Parametrized Surfaces Just as you describe curves in the plane parametrically with a pair of equations $x=f(t), y=g(t)$ defined on some parameter interval $I,$ you can sometimes describe surfaces in space with a triple of equations $x=f(u, v), y=g(u, v), z=h(u, v)$ defined on some parameter rectangle $a \leq u \leq b, c \leq v \leq d .$ Many computer algebra systems permit you to plot such surfaces in parametric mode. (Parametrized surfaces are discussed in detail in Section 16.5.) Use a CAS to plot the surfaces. Also plot several level curves in the $x y$ -plane.

$$\begin{array}{l}

x=u \cos v, \quad y=u \sin v, \quad z=u, \quad 0 \leq u \leq 2 \\

0 \leq v \leq 2 \pi

\end{array}$$