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A First Course in Analysis

  • Textbook
  • © 1994

Overview

Authors:
  1. George Pedrick

    1. Oakland, USA

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxi
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  2. Background: Number Systems

    1. Background: Number Systems

      • George Pedrick
      Pages 1-33

  3. Analysis

    1. Front Matter

      Pages 35-35
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    2. Approximation: The Real Numbers

      • George Pedrick
      Pages 37-63

    3. The Extreme-Value Problem

      • George Pedrick
      Pages 64-96

    4. Continuous Functions

      • George Pedrick
      Pages 97-130

  4. Foundations of Calculus

    1. Front Matter

      Pages 131-131
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    2. Differentiation

      • George Pedrick
      Pages 133-168

    3. Integration

      • George Pedrick
      Pages 169-217

    4. Infinite Series

      • George Pedrick
      Pages 218-265

  5. Back Matter

    Pages 266-279
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Keywords

About this book

The first course in Analysis, which follows calculus, along with other courses, such as differential equations and elementary linear algebra, in the curricu­ lum, presents special pedagogical challenges. There is a change of stress from computational manipulation to "proof. " Indeed, the course can become more a course in Logic than one in Analysis. Many students, caught short by a weak command of the means of mathematical discourse and unsure of what is expected of them, what "the game" is, suffer bouts of a kind of mental paralysis. This text attempts to address these problems in several ways: First, we have attempted to define "the game" as that of "inquiry," by using a form of exposition that begins with a question and proceeds to analyze, ultimately to answer it, bringing in definitions, arguments, conjectures, exam­ ples, etc. , as they arise naturally in the course of a narrative discussion of the question. (The true, historical narrative is too convoluted to serve for first explanations, so no attempt at historical accuracy has been made; our narra­ tives are completely contrived. ) Second, we have kept the logic informal, especially in the course of preliminary speculative discussions, where common sense and plausibility­ tempered by mild skepticism-serve to energize the inquiry.

Authors and Affiliations

  • Oakland, USA

    George Pedrick

About the author



Bibliographic Information

  • Book Title: A First Course in Analysis

  • Authors: George Pedrick

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4419-8554-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94108-0Published: 11 March 1994

  • Softcover ISBN: 978-1-4612-6435-4Published: 05 September 2012

  • eBook ISBN: 978-1-4419-8554-5Published: 10 September 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XXI, 279

  • Topics: Analysis

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