This is a preliminary version of the first part of our book on the theory of quadrature methods. Further parts will follow soon.
The approximate evaluation of definite integrals is treated in every book on numerical analysis. Our intention is to complete these representations by showing that there is a coherent theory with many interesting (solved and unsolved) problems as well as many elegant and deep results. For more information about the conceptions, we refer to the first chapter.
We emphasize the word ``theory'' in the title. To anyone merely interested in the treatment of a concrete integration problem, we recommend the books of Davis and Rabinowitz or Krommer and Ueberhuber.
We will be grateful for any criticism or comments
Helmut Brass Knut Petras