At the end of the course, each student should be able to…
- S11: GreenStokes. Apply Green’s Theorem and Stokes’s Theorem.
S11: Green’s Theorem and Stokes’s Theorem
- Stokes’s Theorem states that if the boundary \(\partial S\) of a
surface \(S\) is oriented counter-clockwise with respect to the orientation
of \(S\), then \(\int_{\partial S}\vect F\cdot d\vect{r}=
\iint_S\curl\vect F\cdot\vect{n}\,d\sigma\).
- This simplifies to Green’s Theorem when \(S\) is the region \(R\) in the plane oriented by \(\veck\) with counter-clockwise boundary \(C\): \(\int_C \vect F\cdot d\vect{r}=\iint_R \curl\vect F\cdot\veck\,dA = \iint_R(N_x-M_y)\,dA\).
Textbook References
- University Calculus: Early Transcendentals (3rd Ed)
- 15.4 (exercises 5-14, just find circulation)
- 15.7 (exercises 1-6)