Analysis. III, Analytic and differential functions, manifolds and Riemann surfaces [electronic resource] / Roger Godement ; translated by Urmie Ray.
2015
QA300
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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
3319160532 electronic book
9783319160528
Published
Cham : Springer, 2015.
Language
English
Description
1 online resource (vii, 321 pages) : illustrations.
Item Number
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.
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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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Table of Contents
VIII Cauchy Theory
IX Multivariate Differential and Integral Calculus
X The Riemann Surface of an Algebraic Function.
IX Multivariate Differential and Integral Calculus
X The Riemann Surface of an Algebraic Function.