Analysis. III, Analytic and differential functions, manifolds and Riemann surfaces [electronic resource]

• 作者： Godement, Roger.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Analyse mathematique III.
  • Analytic and differential functions, manifolds and Riemann surfaces
  • Analysis 3
  • Universitext
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Universitext
• 主題： Mathematical analysis , Algebra , Mathematics , Real Functions.
• ISBN： 9783319160535 (electronic bk.) 、 9783319160528 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: VIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function.
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• 摘要註: 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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