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A First Course in Real Analysis

  • Textbook
  • © 1994

Overview

Authors:
  1. Sterling K. Berberian

    1. Department of Mathematics, The University of Texas at Austin, Austin, USA

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

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About this book

Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun­ dations of calculus (including the "Fundamental Theorem"), and, along theway, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Axioms for the Field ℝ of Real Numbers

    • Sterling K. Berberian
    Pages 1-14

  3. First Properties of ℝ

    • Sterling K. Berberian
    Pages 15-32

  4. Sequences of Real Numbers, Convergence

    • Sterling K. Berberian
    Pages 33-55

  5. Special Subsets of ℝ

    • Sterling K. Berberian
    Pages 56-79

  6. Continuity

    • Sterling K. Berberian
    Pages 80-97

  7. Continuous Functions on an Interval

    • Sterling K. Berberian
    Pages 98-109

  8. Limits of Functions

    • Sterling K. Berberian
    Pages 110-120

  9. Derivatives

    • Sterling K. Berberian
    Pages 121-134

  10. Riemann Integral

    • Sterling K. Berberian
    Pages 135-178

  11. Infinite Series

    • Sterling K. Berberian
    Pages 179-193

  12. Beyond the Riemann Integral

    • Sterling K. Berberian
    Pages 194-219

  13. Back Matter

    Pages 220-240
    Download chapter PDF
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Authors and Affiliations

  • Department of Mathematics, The University of Texas at Austin, Austin, USA

    Sterling K. Berberian

Accessibility Information

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Bibliographic Information

  • Book Title: A First Course in Real Analysis

  • Authors: Sterling K. Berberian

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4419-8548-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1994

  • Hardcover ISBN: 978-0-387-94217-9Published: 24 June 1994

  • Softcover ISBN: 978-1-4612-6433-0Published: 07 September 2012

  • eBook ISBN: 978-1-4419-8548-4Published: 10 September 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XI, 240

  • Topics: Real Functions

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