Analysis III Analytic and Differential Functions, Manifolds and Riemann Surfaces
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...
Autor principal: | |
---|---|
Autor Corporativo: | |
Formato: | Libro electrónico |
Idioma: | Inglés |
Publicado: |
Cham :
Springer International Publishing
2015.
|
Colección: | Universitext.
Springer eBooks. |
Acceso en línea: | Conectar con la versión electrónica |
Ver en Universidad de Navarra: | https://innopac.unav.es/record=b32921020*spi |
Sumario: | 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). |
---|---|
Descripción Física: | VII, 321 p., 25 il |
Formato: | Forma de acceso: World Wide Web. |
ISBN: | 9783319160535 |