Problems in mathematical analysis

by B.P. Demidovich

PREFACE



This collection of problems and exercises in mathematical analysis covers the maximum requirements of general courses in
higher mathematics for higher technical schools. It contains over
3,000 problems sequentially arranged in Chapters I to X covering
all branches of higher mathematics (with the exception of analytical geometry) given in college courses. Particular attention is
given to the most important sections of the course that require
established skills (the finding of limits, differentiation techniques,
the graphing of functions, integration techniques, the applications
of definite integrals, series, the solution of differential equations).

Since some institutes have extended courses of mathematics,
the authors have included problems on field theory, the Fourier
method, and approximate calculaiions. Experience shows that
the number of problems given in this book not only fully satisfies
the requireiren s of the student, as far as practical mas!ering of
the various sections of the course goes, but also enables the in-
structor to supply a varied choice of problems in each section
and to select problems for tests and examinations.

Each chap.er begins with a brief theoretical introduction that
covers the basic definitions and formulas of that section of the
course. Here the most important typical problems are worked out
in full. We believe that this will greatly simplify the work of
the student. Answers are given to all computational problems;
one asterisk indicates that hints to the solution are given in
the answers, two asterisks, that the solution is given. The
problems are frequently illustrated by drawings.

This collection of problems is the result of many years of
teaching higher mathematics in the technical schools of the Soviet
Union. It includes, in addition to original problems and exam-
ples, a large number of commonly used problems.

Genres: Mathematics, Textbooks

496 pages, Hardcover

First published January 1, 1986

About the author

Boris Pavlovich Demidovich (Russian: Борис Павлович Демидович; Belarusian: Барыс Паўлавіч Дземідовіч; Novogrudok, March 2, 1906 – Moscow, April 23, 1977) was a Soviet/Belorussian mathematician.

Demidovich was born in a family of teachers. His father, Pavel (1871 – 1931), was able to get higher education, graduating in 1897 at Vilensky institute; Pavel Demidovich was a teacher throughout his life, first teaching in different towns in the Minsk and Vilnius provinces, and then in Minsk; he was very attached to his family, and to Belorussian beliefs and rituals. He also recorded some anonymous literary works of the Belorussian tradition. In 1908 Pavel Demidovich was nominated member of the Imperial Officer of the Company Enthusiasts science, Anthropology at Moscow University.
Demidovich's mother, Olympia Platonovna Demidovich (1876–1970), the daughter of a priest, had been a teacher too before her marriage, when she chose to retire, in order to raise their children. Boris Demidovich had three sisters, Zinaida, Evgeniia, Zoya and a younger brother, Paul.
After graduating in 1923 Demidovich attended the physical-mathematical branch of the teaching faculty, that had been established in 1921, at the Belorussian State University. He obtained his degree in 1927 and was recommended to the graduate school faculty of higher mathematics, but Demidovich did not consider that a possibility and went to work in Russia instead.

For four years, Demidovich served as professor of mathematics in secondary schools throughout the Smolensk and Bryansk regions. After casually reading an advertisement in a local newspaper, he moved to Moscow and in 1931, taught in a graduate school of the Research Institute of Mathematics and Mechanics at Moscow State University. At the end of this short term, he obtained the teaching chair in the Transportation and Economic Institute NKPS, and taught there at the Department of Mathematics in 1932–33. In 1933, while retaining his teaching office at T.E.I. NKPS, Demidovich was even enlisted as senior member at the Bureau of Pilot Transport construction NKPS and worked there until 1934.
At the same time, in 1932, Demidovich became a post-graduate student at the Mathematical Institute, Moscow State University, after succeeding a competition. As a postgraduate, Demidovich began to work under the guidance of Andrey Nikolaevich Kolmogorov on the theory of functions of a real variable.
Kolmogorov saw that Demidovich was interested in the problems of differential equations, invited him to join him in studying the qualitative theory of ordinary differential equations under the direction of Vyacheslav Stepanov. Supervising his activities, Stepanov identified himself as the scientific advisor of his younger colleague.
After his graduation, in 1935, Demidovich worked for one semester at the Department of Mathematics at the Institute for the leather industry. And, since February 1936, at the invitation of LA Tumarkin, he served as assistant chair of mathematical analysis of Mechanics and Mathematics Faculty of Moscow State University. Until his death he remained a permanent staff member. In 1935 at the Moscow University, Demidovich discussed his PhD thesis, "On the existence of the integral invariant on a system of periodic orbits" and the following year, he was awarded the degree of Ph.D.
In 1938, Demidovich was granted the rank of assistant professor of mathematical analysis at Mehmata MSU. In 1963, VAK awarded him the degree of Doctor of physical and mathematical sciences, and in 1965, Demidovich was granted the rank of professor in the department of mathematical analysis at Mehmata MSU. In 1968, the Presidium of the Supreme Council of Russia awarded Demidovich the honorary title "Meritorious Scientist of the RSFSR".
Demidovich suddenly died on 23 April in 1977 of acute cardiovascular insufficiency.

Reviews

[Manoj Khatri · Rating 5 out of 5]

This is it. The American way of learning calculus by dividing into I, II and III never worked for me. This teaches how Soviets do their math and looks like they know how to write decent maths' textbook.

[Ahmed قامش · Rating 4 out of 5]

Good but not the best , it needs more solved Examples and more explaination