Skip to main content
SpringerLink
Log in
Book cover

Real Analysis for the Undergraduate

With an Invitation to Functional Analysis

  • Textbook
  • © 2014

Overview

Authors:
  1. Matthew A. Pons

    1. North Central College, Naperville, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Engaging style makes complex concepts accessible to a broad audience

  • Examples and illustrations accompany formal proofs

  • Over 450 exercises help readers develop connections between the concrete and abstract

  • Includes supplementary material: sn.pub/extras

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 69.99
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

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-xviii
    Download chapter PDF

  2. The Real Numbers

    • Matthew A. Pons
    Pages 1-54

  3. Sequences in ℝ

    • Matthew A. Pons
    Pages 55-98

  4. Numerical Series

    • Matthew A. Pons
    Pages 99-135

  5. Continuity

    • Matthew A. Pons
    Pages 137-182

  6. The Derivative

    • Matthew A. Pons
    Pages 183-225

  7. Sequences and Series of Functions

    • Matthew A. Pons
    Pages 227-274

  8. The Riemann Integral

    • Matthew A. Pons
    Pages 275-323

  9. Lebesgue Measure on ℝ

    • Matthew A. Pons
    Pages 325-349

  10. Lebesgue Integration

    • Matthew A. Pons
    Pages 351-396

  11. Back Matter

    Pages 397-409
    Download chapter PDF
Back to top

Keywords

About this book

This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

Reviews

From the book reviews:

“This book is more than just an excellent introduction to real analysis at the undergraduate level. It also provides the basis for students to gain some experience in measure theory, Lebesgue integration, and functional analysis. … Summing Up: Highly recommended. Upper-division undergraduates and above.” (D. P. Turner, Choice, Vol. 52 (2), October, 2014)

“This book contains a reasonably complete exposition of real analysis theory which is needed for beginning undergraduate-level students. It includes basic material connected with this topic as well as more advanced problems. … All the topics are presented thoroughly. The book includes nice graphic illustrations of the problems considered.” (Ryszard J. Paẇlak, Mathematical Reviews, September, 2014)

Authors and Affiliations

  • North Central College, Naperville, USA

    Matthew A. Pons

About the author

Matthew A. Pons is Associate Professor of Mathematics at North Central College.

Bibliographic Information

  • Book Title: Real Analysis for the Undergraduate

  • Book Subtitle: With an Invitation to Functional Analysis

  • Authors: Matthew A. Pons

  • DOI: https://doi.org/10.1007/978-1-4614-9638-0

  • Publisher: Springer New York, NY

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

  • Copyright Information: Springer Science+Business Media New York 2014

  • Hardcover ISBN: 978-1-4614-9637-3Published: 25 January 2014

  • Softcover ISBN: 978-1-4939-4649-5Published: 27 August 2016

  • eBook ISBN: 978-1-4614-9638-0Published: 25 January 2014

  • Edition Number: 1

  • Number of Pages: XVIII, 409

  • Number of Illustrations: 43 b/w illustrations

  • Topics: Analysis, Real Functions, Functional Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation