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.
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