Simpson's Rule for Double Integrals

In a previous paper and UMAP module, this author developed an extension of the trapezoid rule to evaluate double integrals [Gordon 1980; Gordon and Greenwell 19821. Since the derivation is based solely on topics normally encountered in the usual calculus sequence, this three-dimensional trapezoid rule is especially suitable to introduce in calculus, both as a numerical tool and as a means to unify a variety of other topics in the course.