ABSTRACT
We have treated, with considerable generality, two of the major topics of multivariable calculus—differentiation and integration. We now turn to the third topic. It is commonly called “vector integral calculus,” and its major theorems bear the names of Green, Gauss, and Stokes. In calculus, one limits oneself to curves and surfaces in ℝ3. We shall deal more generally with k-manifolds in ℝ n . In dealing with this general situation, one finds that the concepts of linear algebra and vector calculus are no longer adequate. One needs to introduce concepts that are more sophisticated; they constitute a subject called multilinear algebra that is a sequel to linear algebra.
