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Preface to the English Edition

Shortly after the appearance of the German edition we were asked by
Springer to create an English version of our book, and we gratefully ac-
cepted. We took this opportunity not only to correct some misprints and
1
mistakes that have come to our knowledge but also to extend the text at
various places. This mainly concerns the role of the finite difference and
the finite volume methods, which have gained more attention by a slight
extension of Chapters 1 and 6 and by a considerable extension of Chapter
7. Time-dependent problems are now treated with all three approaches (fi-
nite differences, finite elements, and finite volumes), doing this in a uniform
way as far as possible. This also made a reordering of Chapters 6–8 nec-
essary. Also, the index has been enlarged. To improve the direct usability
in courses, exercises now follow each section and should provide enough
material for homework.
This new version of the book would not have come into existence without
our already mentioned team of helpers, who also carried out first versions
of translations of parts of the book. Beyond those already mentioned, the
team was enforced by Cecilia David, Basca Jadamba, Dr. Serge Kr¨autle,
Dr. Wilhelm Merz, and Peter Mirsch. Alexander Prechtel now took charge
of the difficult modification process. Prof. Paul DuChateau suggested im-
provements. We want to extend our gratitude to all of them. Finally, we

1 Users of the German edition may consult
http://www.math.tu-clausthal.de/˜mala/publications/errata.pdf