Analysis III [[electronic resource] ] : Analytic and Differential Functions, Manifolds and Riemann Surfaces / / by Roger Godement

• Autore: Godement Roger
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
• Edizione: 1st ed. 2015.
• Descrizione fisica: 1 online resource (VII, 321 p. 25 illus.)
• Disciplina: 515.8
• Soggetto topico: Functions of real variables; Real Functions
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: VIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function.
• Sommario/riassunto: 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).
• Titolo autorizzato: Analysis III
• ISBN: 3-319-16053-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910299767503321
• Lo trovi qui: Univ. Federico II
• Serie: Universitext, . 0172-5939