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Learning Higher Mathematics

Part I: The Method of Coordinates Part II: Analysis of the Infinitely Small

  • Lev Semenovič Pontrjagin

Part of the Springer Series in Soviet Mathematics book series (SSSOV)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. The Method of Coordinates

    1. Front Matter
      Pages 1-6
    2. Lev Semenovič Pontrjagin
      Pages 7-28
    3. Lev Semenovič Pontrjagin
      Pages 29-70
    4. Lev Semenovič Pontrjagin
      Pages 71-104
  3. Analysis of Infinitely Small

    1. Front Matter
      Pages 105-109
    2. Lev Semenovič Pontrjagin
      Pages 110-181
    3. Lev Semenovič Pontrjagin
      Pages 182-232
    4. Lev Semenovič Pontrjagin
      Pages 233-260
    5. Lev Semenovič Pontrjagin
      Pages 261-302
  4. Back Matter
    Pages 303-306

About this book

Introduction

Lev Semenovic Pontrjagin (1908) is one of the outstanding figures in 20th century mathematics. In a long career he has made fundamental con­ tributions to many branches of mathematics, both pure and applied. He has received every honor that a grateful government can bestow. Though in no way constrained to do so, he has through the years taught mathematics courses at Moscow State University. In the year 1975 he set himself the task of writing a series of books on secondary school and beginning university mathematics. In his own words, "I wished to set forth the foundations of higher mathematics in a form that would have been accessible to myself as a lad, but making use of all my experience as a scientist and a teacher, ac­ cumulated over many years. " The present volume is a translation of the first two out of four moderately sized volumes on this theme planned by Pro­ fessor Pontrjagin. The book begins at the beginning of modern mathematics, analytic ge­ ometry in the plane and 3-dimensional space. Refinements about limits and the nature of real numbers come only later. Many concrete examples are given; these may take the place of formal exercises, which the book does not provide. The book continues with careful treatment of differentiation and integration, of limits, of expansions of elementary functions in power se­ ries.

Keywords

Analysis Analytische Geometrie Derivative Learning Mathematics Taylor series calculus limit of a function

Authors and affiliations

  • Lev Semenovič Pontrjagin
    • 1
  1. 1.Steklov Mathematical InstituteMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-69040-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1984
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-12351-4
  • Online ISBN 978-3-642-69040-2
  • Series Print ISSN 0939-1169
  • Buy this book on publisher's site