LEADER 02832nam 22005175 450 001 9910300118703321 005 20211109143946.0 010 $a3-319-95321-4 024 7 $a10.1007/978-3-319-95321-2 035 $a(CKB)4100000007127638 035 $a(DE-He213)978-3-319-95321-2 035 $a(MiAaPQ)EBC6314726 035 $a(PPN)232472157 035 $a(EXLCZ)994100000007127638 100 $a20181111d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Kurzweil-Henstock Integral for Undergraduates $eA Promenade Along the Marvelous Theory of Integration /$fby Alessandro Fonda 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (X, 216 p. 24 illus., 5 illus. in color.) 225 1 $aCompact Textbooks in Mathematics,$x2296-4568 311 $a3-319-95320-6 327 $aFunctions 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. 330 $aThis beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes?Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach?Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs. 410 0$aCompact Textbooks in Mathematics,$x2296-4568 606 $aFunctions of real variables 606 $aMeasure theory 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 615 0$aFunctions of real variables. 615 0$aMeasure theory. 615 14$aReal Functions. 615 24$aMeasure and Integration. 676 $a515 700 $aFonda$b Alessandro$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756044 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300118703321 996 $aThe Kurzweil-Henstock Integral for Undergraduates$91896723 997 $aUNINA