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 R N , 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 StokesCartan formula. In the appendices, differential calculus in R N is reviewed, with the theory of differentiable manifolds. Also, the BanachTarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.

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

Autorentext
Alessandro Fonda, Università degli Studi di Trieste, Italy.

Inhalt
Functions of one real variable.- Functions of several real variables.- Differential forms.- Differential calculus in R N.- The StokesCartan and the Poincaré theorems.- On differentiable manifolds.- The BanachTarski paradox.- A brief historical note.