Solution
= Solution
Use the global parametrization
$$
X(u,v)=(u,v,h(u,v)).
$$
Its <tangent vectors> are
$$
X_u=(1,0,h_u),
\qquad
X_v=(0,1,h_v),
$$
and
$$
X_u\times X_v=(-h_u,-h_v,1)\ne0.
$$
Thus $X$ is a regular parametrization and the graph is a smooth surface.
The <first fundamental form> is
$$
\boxed{
I=(1+h_u^2)\,du^2+2h_uh_v\,du\,dv+(1+h_v^2)\,dv^2}.
$$
Choosing the upward orientation, the <Gauss map> is
$$
\boxed{
N(u,v)=\frac{(-h_u,-h_v,1)}
{\sqrt{1+h_u^2+h_v^2}}}.
$$