Analysis. Roger Godement ; translated by Urmie Ray. III, Analytic and differential functions, manifolds and Riemann surfaces /
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...
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| Format: | Ebook |
| Language: | English French |
| Published: |
Cham :
Springer,
2015.
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| Series: | Universitext,
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| Subjects: | |
| Online Access: | Springer eBooks |
| Summary: | 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). |
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| Item Description: | Includes index. |
| Physical Description: | 1 online resource (vii, 321 pages) : illustrations. |
| Format: | Mode of access: World Wide Web. |
| ISBN: | 3319160532 9783319160535 |
| ISSN: | 0172-5939 |