20181210

• I-Learn, Problem Set, Class Pictures

1. Draw $\vec r(t) = (0,t,9-t^2)$ for $0\leq t\leq 3$.
2. Draw $\vec r(x,y) = (x,y,9-x^2-y^2)$ for for $0\leq x \leq 3$ and $-3\leq y\leq 3$.
3. Draw $\vec r(u,v) = (u\cos v,u\sin v,9-u^2)$ for $0\leq u\leq 3$ and $0\leq v\leq 2\pi$.
4. For the vector field $\vec F = (x^2,3z+x,2y+4z)$, compute both $\vec \nabla \cdot F$ and $\vec \nabla \times F$.
5. For the same vector field compute each of the following, or explain why they cannot be computed.
   • $\vec \nabla\times(\vec \nabla \cdot \vec F)$
   • $\vec \nabla\cdot (\vec \nabla \times \vec F)$
   • $\vec \nabla\cdot (\vec \nabla \cdot \vec F)$
   • $\vec \nabla\times(\vec \nabla \times \vec F)$
6. For the vector field $\vec F = (M,N,P)$, compute each of the above that can be computed.

Problem Set
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