Analytic and differential functions, manifolds and Riemann surfaces
著者
書誌事項
Analytic and differential functions, manifolds and Riemann surfaces
（Universitext, . Analysis ; 3）
Springer, c2015
- タイトル別名
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Analyse mathématique
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注記
Translation of: Analyse mathématique
Includes index
内容説明・目次
内容説明
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).
目次
VIII Cauchy Theory.- IX Multivariate Differential and Integral Calculus.- X The Riemann Surface of an Algebraic Function.
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