"In truth, it is not knowledge, but learning, not possessing, but
production, not being there, but travelling there, which provides the
greatest pleasure. When I have completely understood something, then I
turn away and move on into the dark; indeed, so curious is the
insatiable man, that when he has completed one house, rather than living
in it peacefully, he starts to build another. " Letter from C. F. Gauss
to W. Bolyai on Sept. 2, 1808 This textbook adds a book devoted to
applied mathematics to the series "Grundwissen Mathematik. " Our goals,
like those of the other books in the series, are to explain connections
and common viewpoints between various mathematical areas, to emphasize
the motivation for studying certain prob- lem areas, and to present the
historical development of our subject. Our aim in this book is to
discuss some of the central problems which arise in applications of
mathematics, to develop constructive methods for the numerical solution
of these problems, and to study the associated questions of accuracy. In
doing so, we also present some theoretical results needed for our
development, especially when they involve material which is beyond the
scope of the usual beginning courses in calculus and linear algebra.
This book is based on lectures given over many years at the Universities
of Freiburg, Munich, Berlin and Augsburg.