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Record Nr. |
UNINA9910299767503321 |
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Autore |
Godement Roger |
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Titolo |
Analysis III : Analytic and Differential Functions, Manifolds and Riemann Surfaces / / by Roger Godement |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
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ISBN |
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Edizione |
[1st ed. 2015.] |
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Descrizione fisica |
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1 online resource (VII, 321 p. 25 illus.) |
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Collana |
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Universitext, , 0172-5939 |
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Disciplina |
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Soggetti |
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Functions of real variables |
Real Functions |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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VIII Cauchy Theory -- IX Multivariate Differential and Integral Calculus -- X The Riemann Surface of an Algebraic Function. |
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Sommario/riassunto |
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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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