Postmodern Analysis

  • Jürgen Jost

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Calculus for Functions of One Variable

  3. Topological Concepts

    1. Front Matter
      Pages 75-75
  4. Calculus in Euclidean and Banach Spaces

    1. Front Matter
      Pages 101-101
    2. Jürgen Jost
      Pages 103-114
    3. Jürgen Jost
      Pages 115-131
    4. Jürgen Jost
      Pages 133-143
    5. Jürgen Jost
      Pages 145-153
  5. The Lebesgue Integral

    1. Front Matter
      Pages 155-155
    2. Jürgen Jost
      Pages 157-163
    3. Jürgen Jost
      Pages 183-193

About this book

Introduction

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 definitely 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 solely on 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.

Keywords

Banach Space Eigenvalue Implicit function Lebesgue integration banach spaces calculus calculus of variations differential calculus differential equation integral integration maximum principle ordinary differential equation partial differentia

Authors and affiliations

  • Jürgen Jost
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-05306-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-43873-1
  • Online ISBN 978-3-662-05306-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book