Lecture Notes in Mathematics
cover

Computational Approach to Riemann Surfaces

Editors: Bobenko, Alexander I., Klein, Christian (Eds.)

  • Self-contained introduction to the theory of Riemann surfaces
  • Detailed explanation of existing codes with examples
  • Visualization of solutions to integrable partial differential equations and surfaces
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About this book

This 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.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Introduction to Compact Riemann Surfaces

    Pages 3-64

    Bobenko, Alexander I.

  • Computing with Plane Algebraic Curves and Riemann Surfaces: The Algorithms of the Maple Package “Algcurves”

    Pages 67-123

    Deconinck, Bernard (et al.)

  • Algebraic Curves and Riemann Surfaces in Matlab

    Pages 125-162

    Frauendiener, Jörg (et al.)

  • Computing Poincaré Theta Series for Schottky Groups

    Pages 165-182

    Schmies, Markus

  • Uniformizing Real Hyperelliptic

    Pages 183-193

    Crowdy, Darren (et al.)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-642-17413-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-642-17412-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Computational Approach to Riemann Surfaces
Editors
  • Alexander I. Bobenko
  • Christian Klein
Series Title
Lecture Notes in Mathematics
Series Volume
2013
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-17413-1
DOI
10.1007/978-3-642-17413-1
Softcover ISBN
978-3-642-17412-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 264
Number of Illustrations
44 b/w illustrations, 14 illustrations in colour
Topics