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© 1983

Undergraduate Analysis

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Review of Calculus

    1. Front Matter
      Pages 1-1
    2. Serge Lang
      Pages 3-15
    3. Serge Lang
      Pages 16-31
    4. Serge Lang
      Pages 32-61
    5. Serge Lang
      Pages 62-72
    6. Serge Lang
      Pages 73-91
    7. Serge Lang
      Pages 92-105
  3. Convergence

    1. Front Matter
      Pages 107-108
    2. Serge Lang
      Pages 109-132
    3. Serge Lang
      Pages 133-156
    4. Serge Lang
      Pages 157-178
    5. Serge Lang
      Pages 179-210
    6. Serge Lang
      Pages 211-238
  4. Applications of the Integral

    1. Front Matter
      Pages 239-240
    2. Serge Lang
      Pages 241-247
    3. Serge Lang
      Pages 248-275
    4. Serge Lang
      Pages 276-296
    5. Serge Lang
      Pages 297-310
  5. Calculus in Vector Spaces

    1. Front Matter
      Pages 311-312

About this book

Introduction

The present volume is a text designed for a first course in analysis. Although it is logically self-contained, it presupposes the mathematical maturity acquired by students who will ordinarily have had two years of calculus. When used in this context, most of the first part can be omitted, or reviewed extremely rapidly, or left to the students to read by themselves. The course can proceed immediately into Part Two after covering Chapters o and 1. However, the techniques of Part One are precisely those which are not emphasized in elementary calculus courses, since they are regarded as too sophisticated. The context of a third-year course is the first time that they are given proper emphasis, and thus it is important that Part One be thoroughly mastered. Emphasis has shifted from computational aspects of calculus to theoretical aspects: proofs for theorems concerning continuous 2 functions; sketching curves like x e-X, x log x, xlix which are usually regarded as too difficult for the more elementary courses; and other similar matters.

Keywords

Analysis Differentialrechnung Fourier series Integralrechnung calculus compactness convergence curve integral derivative differential calculus differential equation integral integration ordinary differential equation real number

Authors and affiliations

  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • Book Title Undergraduate Analysis
  • Authors Serge Lang
  • Series Title Undergraduate Texts in Mathematics
  • DOI https://doi.org/10.1007/978-1-4757-1801-0
  • Copyright Information Springer-Verlag New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-90800-7
  • Softcover ISBN 978-1-4757-1803-4
  • eBook ISBN 978-1-4757-1801-0
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XIII, 546
  • Number of Illustrations 17 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published by Addison-Wesley, Reading, MA 1968
  • Topics Analysis
  • Buy this book on publisher's site
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Reviews

Second Edition

S. Lang

Undergraduate Analysis

"[A] fine book . . . logically self-contained . . . This material can be gone over quickly by the really well-prepared reader, for it is one of the book’s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it."—AMERICAN MATHEMATICAL SOCIETY