Roger Godement

Analysis III (Universitext)

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ISBN 13:
9783319160528
author:
Roger Godement
format:
Paperback
publisher:
Springer
language:
English
Publication Year:
2015
Pages:
332
Dimensions:
15.5 x 1.9 x 23.5 cm
Genre:
Science & Nature, Mathematics, Calculus & Mathematical Analysis
Condition:
New
Availability:
Item usually sent within 5 working days
£33.98

Description

Volume III of Analysis by Roger Godement sets out classical Cauchy theory, focusing on its numerous applications rather than a comprehensive theory of analytic functions. This volume introduces Cauchy-type curvilinear integrals and shows how they generalize to any number of real variables. The fundamentals of the theory of manifolds are presented, providing a "canonical" language and important theorems such as change of variables in integration and differential equations. A final chapter demonstrates how these theorems can be used to construct the compact Riemann surface of an algebraic function, a subject rarely addressed in general literature. This volume builds upon the Lebesgue integral and introduces specialized mathematics that will converge with the content of previous volumes: 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).

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