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

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

Roger Godement, Urmie Ray

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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). click to read more

Categories:
Mathematics – Analysis

Year:
2015

Edition:
1

Publisher:
Springer

Language:
english

Pages:
321 / 325

ISBN 10:
3319160524

ISBN 13:
9783319160535

Series:
Universitext

File:
PDF, 2.18 MB