Analysis III : Analytic and Differential Functions, Manifolds and Riemann Surfaces Paperback / softback
Part of the Universitext series
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).
- Format: Paperback / softback
- Pages: 321 pages, 25 black & white illustrations, biography
- Publisher: Springer International Publishing AG
- Publication Date: 05/04/2015
- Category: Real analysis, real variables
- ISBN: 9783319160528
- PDF from £15.29