A Course of Higher Mathematics vol 1 - V. Smirnov
A COURSE OF
ADIWES INTERNATIONAL SERIES TT. 1 ¦» * 1
in mathematics Higher Matnematics
A. J. LOHWATER VOLUME I
Consulting Editor
V. I. SMIRNOV
Translated by
D. E. BROWN
Translation edited and
additions made by
I. N. SNEDDON
Simson Professor in Mathematics
University of Glasgoiv
PERGAMON PRESS
OXFORD •LONDON¦EDINBURGH•NEW YORK
PARIS • FRANKFURT
ADDISON-WESLEY PUBLISHING COMPANY, INC.
READING, MASSACHUSETTS • PALO ALTO • LONDON
1964
INTRODUCTION
This is the first volume of a five-volume course of higher mathematics
which has been studied by Soviet mathematicians, physicists and
engineers for forty years. In the first two editions A924, 1927), which
were practically identical, this first volume was written jointly by
J. D. Tamarkin and V. I. Smirnov, but on the title page of later
editions, prepared without the late Professor Tamarkin's cognizance
and deviating from the two earlier editions in many respects, Professor
Smirnov's name appears alone.
Professor Tamarkin's career and his contributions to both Russian
and American mathematics are well known to British and American
readers, but the achievements of Professor Smirnov are known to a
more restricted circle. Vladimir Ivanovitch Smirnov, who was born
in 1887, has had a distinguished career in research and teaching which
fits him ideally for the writing of a comprehensive work of extensive
proportions. His research has been mainly in the theory of functions
and of differential equations but he has made valuable contributions
to applied mathematics and, in particular, to theoretical seismology
and all his work has been characterized by a broad scientific outlook
and he has done more than any other Soviet mathematician to main-
maintain and strengthen the connections between mathematics and physics.
His pupils, among whom are numbered S. L. Sobolev, N. E. Kochin
and I. A. Lappo-Danilevskii, have maintained this tradition of work-
working in both pure and applied mathematics, a tradition which Smirnov
inherited from his teacher V. A. Steklov.
Professor Smirnov's teaching experience in the old Institute of
Transport, in a technical high school, in the Physics Department of
¦ the Mathematics and Physics Faculty of the University of Lenin-
Leningrad, and as Director of the Theoretical Section of the Institute of
Seismology, Moscow, led him to study the design of a special course
; of higher mathematics for physicists and engineers, a project in the
course of which he received the counsel of his many physicist friends
particularly V. A. Fock and T. V. Kravets. The five-volume set of
which the present volume is the first is the outcome of that study. It
•is, of course, designed as a first course for pure mathematicians in the
topics considered as well as for students and research workers whose
main interest lies in the applications of mathematics.
The whole work is notable not only for the wealth of the illustrations
it draws from physics and technology to illuminate points in pure
mathematics, but also for the clarity of the exposition. This has al-
already been recognized in the Soviet Union by the esteem by which
the author's work is held by academic teachers, by the award in 1947
of the State Prize (previously called the Stalin Prize) to the author for
this work, and it is to be hoped that through Mr. Brown's translation
its merits will become just as well known in the English-speaking
world.
The present volume is an introduction to calculus and to the prin-
principles of mathematical analysis including some introductory material
on functions of several variables as well as on functions of a single
variable. As well as providing the material necessary for the under-
understanding of the methods of mathematical physics it is an excellent
introduction to these subjects for students of pure mathematics.
I. N. Sneddon
A COURSE OF
ADIWES INTERNATIONAL SERIES TT. 1 ¦» * 1
in mathematics Higher Matnematics
A. J. LOHWATER VOLUME I
Consulting Editor
V. I. SMIRNOV
Translated by
D. E. BROWN
Translation edited and
additions made by
I. N. SNEDDON
Simson Professor in Mathematics
University of Glasgoiv
PERGAMON PRESS
OXFORD •LONDON¦EDINBURGH•NEW YORK
PARIS • FRANKFURT
ADDISON-WESLEY PUBLISHING COMPANY, INC.
READING, MASSACHUSETTS • PALO ALTO • LONDON
1964
INTRODUCTION
This is the first volume of a five-volume course of higher mathematics
which has been studied by Soviet mathematicians, physicists and
engineers for forty years. In the first two editions A924, 1927), which
were practically identical, this first volume was written jointly by
J. D. Tamarkin and V. I. Smirnov, but on the title page of later
editions, prepared without the late Professor Tamarkin's cognizance
and deviating from the two earlier editions in many respects, Professor
Smirnov's name appears alone.
Professor Tamarkin's career and his contributions to both Russian
and American mathematics are well known to British and American
readers, but the achievements of Professor Smirnov are known to a
more restricted circle. Vladimir Ivanovitch Smirnov, who was born
in 1887, has had a distinguished career in research and teaching which
fits him ideally for the writing of a comprehensive work of extensive
proportions. His research has been mainly in the theory of functions
and of differential equations but he has made valuable contributions
to applied mathematics and, in particular, to theoretical seismology
and all his work has been characterized by a broad scientific outlook
and he has done more than any other Soviet mathematician to main-
maintain and strengthen the connections between mathematics and physics.
His pupils, among whom are numbered S. L. Sobolev, N. E. Kochin
and I. A. Lappo-Danilevskii, have maintained this tradition of work-
working in both pure and applied mathematics, a tradition which Smirnov
inherited from his teacher V. A. Steklov.
Professor Smirnov's teaching experience in the old Institute of
Transport, in a technical high school, in the Physics Department of
¦ the Mathematics and Physics Faculty of the University of Lenin-
Leningrad, and as Director of the Theoretical Section of the Institute of
Seismology, Moscow, led him to study the design of a special course
; of higher mathematics for physicists and engineers, a project in the
course of which he received the counsel of his many physicist friends
particularly V. A. Fock and T. V. Kravets. The five-volume set of
which the present volume is the first is the outcome of that study. It
•is, of course, designed as a first course for pure mathematicians in the
topics considered as well as for students and research workers whose
main interest lies in the applications of mathematics.
The whole work is notable not only for the wealth of the illustrations
it draws from physics and technology to illuminate points in pure
mathematics, but also for the clarity of the exposition. This has al-
already been recognized in the Soviet Union by the esteem by which
the author's work is held by academic teachers, by the award in 1947
of the State Prize (previously called the Stalin Prize) to the author for
this work, and it is to be hoped that through Mr. Brown's translation
its merits will become just as well known in the English-speaking
world.
The present volume is an introduction to calculus and to the prin-
principles of mathematical analysis including some introductory material
on functions of several variables as well as on functions of a single
variable. As well as providing the material necessary for the under-
understanding of the methods of mathematical physics it is an excellent
introduction to these subjects for students of pure mathematics.
I. N. Sneddon
