Authors:
- Prefers ideas to calculations
- Explains the ideas without parsimony of words
- Based on 35 years of teaching at Paris University
- Blends mathematics skillfully with didactical and historical considerations
Part of the book series: Universitext (UTX)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
About this book
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).
Authors and Affiliations
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Paris, France
Roger Godement
About the author
Bibliographic Information
Book Title: Analysis III
Book Subtitle: Analytic and Differential Functions, Manifolds and Riemann Surfaces
Authors: Roger Godement
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-16053-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-16052-8Published: 16 April 2015
eBook ISBN: 978-3-319-16053-5Published: 04 April 2015
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: VII, 321
Number of Illustrations: 25 b/w illustrations
Topics: Real Functions