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Analysis.III,Analytic and differenti...

Godement, Roger.

Analysis.III,Analytic and differential functions, manifolds and Riemann surfaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analysis.by Roger Godement.
remainder title:	Analytic and differential functions, manifolds and Riemann surfaces
Author:	Godement, Roger.
Published:	Cham :Springer International Publishing :2015.
Description:	vii, 321 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematical analysis.
Online resource:	http://dx.doi.org/10.1007/978-3-319-16053-5
ISBN:	9783319160535 (electronic bk.)

Analysis.III,Analytic and differential functions, manifolds and Riemann surfaces
Godement, Roger.

Analysis.III,Analytic and differential functions, manifolds and Riemann surfaces[electronic resource] /Analytic and differential functions, manifolds and Riemann surfacesby Roger Godement. - Cham :Springer International Publishing :2015. - vii, 321 p. :ill., digital ;24 cm. - 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 (electronic bk.)

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

186133
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Analysis.III,Analytic and differential functions, manifolds and Riemann surfaces
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245 1 0 $a Analysis. $n III, $p Analytic and differential functions, manifolds and Riemann surfaces $h [electronic resource] / $c by Roger Godement.
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300 $a vii, 321 p. : $b ill., digital ; $c 24 cm.
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505 0 $a VIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function.
520 $a 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)
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