| 期刊全稱 | Analysis III | | 期刊簡稱 | Analytic and Differe | | 影響因子2023 | Roger Godement | | 視頻video | http://file.papertrans.cn/157/156138/156138.mp4 | | 發(fā)行地址 | 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 consideration | | 學(xué)科分類 | Universitext | | 圖書封面 |  | | 影響因子 | .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).. | | Pindex | Textbook 2015 |
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