Lectures on mathematical analysis. Semester I (Q2865667)

This book is the second edition of a part of lecture notes corresponding to the material of the first semester lectures on mathematical analysis for students in mathematics. 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.NEWLINENEWLINENEWLINEThe high educational standard of the mechanical-mathematical faculty of MSU is well-known. Therefore, it is possible to deliver lectures at the deep rigors. Anyway, since mathematical analysis is one of the most difficult discipline at the first semester, the lecturer should combine the presentation of the most important ideas of analysis with all possible explanations which make this material understandable and even attractive.NEWLINENEWLINEThe book by Prof\ . S. A. Telyakovskiĭ has exactly such a character. The main material is illustrated by a large collection of examples, and the principal ideas are discussed in their historical retrospective.NEWLINENEWLINEThe following material is presented in the book: ``Real numbers'', ``Limit of sequences'', ``Limit of functions'', ``Continuous functions'', ``Derivatives and differentials'', ``Properties of differentiable functions'', ``Curves in three-dimensional space''.