2 Basic Integral Theorems
2.1 Gauss and Stokes’s Theorems
The divergence theorem of Gauss may be expressed as follows:
THEOREM 2.1: If V is a volume bounded by the closed surface S and A is a vector field that possesses continuous derivatives (and is singled valued in V), then
where n is the outward pointing unit normal vector to S. Note that we may extend this result to the case where A is a tensor field with the same proviso’s. The basic theorem is proven below.
Stokes’s theorem takes the following form:
THEOREM 2.2: If is an open, ...