解析３：解析・微分関数、多様性とリーマン面（テキスト・英訳） Analysis III : Analytic and Differential Functions, Manifolds and Riemann Surfaces (Universitext) （2015）

Godement, Roger/ Ray, Urmie (TRN)

Springer International Publishing AG（2015/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 321 p.
• 商品コード 9783319160528

Full Description

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).

Contents

VIII Cauchy Theory.- IX Multivariate Differential and Integral Calculus.- X The Riemann Surface of an Algebraic Function.