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020 _a9783642174131
_9978-3-642-17413-1
024 7 _a10.1007/978-3-642-17413-1
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
245 1 0 _aComputational Approach to Riemann Surfaces
_h[electronic resource] /
_cedited by Alexander I. Bobenko, Christian Klein.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2011.
300 _aXII, 264 p. 58 illus., 14 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2013
505 0 _aIntroduction to Compact Riemann Surfaces -- Computing with plane algebraic curves and Riemann surfaces: the algorithms of the Maple package “algcurves” -- Algebraic curves and Riemann surfaces in Matlab -- Computing Poincaré Theta Series for Schottky Groups -- Uniformizing real hyperelliptic M-curves using the Schottky-Klein prime function -- Numerical Schottky Uniformizations: Myrberg’s Opening Process -- Period Matrices of Polyhedral Surfaces -- On the spectral theory of the Laplacian on compact polyhedral surfaces of arbitrary genus.
520 _aThis volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.
650 0 _aGeometry, algebraic.
650 0 _aFunctions of complex variables.
650 0 _aNumerical analysis.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aFunctions of a Complex Variable.
_0http://scigraph.springernature.com/things/product-market-codes/M12074
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
700 1 _aBobenko, Alexander I.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aKlein, Christian.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642174124
776 0 8 _iPrinted edition:
_z9783642174148
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2013
856 4 0 _uhttps://doi.org/10.1007/978-3-642-17413-1
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c12051
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