Analysis III : Analytic and Differential Functions, Manifolds and Riemann Surfaces Paperback / softback
by Roger Godement
Part of the Universitext series
Paperback / softback
Description
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).
Information
-
Out of stock
- Format:Paperback / softback
- Pages:321 pages, 25 Illustrations, black and white; VII, 321 p. 25 illus.
- Publisher:Springer International Publishing AG
- Publication Date:16/04/2015
- Category:
- ISBN:9783319160528
Other Formats
- PDF from £19.54
Information
-
Out of stock
- Format:Paperback / softback
- Pages:321 pages, 25 Illustrations, black and white; VII, 321 p. 25 illus.
- Publisher:Springer International Publishing AG
- Publication Date:16/04/2015
- Category:
- ISBN:9783319160528
