LEADER 03055nam 22005775 450 001 9910299767503321 005 20200701133757.0 010 $a3-319-16053-2 024 7 $a10.1007/978-3-319-16053-5 035 $a(CKB)3710000000404032 035 $a(SSID)ssj0001501324 035 $a(PQKBManifestationID)11830580 035 $a(PQKBTitleCode)TC0001501324 035 $a(PQKBWorkID)11522619 035 $a(PQKB)10401167 035 $a(DE-He213)978-3-319-16053-5 035 $a(MiAaPQ)EBC6314505 035 $a(MiAaPQ)EBC5587969 035 $a(Au-PeEL)EBL5587969 035 $a(OCoLC)1066182310 035 $a(PPN)185489885 035 $a(EXLCZ)993710000000404032 100 $a20150404d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis III $eAnalytic and Differential Functions, Manifolds and Riemann Surfaces /$fby Roger Godement 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (VII, 321 p. 25 illus.) 225 1 $aUniversitext,$x0172-5939 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-16052-4 327 $aVIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function. 330 $aVolume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a "canonical'' language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques. Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular functions and its modern version using the structure of the Lie algebra of SL(2,R). 410 0$aUniversitext,$x0172-5939 606 $aFunctions of real variables 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 615 0$aFunctions of real variables. 615 14$aReal Functions. 676 $a515.8 700 $aGodement$b Roger$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441293 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299767503321 996 $aAnalysis III$92508613 997 $aUNINA