Lectures on mathematical analysis. Semester II (Q2863729)

This book is the second edition of the second part of lecture notes corresponding to the material of the second semester lectures on mathematical analysis for students in mathematics (for the first part see [Zbl 1280.26003]). These lectures were delivered by the author at the mechanical-mathematical faculty of the M. V. Lomonosov Moscow State University.NEWLINENEWLINENEWLINEThis edition is published in the framework of the programme ``Lectures of NOTs (Scientific-educational Center)'' realized by the V. A. Steklov Mathematical Institute of RAS.NEWLINENEWLINEThe high educational standard of the mechanical-mathematical faculty of MSU is well-known. Therefore, it is possible to deliver lectures at the deep rigors. In the present book the material of the second semester is presented 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 deeply into modern generalizations of these results.NEWLINENEWLINENEWLINEThe book consists of seven chapters: ``Indefinite integral (primitives)'', ``Definite integral'' (in Riemann's sense), ``Riemann-Stieltjes integral'', ``Differential calculus of the functions of several variables'', ``Implicit functions'', ``Extremums of functions of several variables''. 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 self-education are presented.