Section 8.3 Regions with Two Boundaries
The Divergence theorem enables a pretty nifty trick. Suppose the boundary of a 3D region has two disconnected components, like an inside surface and an outside surface. In this case when you apply the Divergence Theorem it gives the sum of the two surface integrals, and fair warning we will have to be quite careful about signs here. This is going to be particularly useful when the Divergence is zero.
Learning Objectives:
- Describe the Divergence Theorem when the region has a boundary consisting of two disconnected components.
