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A First Course in Analysis

  • George Pedrick

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

  • George Pedrick
    • 1
  1. 1.OaklandUSA

Bibliographic information

  • 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
  • Print ISBN 978-1-4612-6435-4
  • Online ISBN 978-1-4419-8554-5
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site