{"product_id":"9783319160528","title":"Universitext: Analytic and Differential Functions, Manifolds and Riemann Surfaces","description":"\u003ch1\u003eUniversitext: Analytic and Differential Functions, Manifolds and Riemann Surfaces\u003c\/h1\u003e \u003ch2\u003eGodement, Roger; Ray, Urmie\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eVolume 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.\u003c\/p\u003e\u003cp\u003eBesides 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).\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2015-04-16\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319160528\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-16053-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 321\u003c\/p\u003e ","brand":"Springer-Verlag Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":45987047800972,"sku":"9783319160528","price":71.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319160528.jpg?v=1775729241","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319160528","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}