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Analysis III : Analytic and Differential Functions, Manifolds and Riemann Surfaces, Paperback / softback Book

Analysis III : Analytic and Differential Functions, Manifolds and Riemann Surfaces Paperback / softback

Part of the Universitext series

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

  • Format: Paperback / softback
  • Pages: 321 pages, 25 black & white illustrations, biography
  • Publisher: Springer International Publishing AG
  • Publication Date:
  • Category: Real analysis, real variables
  • ISBN: 9783319160528

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