The present text is based on the premise that the introductory course should
provide a fairly substantial grounding in the basic operations of computation,
approximation, interpolation, numerical differentiation and integration, and the
numerical solution of equations, as well as in applications to such processes as the
smoothing of data, the numerical summation of series, and the numerical solution of
ordinary differential equations. It is believed that this course not only should exhibit
techniques available for each purpose, but also should attempt to derive the relevant
formulas in such a way that the underlying hypotheses are in evidence and that methods
of generalization and modification are reasonably apparent, and that the problems of
error analysis, convergence, and stability should be treated as adequately as time and
preparation permit.