How to find a parametric equation to the surface S that is bounded between $z=x^2-y^2$ inside the cylinder $x^2+y^2=1$, and while C be the the Boundary of that surface.
While reading the solution of one of the questions they said that a parametric equation for surface S is:
$\vec r(\rho$,$\theta$) = $\rho$cos$\theta$$\hat i$ + $\rho$sin$\theta$$\hat j$ + $\rho^2$cos$2\theta$$\hat k$ while $0\le$ $\theta \le 2\pi$ , $0\le$ $\rho$ $ \le 1$
a parametric equation for curve/boundary C is:
$\vec r(\theta$)= cos$\theta$$\hat i$ + sin$\theta$$\hat j$ + cos$2\theta$$\hat k$ while $0\le$ $\theta \le 2\pi$
but how did they reach these equations? I would appreciate any kind of help.