From Calculus to Analysis

  • Steen Pedersen

Table of contents

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

    1. Front Matter
      Pages 1-2
    2. Steen Pedersen
      Pages 3-43
    3. Steen Pedersen
      Pages 45-50
    4. Steen Pedersen
      Pages 51-68
    5. Steen Pedersen
      Pages 69-75
    6. Steen Pedersen
      Pages 77-89
    7. Steen Pedersen
      Pages 91-126
    8. Steen Pedersen
      Pages 127-155
    9. Steen Pedersen
      Pages 157-173
  3. Part II

    1. Front Matter
      Pages 174-175
    2. Steen Pedersen
      Pages 177-204
    3. Steen Pedersen
      Pages 205-228
    4. Steen Pedersen
      Pages 229-245
    5. Steen Pedersen
      Pages 247-279
    6. Steen Pedersen
      Pages 281-295
  4. Back Matter
    Pages 297-342

About this book

Introduction

This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers.  In addition to the standard results of advanced calculus, the book  contains several interesting applications of these results.

The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section

Keywords

Derivatives Fourier Series Number Theory Real Variables Set Theory

Authors and affiliations

  • Steen Pedersen
    • 1
  1. 1.Department of MathematicsWright State UniversityDaytonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-13641-7
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-13640-0
  • Online ISBN 978-3-319-13641-7
  • About this book
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