**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*

(2.1) |

*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, ...*

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