03055nam 22005775 450 991029976750332120200701133757.03-319-16053-210.1007/978-3-319-16053-5(CKB)3710000000404032(SSID)ssj0001501324(PQKBManifestationID)11830580(PQKBTitleCode)TC0001501324(PQKBWorkID)11522619(PQKB)10401167(DE-He213)978-3-319-16053-5(MiAaPQ)EBC6314505(MiAaPQ)EBC5587969(Au-PeEL)EBL5587969(OCoLC)1066182310(PPN)185489885(EXLCZ)99371000000040403220150404d2015 u| 0engurnn#008mamaatxtccrAnalysis III Analytic and Differential Functions, Manifolds and Riemann Surfaces /by Roger Godement1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (VII, 321 p. 25 illus.)Universitext,0172-5939Bibliographic Level Mode of Issuance: Monograph3-319-16052-4 VIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function.Volume 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).Universitext,0172-5939Functions of real variablesReal Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12171Functions of real variables.Real Functions.515.8Godement Rogerauthttp://id.loc.gov/vocabulary/relators/aut441293MiAaPQMiAaPQMiAaPQBOOK9910299767503321Analysis III2508613UNINA