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Analysis III = Analytic and Differential Functions, Manifolds and Riemann Surfaces /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Analysis III/ by Roger Godement.
Reminder of title:	Analytic and Differential Functions, Manifolds and Riemann Surfaces /
Author:	Godement, Roger.
Description:	VII, 321 p. 25 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functions of real variables. -
Online resource:	https://doi.org/10.1007/978-3-319-16053-5
ISBN:	9783319160535

Analysis III = Analytic and Differential Functions, Manifolds and Riemann Surfaces /
Godement, Roger.

Analysis IIIAnalytic and Differential Functions, Manifolds and Riemann Surfaces /[electronic resource] :by Roger Godement. - 1st ed. 2015. - VII, 321 p. 25 illus.online resource. - Universitext,0172-5939. - Universitext,.

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).

ISBN: 9783319160535

Standard No.: 10.1007/978-3-319-16053-5doiSubjects--Topical Terms:

792248
Functions of real variables.

LC Class. No.: QA331.5

Dewey Class. No.: 515.8

Analysis III = Analytic and Differential Functions, Manifolds and Riemann Surfaces /
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