V. L. German, G. I Drinfeld,
A D. Myshkis, N. I. Akhiezer, P. K Rashevsky, V, A.
Marchenko and N.V. Yefimov.
VECTOR AND TENSOR ANALYSIS WITH APPLICATIONS
A.I. Borisenko and I.E.Tarapov
". . . the exposition is clear and the choice of topics is excellent . . ."
Prof. R.E. Williamson
Univ of Sussex, Brighton, England
This concise introduction to a basic branch of applied mathematics is indispensable to mathematicians, physicists and engineers. Eminently readable,
it covers the elements of vector and tensor analysis, with applications of the theory to specific physics and engineering problems. It lays particular
stress on the applications of the theory to fluid dynamics.
The authors begin with a definition of vectors and a discussion of algebraic operations on vectors. The vector concept is then generalized in a natural
way, leading to the concept of a tensor. Chapter Three considers algebraic operations on tensors. Next, the authors turn to a systematic study of the
differential and integral calculus of vector and tensor functions of space and lime. Finally, vector and tensor analysis is considered from both a
rudimentary standpoint, and in its fuller ramifications, concluding the volume.
The strength of the book lies in the completely worked out problems and solutions at the end of each chapter. In addition, each chapter incorporates
abundant exercise material. Intended primarily for advanced undergraduates and graduate students of math, physics and engineering, the work is
self-contained and accessible to any student with a good background in calculus.
Vector and Tensor Analysis With Applications is one of a series of SELECTED RUSSIAN PUBLICATIONS IN THE MATHEMATICAL SCIENCES, several of which have
already been published by Dover. The authors are distinguished Russian mathematicians and specialists in gas dynamics and numerical analysis Richard
A Silverman, editor of the series as well as editor and translator of this volume, has revised and improved the original edition and added a bibliography.
" . . a concise, clear and comprehensive treatment…"
Prof. Henry C. Booker
University of California, San Diego