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Problems and Theorems in Analysis

Series · Integral Calculus · Theory of Functions

  • Textbook
  • © 1972

Overview

Authors:
  1. George Pólya

    1. Department of Mathematics, Stanford University, Stanford, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Gabor Szegö

    1. Department of Mathematics, Stanford University, Stanford, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Study Edition (SSE)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Infinite Series and Infinite Sequences

    1. Operations with Power Series

      • George Pólya, Gabor Szegö
      Pages 1-15

    2. Linear Transformations of Series. A Theorem of Cesàro

      • George Pólya, Gabor Szegö
      Pages 15-23

    3. The Structure of Real Sequences and Series

      • George Pólya, Gabor Szegö
      Pages 23-32

    4. Miscellaneous Problems

      • George Pólya, Gabor Szegö
      Pages 32-45

  3. Integration

    1. The Integral as the Limit of a Sum of Rectangles

      • George Pólya, Gabor Szegö
      Pages 46-62

    2. Inequalities

      • George Pólya, Gabor Szegö
      Pages 62-75

    3. Some Properties of Real Functions

      • George Pólya, Gabor Szegö
      Pages 75-84

    4. Various Types of Equidistribution

      • George Pólya, Gabor Szegö
      Pages 85-95

    5. Functions of Large Numbers

      • George Pólya, Gabor Szegö
      Pages 95-102

  4. Functions of One Complex Variable. General Part

    1. Complex Numbers and Number Sequences

      • George Pólya, Gabor Szegö
      Pages 103-113

    2. Mappings and Vector Fields

      • George Pólya, Gabor Szegö
      Pages 113-124

    3. Some Geometrical Aspects of Complex Variables

      • George Pólya, Gabor Szegö
      Pages 125-132

    4. Cauchy’s Theorem. The Argument Principle

      • George Pólya, Gabor Szegö
      Pages 133-145

    5. Sequences of Analytic Functions

      • George Pólya, Gabor Szegö
      Pages 145-157

    6. The Maximum Principle

      • George Pólya, Gabor Szegö
      Pages 157-172

  5. Back Matter

    Pages 173-392
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Keywords

About this book

The present English edition is not a mere translation of the German original. Many new problems have been added and there are also other changes, mostly minor. Yet all the alterations amount to less than ten percent of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not introduced any essentially new subject matter, although the mathematical fashion has greatly changed since 1924. We have restricted ourselves to supplementing the topics originally chosen. Some of our problems first published in this work have given rise to extensive research. To include all such developments would have changed the character of the work, and even an incomplete account, which would be unsatisfactory in itself, would have cost too much labor and taken up too much space. We have to thank many readers who, since the publication of this work almost fifty years ago, communicated to us various remarks on it, some of which have been incorporated into this edition. We have not listed their names; we have forgotten the origin of some contributions, and an incomplete list would have been even less desirable than no list. The first volume has been translated by Mrs. Dorothee Aeppli, the second volume by Professor Claude Billigheimer. We wish to express our warmest thanks to both for the unselfish devotion and scrupulous conscientiousness with which they attacked their far from easy task.

Authors and Affiliations

  • Department of Mathematics, Stanford University, Stanford, USA

    George Pólya, Gabor Szegö

Bibliographic Information

  • Book Title: Problems and Theorems in Analysis

  • Book Subtitle: Series · Integral Calculus · Theory of Functions

  • Authors: George Pólya, Gabor Szegö

  • Series Title: Springer Study Edition

  • DOI: https://doi.org/10.1007/978-1-4757-1640-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1972

  • Softcover ISBN: 978-0-387-90224-1Published: 20 December 1976

  • eBook ISBN: 978-1-4757-1640-5Published: 17 April 2013

  • Series ISSN: 0172-6234

  • Edition Number: 1

  • Number of Pages: XIX, 392

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: Originally published as Band 193 of the series: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen

  • Topics: Real Functions

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