The present book is an edition of the manuscripts to the courses
"Numerical Methods I" and "Numerical Mathematics I and II" which
Professor H. Rutishauser held at the E.T.H. in Zurich. The first-named
course was newly conceived in the spring semester of 1970, and intended
for beginners, while the two others were given repeatedly as elective
courses in the sixties. For an understanding of most chapters the funda-
mentals of linear algebra and calculus suffice. In some places a little
complex variable theory is used in addition. However, the reader can get
by without any knowledge of functional analysis. The first seven
chapters discuss the direct solution of systems of linear equations, the
solution of nonlinear systems, least squares prob- lems, interpolation
by polynomials, numerical quadrature, and approxima- tion by Chebyshev
series and by Remez' algorithm. The remaining chapters include the
treatment of ordinary and partial differential equa- tions, the
iterative solution of linear equations, and a discussion of eigen- value
problems. In addition, there is an appendix dealing with the qd-
algorithm and with an axiomatic treatment of computer arithmetic.