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Learning Higher Mathematics

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

  • Textbook
  • © 1984

Overview

Authors:
  1. Lev Semenovič Pontrjagin

    1. Steklov Mathematical Institute, Moscow, USSR

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VIII
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  2. The Method of Coordinates

    1. Front Matter

      Pages 1-6
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    2. Coordinates in the Plane

      • Lev Semenovič Pontrjagin
      Pages 7-28

    3. Coordinates and Lines in the Plane

      • Lev Semenovič Pontrjagin
      Pages 29-70

    4. Analytic Geometry in the Plane

      • Lev Semenovič Pontrjagin
      Pages 71-104

  3. Analysis of Infinitely Small

    1. Front Matter

      Pages 105-109
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    2. Series

      • Lev Semenovič Pontrjagin
      Pages 110-181

    3. The Differential Calculus

      • Lev Semenovič Pontrjagin
      Pages 182-232

    4. The Integral Calculus

      • Lev Semenovič Pontrjagin
      Pages 233-260

    5. Analytic Functions

      • Lev Semenovič Pontrjagin
      Pages 261-302

  4. Back Matter

    Pages 303-306
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Keywords

About this book

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.

Authors and Affiliations

  • Steklov Mathematical Institute, Moscow, USSR

    Lev Semenovič Pontrjagin

Bibliographic Information

  • Book Title: Learning Higher Mathematics

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

  • Authors: Lev Semenovič Pontrjagin

  • Series Title: Springer Series in Soviet Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-69040-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1984

  • Softcover ISBN: 978-3-540-12351-4Published: 01 December 1983

  • eBook ISBN: 978-3-642-69040-2Published: 11 November 2013

  • Series ISSN: 0939-1169

  • Edition Number: 1

  • Number of Pages: VIII, 308

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: Originally published with the title: Pt. 1: Method koordinat; Pt. 2: Analiz beskonecno malych

  • Topics: Analysis

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