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Primer of Modern Analysis

  • Kennan T. Smith

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Part I

    1. Front Matter
      Pages 1-1
    2. Kennan T. Smith
      Pages 3-14
    3. Kennan T. Smith
      Pages 15-33
    4. Kennan T. Smith
      Pages 34-49
    5. Kennan T. Smith
      Pages 50-79
    6. Kennan T. Smith
      Pages 80-88
    7. Kennan T. Smith
      Pages 89-119
  3. Part II

    1. Front Matter
      Pages 121-121
    2. Kennan T. Smith
      Pages 123-157
    3. Kennan T. Smith
      Pages 158-177
    4. Kennan T. Smith
      Pages 178-222
    5. Kennan T. Smith
      Pages 223-248
    6. Kennan T. Smith
      Pages 249-277
    7. Kennan T. Smith
      Pages 278-288
  4. Part III

    1. Front Matter
      Pages 289-289
    2. Kennan T. Smith
      Pages 291-347
    3. Kennan T. Smith
      Pages 348-370
    4. Kennan T. Smith
      Pages 371-395
    5. Kennan T. Smith
      Pages 396-415
    6. Kennan T. Smith
      Pages 416-442
  5. Back Matter
    Pages 443-447

About this book

Introduction

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.

Keywords

Algebra Analysis Calculation Derivative Manifold Maximum Minimum calculus differential equation fixed-point theorem function geometry logarithm measure theorem

Authors and affiliations

  • Kennan T. Smith
    • 1
  1. 1.Mathematics DepartmentOregon State UniversityCorvallisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1144-0
  • Copyright Information Springer Science+Business Media New York 1983
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7021-8
  • Online ISBN 978-1-4612-1144-0
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site