
06235527
b
2014b.00667
Telyakovski\u{\i}, S. A.
Lectures on mathematical analysis. Semester III. ({\cyr Kurs lektsii0 po matematicheskomu analizu. Semestr} III.)
Lektsionnye Kursy NOTs 20. Moskva: Matematicheski\u{\i} Institut im. V. A. Steklova, RAN (ISBN 9785984190497). 241~p. (2013).
2013
Moskva: Matematicheski\u{\i} Institut im. V. A. Steklova, RAN
RU
I15
I35
I65
I55
real analysis
textbook
real numbers
limits
differentiation
curves
fourier series
Hilbert space
parameterdependent integral
Zbl 1280.26004
Zbl 1280.26003
doi:10.4213/lkn20
http://www.mathnet.ru/php/getBook.phtml?jrnid=lkn&bookid=1473&option_lang=eng
This book is the second edition of the third part of lecture notes corresponding to the material of the third semester lectures on mathematical analysis for students in mathematics (for the first part see [Zbl 1280.26003], and for the second part [Zbl 1280.26004]). These lectures were delivered by the author at the mechanicalmathematical faculty of the M. V. Lomonosov Moscow State University. This edition is published in the framework of the programme ``Lectures of NOTs (Scientificeducational Center)'' realized by the V. A. Steklov Mathematical Institute of RAS. The high educational standard of the mechanicalmathematical faculty of MSU is wellknown. Therefore, it is possible to deliver lectures at the deep rigors. In the present book the material of the third semester is presented mainly on the base of traditional point of view. The author supposes that students have to understand first the classical ideas and results, then entering for themselves into deep modern generalizations of these results. The only exclusion is the material related to orthonormal systems in Hilbert space. This chapter contains few necessary results from functional analysis which are in style of classical mathematical analysis. They serve to deliver lectures on Fourier series on the proper level. The book consists of five chapters: ``Number series'', ``Functional sequences and series'', ``Parameterdependent integrals'', ``Orthonormal systems in Hilbert space'', ``Fourier series on the trigonometric system''. The main material is illustrated by a large collection of examples, and the principal ideas are discussed in their historical retrospective. At the end of some chapters few exercises for selfeducation are presented.
Sergei V. Rogosin (Minsk)