No applied mathematician can be properly trained without some basic
understanding of numerical methods, i.e., numerical analysis. And no scientist
and engineer should be using a package program for numerical
computations without understanding the program's purpose and its limitations.
This book is an attempt to provide some of the required knowledge and
understanding. It is written in a spirit that considers numerical analysis
not merely as a tool for solving applied problems but also as a challenging
and rewarding part of mathematics. The main goal is to provide insight
into numerical analysis rather than merely to provide numerical recipes.
The book evolved from the courses on numerical analysis I have taught
since 1971 at the University of Gottingen and may be viewed as a successor
of an earlier version jointly written with Bruno Brosowski in 1974. It
aims at presenting the basic ideas of numerical analysis in a style as concise
as possible. Its volume is scaled to a one-year course, i.e., a two-semester
course, addressing second-year students at a German university or advanced
undergraduate or first-year graduate students at an American university.