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Compact Textbooks in Mathematics

The Kurzweil-Henstock Integral for Undergraduates

A Promenade Along the Marvelous Theory of Integration

Authors: Fonda, Alessandro

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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
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  • ISBN 978-3-319-95321-2
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Softcover $49.99
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  • ISBN 978-3-319-95320-5
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About this Textbook

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.

About the authors

Alessandro Fonda, Università degli Studi di Trieste, Italy.

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)

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $39.99
price for USA
  • ISBN 978-3-319-95321-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-95320-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
The Kurzweil-Henstock Integral for Undergraduates
Book Subtitle
A Promenade Along the Marvelous Theory of Integration
Authors
Series Title
Compact Textbooks in Mathematics
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-95321-2
DOI
10.1007/978-3-319-95321-2
Softcover ISBN
978-3-319-95320-5
Series ISSN
2296-4568
Edition Number
1
Number of Pages
X, 216
Number of Illustrations
19 b/w illustrations, 5 illustrations in colour
Topics

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