- Consider the parametric surface $\vec r(x,y) = (x, y, x^2+y^2)$. It's a paraboloid.
- Compute the differential $\vec dr$ and write it in both vector and matrix form.
- At the point $\vec r(2,1)=(2,1,5)$, state two tangent vectors to the surface.
- Give an equation of the tangent plane to the surface at $\vec r(2,1)$.
- For the function $f(x,y)=3xy^2+2x^3$, compute the differntial $df$. Then state the derivative $Df(x,y)$. Then state the partials $\frac{\partial f}{\partial x}$ and $f_y$.
- For the function $f(u,v)=u^2\cos v$, state both $f_u$ and $\frac{\partial f}{\partial v}$. Then state the derivative $Df(u,v)$. Then state the differntial $df$.
- For the function $\vec r(u,v)=(u\cos v, u\sin v, u^2)$, state both partials $\vec r_u$ and $\frac{\partial \vec r}{\partial v}$. Then $D\vec r(u,v)$ and $df$.
- Repeate the previous two problems with any functions you want. The goal is to get good at finding partial derivatives, derivatives, and differentials, and being able to correctly name each part.
|
Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |