LEADER 03822nam 2200589Ia 450 001 9910484474003321 005 20200520144314.0 010 $a9783642174131 010 $a3642174132 024 7 $a10.1007/978-3-642-17413-1 035 $a(CKB)2670000000072047 035 $a(SSID)ssj0000475984 035 $a(PQKBManifestationID)11288626 035 $a(PQKBTitleCode)TC0000475984 035 $a(PQKBWorkID)10479168 035 $a(PQKB)11341138 035 $a(DE-He213)978-3-642-17413-1 035 $a(MiAaPQ)EBC3066415 035 $a(PPN)151586403 035 $a(EXLCZ)992670000000072047 100 $a20110220d2011 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aComputational approach to Riemann surfaces /$fAlexander Bobenko, Christian Klein 205 $a1st ed. 2011. 210 $aNew York $cSpringer$d2011 215 $a1 online resource (XII, 264 p. 58 illus., 14 illus. in color.) 225 0 $aLecture notes in mathematics ;$v2013 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642174124 311 08$a3642174124 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2013 606 $aRiemann surfaces 606 $aMathematical analysis$xData processing 615 0$aRiemann surfaces. 615 0$aMathematical analysis$xData processing. 676 $a515.93 700 $aAlexander$b Bobenko$01760423 701 $aKlein$b Christian$0426675 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484474003321 996 $aComputational approach to Riemann surfaces$94199392 997 $aUNINA