Analysis Iii: Analytic and Differential Functions, Manifolds and Riemann Surfaces by Roger GodementAnalysis Iii: Analytic and Differential Functions, Manifolds and Riemann Surfaces by Roger Godement

Analysis Iii: Analytic and Differential Functions, Manifolds and Riemann Surfaces

byRoger GodementEditorUrmie Ray

Paperback | April 16, 2015

Pricing and Purchase Info

$87.35 online 
$103.50 list price save 15%
Earn 437 plum® points

Prices and offers may vary in store

Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

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).

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major ...
Loading
Title:Analysis Iii: Analytic and Differential Functions, Manifolds and Riemann SurfacesFormat:PaperbackDimensions:321 pagesPublished:April 16, 2015Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319160524

ISBN - 13:9783319160528

Reviews

Table of Contents

VIII Cauchy Theory.- IX Multivariate Differential and Integral Calculus.- X The Riemann Surface of an Algebraic Function.