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Springer Analyse mathématique III: Fonctions analytiques, différentielles et variétés, surfaces de Riemann: 3

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Description

Ce vol. III expose la théorie classique de Cauchy dans un esprit orienté bien davantage vers ses innombrables utilisations que vers une théorie plus ou moins complète des fonctions analytiques. On montre ensuite comment les intégrales curvilignes à la Cauchy se généralisent à un nombre quelconque de variables réelles (formes différentielles, formules de type Stokes). Les bases de la théorie des variétés sont ensuite exposées, principalement pour fournir au lecteur le langage "canonique" et quelques théorèmes importants (changement de variables dans les intégrales, équations différentielles). Un dernier chapitre montre comment on peut utiliser ces théories pour construire la surface de Riemann compacte d'une fonction algébrique, sujet rarement traité dans la littérature non spécialisée bien que n'éxigeant que des techniques élémentaires. Un volume IV exposera, outre, l'intégrale de Lebesgue, un bloc de mathématiques spécialisées vers lequel convergera tout le contenu des volumes précédents: séries et produits infinis de Jacobi, Riemann, Dedekind, fonctions elliptiques, théorie classique des fonctions modulaires et la version moderne utilisant la structure de groupe de Lie de SL (2, R).

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
20 November 2001
Listed Since
31 December 2006

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