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The Kurzweil-Henstock Integral for Undergraduates

A Promenade Along the Marvelous Theory of Integration

  • Textbook
  • © 2018

Overview

Authors:
  1. Alessandro Fonda

    1. Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Trieste, Italy

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  • First undergraduate book on the Kurzweil-Henstock integral
  • Theory is developed also for functions of several variables and for differential forms
  • Didactical exposition of the subject
  • Avoid as much as possible unnecessary technicalities

Part of the book series: Compact Textbooks in Mathematics (CTM)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xii
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  2. Functions of One Real Variable

    • Alessandro Fonda
    Pages 1-59

  3. Functions of Several Real Variables

    • Alessandro Fonda
    Pages 61-123

  4. Differential Forms

    • Alessandro Fonda
    Pages 125-173

  5. Back Matter

    Pages 175-222
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Keywords

About this book

This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes–Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach–Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.

Reviews

“The author maintains here the exposition at a very didactic level, trying to avoid as much as possible unnecessary technicalities, which is a big advantage of this book. … In my point of view, the presented book is a useful tool for all mathematicians (not only for students) and I find it regrettable that this book was not written when I was a student.” (Andrey Zahariev, zbMath 1410.26007, 2019)

Authors and Affiliations

  • Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Trieste, Italy

    Alessandro Fonda

About the author

Alessandro Fonda, Università degli Studi di Trieste, Italy.

Bibliographic Information

  • Book Title: The Kurzweil-Henstock Integral for Undergraduates

  • Book Subtitle: A Promenade Along the Marvelous Theory of Integration

  • Authors: Alessandro Fonda

  • Series Title: Compact Textbooks in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-95321-2

  • Publisher: Birkhäuser Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Softcover ISBN: 978-3-319-95320-5Published: 22 November 2018

  • eBook ISBN: 978-3-319-95321-2Published: 11 November 2018

  • Series ISSN: 2296-4568

  • Series E-ISSN: 2296-455X

  • Edition Number: 1

  • Number of Pages: X, 216

  • Number of Illustrations: 19 b/w illustrations, 5 illustrations in colour

  • Topics: Real Functions, Measure and Integration

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