Analysis III: Analytic and Differential Functions, Manifolds and Riemann Surfaces (Universitext)
Language: English
Published by Springer, 2015
Series: Book 178 of 261 - Universitext
- Softcover
- New
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In English.
Seller Inventory # ria9783319160528_new
- Title
- Analysis III: Analytic and Differential Functions, Manifolds and Riemann Surfaces (Universitext)
- Author
- Godement, Roger
- Publisher
- Springer
- Publication year
- 2015
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 3319160524
- ISBN 13
- 9783319160528
- Series
- Book 178 of 261: Universitext
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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