Dave's Web Corner

MTH-261 Week 14 (November 24-30)

recommended exercises
- 3, 5, 9, 11, 13-18, 21, 23, 25, 29, 32, 35,41, 45, 47, 49, 53, 59, 61, 63
learning objectives
- find the parametric representations of a cylinder, a cone, and a sphere
- use a surface integral to calculate the area of a given surface
- explain the meaning of an oriented surface, giving an example
additional notes
- the area of a surface \( S: \vec{r}(u,v) \)
  - \( \displaystyle{\int\int_{S}\,dS = \int\int_{R} \left\|\frac{\partial \vec{r}}{\partial u}\times\frac{\partial \vec{r}}{\partial v}\right\| \,dA }\)

recommended exercises
- 5, 9, 11, 15, 17, 20, 23, 25, 28, 29, 34, 39, 40
learning objectives
- describe the surface integral of a scalar-valued function over a parametric surface
- describe the surface integral of a vector field
- use surface integrals to solve applied problems
additional notes
- the contribution of a function to a surface \( S: \vec{r}(u,v) \)
  - \( \displaystyle{\int\int_{S}f\,dS = \int\int_{R} f\left(\vec{r}(u,v)\right)\left\|\frac{\partial \vec{r}}{\partial u}\times\frac{\partial \vec{r}}{\partial v}\right\| \,dA }\)
- orientable surfaces and flux
  - \( \displaystyle{\int\int_{S}\vec{F}\cdot\vec{N}\,dS = \int\int_{R} \vec{F}\left(\vec{r}(u,v)\right)\cdot\left(\frac{\partial \vec{r}}{\partial u}\times\frac{\partial \vec{r}}{\partial v}\right) \,dA }\)

Deadlines
- All homework is due at the beginning of class on the date indicated.
- All exams are given in class on the date indicated.
- Late homework is not accepted and there are no make-ups for missed exams. Contact me before the deadline if you have a conflict with a deadline and we will find a mutually agreeable solution.
- Solutions are posted under these links after the deadline.
Homework
- due Tuesday, November 26:
  - 16.3 - , 16.4 - , 16.5 -
- due Tuesday, December 3:
  - 16.6 - , 16.7 -
- due Tuesday, December 10:
  - 16.8 - , 16.9 - , 16.10 -
Exams
- Thursday, December 12: Exam 3
  - Exam 3 (solutions)
  - Exam 3 covers sections 15.8-15.10 and 16.1-16.10