Chapter 15
Section 15.8: Stokes's Theorem

• Orintation: right hand rule.
• Let `S` be an oriented surface with unit normal vector `bbN` bounded by a piecewise smooth closed curve `C` with a positive orientation. If `bbF` is a vector field whose component functions have continuous first partial derivatives on an open region containing `S` and `C`, then

  `int_C bbF•dbbr = int_Sint (curl\quad bbF)•bbN\quaddS`.

• Then, remember from section 15.6, that if we can express the surface `S` as `z = g(x,y)` then we could rewrite

  `int_Sint (curl\quad bbF)•bbN\quaddS = int_Rint (curl\quad bbF)•[-g_x(x,y)bbi-g_y(x,y)bbj +bbk]dA`.