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The Kurzweil-Henstock integral for u...

Fonda, Alessandro.

The Kurzweil-Henstock integral for undergraduatesa promenade along the marvelous theory of integration /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Kurzweil-Henstock integral for undergraduatesby Alessandro Fonda.
Reminder of title:	a promenade along the marvelous theory of integration /
Author:	Fonda, Alessandro.
Published:	Cham :Springer International Publishing :2018.
Description:	x, 216 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Henstock-Kurzweil integral.
Online resource:	https://doi.org/10.1007/978-3-319-95321-2
ISBN:	9783319953212$q(electronic bk.)

The Kurzweil-Henstock integral for undergraduatesa promenade along the marvelous theory of integration /
Fonda, Alessandro.

The Kurzweil-Henstock integral for undergraduatesa promenade along the marvelous theory of integration /[electronic resource] :by Alessandro Fonda. - Cham :Springer International Publishing :2018. - x, 216 p. :ill. (some col.), digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

Functions of one real variable -- Functions of several real variables -- Differential forms -- Differential calculus in RN -- The Stokes-Cartan and the Poincare theorems -- On differentiable manifolds -- The Banach-Tarski paradox -- A brief historical note.

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.

ISBN: 9783319953212$q(electronic bk.)

Standard No.: 10.1007/978-3-319-95321-2doiSubjects--Topical Terms:

247411
Henstock-Kurzweil integral.

LC Class. No.: QA312 / .F663 2018

Dewey Class. No.: 515.43

The Kurzweil-Henstock integral for undergraduatesa promenade along the marvelous theory of integration /
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520 $a 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.
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