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© 2003

Postmodern Analysis

Textbook

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 partial differential equations

Authors and affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

Bibliographic information

  • Book Title Postmodern Analysis
  • Authors Jürgen Jost
  • Series Title Universitext
  • 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
  • Softcover ISBN 978-3-540-43873-1
  • eBook ISBN 978-3-662-05306-5
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 2
  • Number of Pages XVII, 371
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Partial Differential Equations
  • Buy this book on publisher's site
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Reviews

From the reviews:

"...well thought out concept. Provides students at master's level with both a revision and a continuation of their undergraduate analysis lectures. New elements of advanced analysis are motivated by their applications to variational problems and elliptic PDE, thus illustrating their significance in the important area of current mathematics. The book will serve some readers seeking to deepen their mathematical knowledge, it is however designed to arouse curiosity for one of the most attractive fields of mathematics. ..." Heinrich Begehr in Mathematische Semesterberichte 1999 (transl.)

From the reviews of the second edition:

"The second edition of this excellent monograph, called ‘Postmodern analysis’ in reaction to the Bourbaki style of Dieudonne’s ‘Modern Analysis’ keeps the spirit of the first edition. … . This new edition is a very valuable addition to the literature." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 11 (4), 2004)

"This book in the Universitext series of Springer-Verlag blends analysis on an advanced level with relatively concrete parts of functional analysis. … The book is to be recommended to a broad readership. It is to be addressed especially to those who like a quick and unconventional course of higher analysis." (R. Schimming, Zeitschrift für Analysis und ihre Anwendungen, Vol. 22 (3), 2003)