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© 1994

A First Course in Analysis

Textbook

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

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Background: Number Systems

    1. George Pedrick
      Pages 1-33
  3. Analysis

    1. Front Matter
      Pages 35-35
    2. George Pedrick
      Pages 37-63
    3. George Pedrick
      Pages 64-96
    4. George Pedrick
      Pages 97-130
  4. Foundations of Calculus

    1. Front Matter
      Pages 131-131
    2. George Pedrick
      Pages 133-168
    3. George Pedrick
      Pages 169-217
    4. George Pedrick
      Pages 218-265
  5. Back Matter
    Pages 266-279

About this book

Introduction

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.

Keywords

Derivative Fourier series Fundamental theorem of calculus calculus compactness continuous function differential equation improper integral logarithm measure

Authors and affiliations

  1. 1.OaklandUSA

About the authors


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
  • Copyright Information Springer-Verlag New York, Inc. 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-94108-0
  • Softcover ISBN 978-1-4612-6435-4
  • eBook ISBN 978-1-4419-8554-5
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages XXI, 279
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site