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Primer of Modern Analysis

Directions for Knowing All Dark Things, Rhind Papyrus, 1800 B.C.

  • Textbook
  • © 1983

Overview

Authors:
  1. Kennan T. Smith

    1. Mathematics Department, Oregon State University, Corvallis, USA

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xv
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  2. Part I

    1. Front Matter

      Pages 1-1
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    2. Applications

      • Kennan T. Smith
      Pages 3-14

    3. Calculation of Derivatives

      • Kennan T. Smith
      Pages 15-33

    4. Deeper Properties of Continuous Functions

      • Kennan T. Smith
      Pages 34-49

    5. Riemann Integration

      • Kennan T. Smith
      Pages 50-79

    6. Taylor’s Formula

      • Kennan T. Smith
      Pages 80-88

    7. Sequences and Series

      • Kennan T. Smith
      Pages 89-119

  3. Part II

    1. Front Matter

      Pages 121-121
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    2. Metric Spaces

      • Kennan T. Smith
      Pages 123-157

    3. Functions from R1 to Rn

      • Kennan T. Smith
      Pages 158-177

    4. Algebra and Geometry in Rn

      • Kennan T. Smith
      Pages 178-222

    5. Linear Approximation

      • Kennan T. Smith
      Pages 223-248

    6. Surfaces

      • Kennan T. Smith
      Pages 249-277

    7. Higher Derivatives

      • Kennan T. Smith
      Pages 278-288

  4. Part III

    1. Front Matter

      Pages 289-289
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    2. Integration

      • Kennan T. Smith
      Pages 291-347

    3. Differentiation

      • Kennan T. Smith
      Pages 348-370

    4. Surface Area

      • Kennan T. Smith
      Pages 371-395

    5. The Brouwer Degree

      • Kennan T. Smith
      Pages 396-415
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Keywords

About this book

This book discusses some of the first principles of modern analysis. I t can be used for courses at several levels, depending upon the background and ability of the students. It was written on the premise that today's good students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.

Authors and Affiliations

  • Mathematics Department, Oregon State University, Corvallis, USA

    Kennan T. Smith

Bibliographic Information

  • Book Title: Primer of Modern Analysis

  • Book Subtitle: Directions for Knowing All Dark Things, Rhind Papyrus, 1800 B.C.

  • Authors: Kennan T. Smith

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1144-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

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

  • Hardcover ISBN: 978-0-387-90797-0Published: 08 August 1983

  • Softcover ISBN: 978-1-4612-7021-8Published: 27 September 2012

  • eBook ISBN: 978-1-4612-1144-0Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 2

  • Number of Pages: XV, 446

  • Additional Information: Originally published by Bogden & Guigley, Inc.

  • Topics: Analysis

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