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OverviewThis 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. Full Product DetailsAuthor: Alessandro FondaPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: 1st ed. 2018 Weight: 0.454kg ISBN: 9783319953205ISBN 10: 3319953206 Pages: 216 Publication Date: 22 November 2018 Audience: College/higher education , Undergraduate Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsFunctions of one real variable.- Functions of several real variables.- Differential forms.- Differential calculus in RN.- The Stokes–Cartan and the Poincaré theorems.- On differentiable manifolds.- The Banach–Tarski paradox.- A brief historical note.ReviewsThe 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) “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) Author InformationAlessandro Fonda, Università degli Studi di Trieste, Italy. Tab Content 6Author Website:Countries AvailableAll regions |
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