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Functions of complex variables --- Geometric function theory
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Riemann surfaces. --- Functions of complex variables. --- Geometry, Analytic.
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Functions of complex variables --- Geometry, Analytic --- Riemann surfaces
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Elliptic functions. --- Functions, Theta. --- Theta functions --- Elliptic integrals --- Functions, Elliptic --- Integrals, Elliptic --- Transcendental functions --- Functions of complex variables --- Integrals, Hyperelliptic
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H. Cartan: Faisceaux analytiques cohérents.- P. Lelong: Fonctions plurisousharmoniques et formes différentielles positives.- E. Vesentini: Coomologia sulle varietà complesse, I.- A. Andreotti: Coomologia sulle varietà complesse, II.
Functional analysis -- Congresses. --- Functions of complex variables -- Congresses. --- Geometry, Algebraic -- Congresses. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Functions of complex variables --- Analytic functions --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Series, Taylor's --- Differential equations, partial. --- Partial differential equations --- Complex variables --- Elliptic functions --- Functions of real variables
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The book provides a complete presentation of complex analysis, starting with the theory of Riemann surfaces, including uniformization theory and a detailed treatment of the theory of compact Riemann surfaces, the Riemann-Roch theorem, Abel's theorem and Jacobi's inversion theorem. This motivates a short introduction into the theory of several complex variables, followed by the theory of Abelian functions up to the theta theorem. The last part of the book provides an introduction into the theory of higher modular functions.
Functions of complex variables -- Congresses. --- Mathematical analysis -- Congresses. --- Functions of complex variables --- Riemann surfaces --- Topology --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical analysis --- 517.1 Mathematical analysis --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Functions of a Complex Variable. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Differential equations, partial. --- Partial differential equations --- Riemann surfaces. --- Topology.
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Ce manuel introductif s'adresse à tout étudiant (classe préparatoire, université, école ingénieurs) connaissant les principes de bases en algèbre linéaire, calcul différentiel et intégral. Il aborde notamment les notions de : • fonctions holomorphes, • fonctions analytiques, • équations différentielles ordinaires, • séries de Fourier, • applications aux équations aux dérivées partielles. Il contient un grand nombre d'exemples illustrant en détail les nouveaux concepts et résultats. À la fin de chaque chapitre, l'étudiant trouvera des exercices de difficulté progressive, toujours accompagnés de leurs solutions. L'ouvrage « Exercices d'Analyse Complexe et Équations Différentielles » de Barreira et Valls, dans la même collection, lui permettra de compléter son étude.
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Banach spaces. --- Banach algebras. --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Functions of complex variables --- Generalized spaces --- Topology
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