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

Format:

Book

Author/Creator:

Godement, Roger, Author.

Series:

Universitext, 0172-5939

Language:

English

Subjects (All):

Functions of real variables.

Real Functions.

Local Subjects:

Real Functions.

Physical Description:

1 online resource (VII, 321 p. 25 illus.)

Edition:

1st ed. 2015.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2015.

Language Note:

English

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).

Contents:

VIII Cauchy Theory

IX Multivariate Differential and Integral Calculus

X The Riemann Surface of an Algebraic Function.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-16053-2

OCLC:

1066182310