Analysis. III, Analytic and differential functions, manifolds and Riemann surfaces [electronic resource] / Roger Godement ; translated by Urmie Ray.
Godement, Roger, author.; Ray, Urmie, translator.
2015
QA300
Available Online

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Title Analysis. III, Analytic and differential functions, manifolds and Riemann surfaces [electronic resource] / Roger Godement ; translated by Urmie Ray.
Author Godement, Roger, author.
Uniform Title Analyse mathematique III. English
ISBN 9783319160535 electronic book
3319160532 electronic book
9783319160528
DOI https://doi.org/10.1007/978-3-319-16053-5
Published Cham : Springer, 2015.
Language English
Description 1 online resource (vii, 321 pages) : illustrations.
Other Standard Identifiers 10.1007/978-3-319-16053-5 doi
Call Number QA300
Dewey Decimal Classification 515
Summary 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).
Note Includes index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed April 10, 2015).
Added Author Ray, Urmie, translator.
Series Universitext.
Available in Other Form Print version: 9783319160528
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VIII Cauchy Theory
IX Multivariate Differential and Integral Calculus
X The Riemann Surface of an Algebraic Function.

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