Overview
- 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)
Keywords
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
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