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  • Textbook
  • © 2015

From Calculus to Analysis

Authors:

  • Exercises embedded in the text with solutions at the end of each section

  • Approaches the real numbers through infinite decimals

  • Classroom tested with both mathematics and mathematics education majors

  • Includes supplementary material: sn.pub/extras

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xix
  2. Part I

    1. Front Matter

      Pages 1-2
    2. Limits

      • Steen Pedersen
      Pages 3-43
    3. Introduction to Continuity

      • Steen Pedersen
      Pages 45-50
    4. Sets of Real Numbers

      • Steen Pedersen
      Pages 51-68
    5. Counting

      • Steen Pedersen
      Pages 69-75
    6. Continuity

      • Steen Pedersen
      Pages 77-89
    7. Derivatives and Their Applications

      • Steen Pedersen
      Pages 91-126
    8. The Riemann Integral

      • Steen Pedersen
      Pages 127-155
    9. The Logarithm and the Exponential Function

      • Steen Pedersen
      Pages 157-173
  3. Part II

    1. Front Matter

      Pages 174-175
    2. Convergence of Sequences

      • Steen Pedersen
      Pages 177-204
    3. Series

      • Steen Pedersen
      Pages 205-228
    4. Trigonometric Functions and Applications

      • Steen Pedersen
      Pages 229-245
    5. Fourier Series

      • Steen Pedersen
      Pages 247-279
    6. Topology

      • Steen Pedersen
      Pages 281-295
  4. Back Matter

    Pages 297-342

About this book

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.

Reviews

“This book is mainly addressed to undergraduate students and it is intended to be a two-semester analysis course for these students. … As the title suggests, this textbook is intended to fill the gap between a calculus course and a student’s first serious real analysis course. … Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide.” (Teodora-Liliana Rădulescu, zbMATH 1315.26001, 2015)

Authors and Affiliations

  • Department of Mathematics, Wright State University, Dayton, USA

    Steen Pedersen

About the author

Steen Pedersen, Ph.D. is a Professor of Mathematics at Wright State University in Dayton, Ohio, USA.  His research interests include fractals, metric geometry, fourier analysis, spectral theory, and operator algebras.

Bibliographic Information

  • Book Title: From Calculus to Analysis

  • Authors: Steen Pedersen

  • DOI: https://doi.org/10.1007/978-3-319-13641-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-13640-0Published: 07 April 2015

  • Softcover ISBN: 978-3-319-38136-7Published: 09 October 2016

  • eBook ISBN: 978-3-319-13641-7Published: 21 March 2015

  • Edition Number: 1

  • Number of Pages: XIX, 342

  • Number of Illustrations: 34 b/w illustrations, 14 illustrations in colour

  • Topics: Integral Equations, Algebra, Analysis

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 79.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access