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000726465 020__ $$a9783319160535$$qelectronic book
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000726465 0247_ $$a10.1007/978-3-319-16053-5$$2doi
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000726465 050_4 $$aQA300
000726465 08204 $$a515$$223
000726465 1001_ $$aGodement, Roger,$$eauthor.
000726465 24010 $$aAnalyse mathematique III.$$lEnglish
000726465 24510 $$aAnalysis.$$nIII,$$pAnalytic and differential functions, manifolds and Riemann surfaces$$h[electronic resource] /$$cRoger Godement ; translated by Urmie Ray.
000726465 24630 $$aAnalytic and differential functions, manifolds and Riemann surfaces
000726465 2463_ $$aAnalysis 3
000726465 264_1 $$aCham :$$bSpringer,$$c2015.
000726465 300__ $$a1 online resource (vii, 321 pages) :$$billustrations.
000726465 336__ $$atext$$btxt$$2rdacontent
000726465 337__ $$acomputer$$bc$$2rdamedia
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000726465 4901_ $$aUniversitext,$$x0172-5939
000726465 500__ $$aIncludes index.
000726465 5050_ $$aVIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function.
000726465 506__ $$aAccess limited to authorized users.
000726465 520__ $$aVolume III sets out classical Cauchy theory. It is much more geared towards its innumerable applications than towards a more or less complete theory of analytic functions. Cauchy-type curvilinear integrals are then shown to generalize to any number of real variables (differential forms, Stokes-type formulas). The fundamentals of the theory of manifolds are then presented, mainly to provide the reader with a "canonical'' language and with some important theorems (change of variables in integration, differential equations). A final chapter shows how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject that is rarely addressed in the general literature though it only requires elementary techniques. Besides the Lebesgue integral, Volume IV will set out a piece of specialized mathematics towards which the entire content of the previous volumes will converge: Jacobi, Riemann, Dedekind series and infinite products, elliptic functions, classical theory of modular functions and its modern version using the structure of the Lie algebra of SL(2,R).
000726465 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed April 10, 2015).
000726465 650_0 $$aMathematical analysis.
000726465 650_0 $$aAlgebra.
000726465 7001_ $$aRay, Urmie,$$etranslator.
000726465 77608 $$iPrint version:$$z9783319160528
000726465 830_0 $$aUniversitext.
000726465 852__ $$bebk
000726465 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-16053-5$$zOnline Access$$91397441.1
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