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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).
| Autorius: | Roger Godement |
| Serija: | Universitext |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2015 |
| Knygos puslapių skaičius: | 332 |
| ISBN-10: | 3319160524 |
| ISBN-13: | 9783319160528 |
| Formatas: | 235 x 155 x 19 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Analysis III: Analytic and Differential Functions, Manifolds and Riemann Surfaces“
