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Book cover
  • Textbook
  • © 1998

Postmodern Analysis

Authors:

  1. Jürgen Jost

    1. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

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  • A very streamlined text on mathematical analysis at the "advanced calculus" level, particularly adapted in the need of those going on to applications in physics

Part of the book series: Universitext (UTX)

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Table of contents (26 chapters)

  1. Front Matter

    Pages I-XV
    PDF

  3. Topological Concepts

    1. Front Matter

      Pages 73-73
      PDF

  4. Calculus in Euclidean and Banach Spaces

    1. Front Matter

      Pages 97-97
      PDF

    2. Differentiation in Banach Spaces

      • Jürgen Jost
      Pages 99-110

    3. Differential Calculus in ℝd

      • Jürgen Jost
      Pages 111-126

    4. The Implicit Function Theorem. Applications

      • Jürgen Jost
      Pages 127-137

    5. Curves in ℝd. Systems of ODEs

      • Jürgen Jost
      Pages 139-147

  5. The Lebesgue Integral

    1. Front Matter

      Pages 149-149
      PDF

    2. Preparations. Semicontinuous Functions

      • Jürgen Jost
      Pages 151-157

    4. Lebesgue Integrable Functions and Sets

      • Jürgen Jost
      Pages 177-187
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About this book

What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the approach to analysis presented here from what has been called "Modern Analysis" by its protagonists. "Modern Analysis" as represented in the works of the Bour­ baki group or in the textbooks by Jean Dieudonne is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degen­ erate into a collection of rather unconnected tricks to solve special problems, this definitively represented a healthy achievement. In any case, for the de­ velopment of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solelyon the internal problems and structures and to neglect the relations to other fields of scientific, even of mathematical study for a certain while. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathematical theory can acquire. However, once this level has been reached, it might be useful to open one's eyes again to the inspiration coming from concrete ex­ ternal problems.
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Keywords

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Authors and Affiliations

  • Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Jürgen Jost

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Bibliographic Information

  • Book Title: Postmodern Analysis

  • Authors: Jürgen Jost

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-662-03635-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1998

  • eBook ISBN: 978-3-662-03635-8Published: 09 March 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XV, 356

  • Topics: Analysis

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eBook USD 74.99
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  • Available as PDF
  • Read on any device
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