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The Kurzweil-Henstock Integral for Undergraduates: A Promenade Along the Marvelous Theory of Integration

By Alessandro Fonda

Book information

Publisher
Birkhäuser
Year
2018
ISBN
3319953206, 9783319953205
Language
english
Format
PDF
Filesize
3 MB (3248941 bytes)
Series
Compact Textbooks in Mathematics
Pages
xii+222\227
Time added
2018-12-21 10:55:39

Description

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 and easy to understand. 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.

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