Chapter 15
Section 15.7: Divergence Theorem

• Recall alternative form of Green's theorem:

  `int_CM \quad dx + N \quad dy = int_Rint ((del N)/(del x) - (del M)/(del y) )dA`

  `int_C bbF•bbN\quad ds = int_Rint div\quad bbF\quad dA`

• The Divergence Theorem:
  Let `Q` be a solid bounded by a closed surface `S` oriented by a unit normal vector `bbN` directed outward from `Q`. If `bbF` is a vector field whose component function have continuous first derivatives in `Q`, then

  `int_SintbbF•\quaddS = int int_Q int div\quad bbF \quad dV`