Summary of Newton Cotes Rules

• Both these are equi-spaced (in ) rules with and the generalization to arbitrary n are called Newton-Cotes formulae (see Abramowitz and Stegun to find them explicitly written out).

• We can relax restrictions:

  (a) equidistant

  (b) and/or

  (c)

• The reader need only solve (NI.5) to find relevant formulae for any n.

• You will find in the books, discussions of so called open formulae where as above, but one omits one or both of the end-points. The remaining n or n-1 points ( or or ) are still equidistant.

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu