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The Kurzweil-Henstock Integral for Undergraduates

A Promenade Along the Marvelous Theory of Integration

  • Alessandro Fonda

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Alessandro Fonda
    Pages 1-59
  3. Alessandro Fonda
    Pages 61-123
  4. Alessandro Fonda
    Pages 125-173
  5. Back Matter
    Pages 175-222

About this book

Introduction

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.

Keywords

integration kurzweil–henstock integral riemann sums fundamental theorem of calculus lebesgue integral differential forms gauss formula stokes–cartan formula banach–tarski paradox

Authors and affiliations

  • Alessandro Fonda
    • 1
  1. 1.Dipartimento di Matematica e GeoscienzeUniversità degli Studi di TriesteTriesteItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-95321-2
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-95320-5
  • Online ISBN 978-3-319-95321-2
  • Series Print ISSN 2296-4568
  • Series Online ISSN 2296-455X
  • Buy this book on publisher's site
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