Hidden Bibliographic Details
| Varying Form of Title: | Analytic and differential functions, manifolds and Riemann surfaces
Analysis 3
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| Other authors / contributors: | Ray, Urmie, translator.
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| ISBN: | 9783319160535
3319160532
3319160524
9783319160528
9783319160528
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| Digital file characteristics: | text file PDF
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| Notes: | Includes index.
Online resource; title from PDF title page (SpringerLink, viewed April 10, 2015).
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| Summary: | 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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| Other form: | Printed edition: 9783319160528
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| Standard no.: | 10.1007/978-3-319-16053-5
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