Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

A Handbook of Real Variables

With Applications to Differential Equations and Fourier Analysis

  • Book
  • © 2004

Overview

Authors:
  1. Steven G. Krantz

    1. Department of Mathematics, Washington University, St. Louis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Completely self-contained, methodical exposition for the mathematically-inclined researcher; also valuable as a study guide for students
  • Realistic, meaningful connections to ordinary differential equations, boundary value problems, and Fourier analysis
  • Example-driven, incisive explanations of every important idea, with suitable cross-references for ease of use

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
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 (11 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Basics

    • Steven G. Krantz
    Pages 1-10

  3. Sequences

    • Steven G. Krantz
    Pages 11-19

  4. Series

    • Steven G. Krantz
    Pages 21-38

  5. The Topology of the Real Line

    • Steven G. Krantz
    Pages 39-52

  6. Limits and the Continuity of Functions

    • Steven G. Krantz
    Pages 53-69

  7. The Derivative

    • Steven G. Krantz
    Pages 71-84

  8. The Integral

    • Steven G. Krantz
    Pages 85-101

  9. Sequences and Series of Functions

    • Steven G. Krantz
    Pages 103-112

  10. Some Special Functions

    • Steven G. Krantz
    Pages 113-138

  11. Advanced Topics

    • Steven G. Krantz
    Pages 139-152

  12. Differential Equations

    • Steven G. Krantz
    Pages 153-176

  13. Back Matter

    Pages 177-201
    Download chapter PDF
Back to top

Keywords

About this book

The subject of real analysis dates to the mid-nineteenth century - the days of Riemann and Cauchy and Weierstrass. Real analysis grew up as a way to make the calculus rigorous. Today the two subjects are intertwined in most people's minds. Yet calculus is only the first step of a long journey, and real analysis is one of the first great triumphs along that road. In real analysis we learn the rigorous theories of sequences and series, and the profound new insights that these tools make possible. We learn of the completeness of the real number system, and how this property makes the real numbers the natural set of limit points for the rational numbers. We learn of compact sets and uniform convergence. The great classical examples, such as the Weierstrass nowhere-differentiable function and the Cantor set, are part of the bedrock of the subject. Of course complete and rigorous treatments of the derivative and the integral are essential parts of this process. The Weierstrass approximation theorem, the Riemann integral, the Cauchy property for sequences, and many other deep ideas round out the picture of a powerful set of tools.

Reviews

"In eleven chapters, Krantz's book succeeds in providing a reference work for 'the working engineer or scientist' encompassing the essence of real analysis...Krantz's book suceeds in providing a reference work for "the working engineer or scientist" encompassing the essence of real analysis. ... True to the idea of a handbook, there are good, but brief, explanations, well-chosen examples, and only a few proofs. In addition to the book's principal audience, students preparing for exams at either the undergraduate or master's level will find this a valuable resource." (MAA Reviews)

"The purpose of this book is to acknowledge that there is a large audience of scientists and others who wish to use the fruits of real analysis, and who are not equipped to stop and appreciate all the theory.  This handbook uses ample examples and brief explanations and must give an opportunity to users of real analysis quickly to look up ideas, without axiomatic machinery and without becoming bogged down in long explanations and proofs. . . This very good written book can be highly recommended to everyone who are teaching or researching in the field of applied mathematics. The book is also of interest to graduate students, researchers in physics, engineering, economics, and other applied sciences." (ZAA)

Authors and Affiliations

  • Department of Mathematics, Washington University, St. Louis, USA

    Steven G. Krantz

Bibliographic Information

  • Book Title: A Handbook of Real Variables

  • Book Subtitle: With Applications to Differential Equations and Fourier Analysis

  • Authors: Steven G. Krantz

  • DOI: https://doi.org/10.1007/978-0-8176-8128-9

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2004

  • Hardcover ISBN: 978-0-8176-4329-4Published: 18 November 2003

  • Softcover ISBN: 978-1-4612-6409-5Published: 05 September 2012

  • eBook ISBN: 978-0-8176-8128-9Published: 28 June 2011

  • Edition Number: 1

  • Number of Pages: XIII, 201

  • Topics: Real Functions, Functional Analysis, Fourier Analysis, Ordinary Differential Equations

Publish with us

Policies and ethics

Back to top

Search

Navigation