An useful application of computer algebra systems is the generation of
algorithms for numerical computations.  We have shown in SIAM Review Vol 41,
Number 3, Sept. 1999 how computer algebra can be used in teaching to derive
numerical methods.  In this paper we extend this work, using essentially the
capability of computer algebra system to construct and manipulate the
interpolating polynomial and to compute a series expansion of a function.  We
will automatically generate formulas for integration and differentiation with
error terms and also generate multi-step methods for integrating differential
equations.