Math 311-101 Current Assignment — Summer I, 2013
Assignment 8 - Due Tuesday, July 2, 2013.
- 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.
- §10.1 (p. 675): 24
- §10.1 (p. 675): 29
- §10.2 (p. 685): 10
- §10.2 (p. 684): 22(a,c)
- §11.2 (p. 739): 14
- §11.2 (p. 739): 22
- §11.3 (p. 755): 4
- §11.3 (p. 755): 5
- §11.3 (p. 755): 8
- §11.3 (p. 755): 11
Updated 6/27/2013 (fjn).