EAN: 9783319160528

Bilder-Quelle: discount24.de - Sport-Freizeit

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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