The Kurzweil-Henstock Integral for Undergraduates - pr_206011

The Kurzweil-Henstock Integral for Undergraduates

A Promenade Along the Marvelous Theory of Integration

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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.

Product code: 9783319953205

ISBN 9783319953205
Dimensions (HxWxD in mm) H235xW155
Series Compact Textbooks in Mathematics
No. Of Pages 216
Publisher Birkhauser Verlag AG
Edition 1st ed. 2018
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.