• Read sections 11.1, 11.2, 11.3. In section 11.1, you need to know the following:
  • Parametrizations for a spheres, cylinders, planes, cones, amd surfaces given by $z=f(x,y)$.
  • The standard normal for a parametrized surface: $\mathbf N = \frac{\partial \mathbf X}{\partial s}\times \frac{\partial \mathbf X}{\partial t}$. (Colley uses $\mathbf T_1 = \frac{\partial \mathbf X}{\partial s}$ and $\mathbf T_2 = \frac{\partial \mathbf X}{\partial t}$.)
  • Tangent plane: This is the plane through the point $\mathbf X(s,t)$ and perpendicular to the standard normal $\mathbf N(s,t)$.
  • The unit normal: $\mathbf n = \mathbf N/|\mathbf N|$
  • Area element: $dS = |\mathbf N|ds dt$.
  • Vector area: $d\mathbf S = \mathbf N dsdt$

• Do the following problems.
  1. §10.1 (p. 675): 24
  2. §10.1 (p. 675): 29
  3. §10.2 (p. 685): 10
  4. §10.2 (p. 684): 22(a,c)
  5. §11.2 (p. 739): 14
  6. §11.2 (p. 739): 22
  7. §11.3 (p. 755): 4
  8. §11.3 (p. 755): 5
  9. §11.3 (p. 755): 8
  10. §11.3 (p. 755): 11

Updated 6/27/2013 (fjn).