ABSTRACT
In this chapter, we begin the task of extending the results of the previous section to higher dimensions. The first step is defining surface integrals for surfaces in R 3. As with line integrals, there are two sorts of surface integrals: integrals of functions and integrals of vector fields. We next relate the surface integral of a vector field to the line integral of a related vector field along the boundary of the surface. This result, Stokes’ theorem, is an analog of Green’s theorem. We state it here and give an application to hydrodynamics. The proof is given in Chapter 16.
