Analysis III : Analytic and Differential Functions, Manifolds and Riemann Surfaces / by Roger Godement
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | Cham : Springer International Publishing : Imprint: Springer |
| 出版年 | 2015 |
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| 書誌ID | OB01016497 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | VIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function. License restrictions may limit access 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) |
| 著者標目 | *Godement, Roger SpringerLink (Online service) |
| 統一書名標目 | Universitext, |
| 件 名 | LCSH:Mathematics FREE:Mathematics FREE:Real Functions |
| 分 類 | LCC:QA331.5 DC23:515.8 |
| 巻冊次 | ISBN:9783319160535 RefWorks出力（各巻） print ; ISBN:9783319160528 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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※2020年8月16日以降