Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Undergraduate Analysis

  • Textbook
  • © 1983

Overview

Authors:
  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (21 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Review of Calculus

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Sets and Mappings

      • Serge Lang
      Pages 3-15

    3. Real Numbers

      • Serge Lang
      Pages 16-31

    4. Limits and Continuous Functions

      • Serge Lang
      Pages 32-61

    5. Differentiation

      • Serge Lang
      Pages 62-72

    6. Elementary Functions

      • Serge Lang
      Pages 73-91

    7. The Elementary Real Integral

      • Serge Lang
      Pages 92-105

  3. Convergence

    1. Front Matter

      Pages 107-108
      Download chapter PDF

    2. Normed Vector Spaces

      • Serge Lang
      Pages 109-132

    3. Limits

      • Serge Lang
      Pages 133-156

    4. Compactness

      • Serge Lang
      Pages 157-178

    5. Series

      • Serge Lang
      Pages 179-210

    6. The Integral in One Variable

      • Serge Lang
      Pages 211-238

  4. Applications of the Integral

    1. Front Matter

      Pages 239-240
      Download chapter PDF

    2. Approximation with Convolutions

      • Serge Lang
      Pages 241-247

    3. Fourier Series

      • Serge Lang
      Pages 248-275

    4. Improper Integrals

      • Serge Lang
      Pages 276-296

    5. The Fourier Integral

      • Serge Lang
      Pages 297-310

  5. Calculus in Vector Spaces

    1. Front Matter

      Pages 311-312
      Download chapter PDF
Back to top

Keywords

About this book

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.

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

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

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

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1983

  • eBook ISBN: 978-1-4757-1801-0Published: 14 March 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XIII, 546

  • Number of Illustrations: 17 b/w illustrations

  • Additional Information: Originally published by Addison-Wesley, Reading, MA 1968

  • Topics: Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation