Codex @codex  0

 Incoming links: Stokes theorem

z = g (x, y)

has upward-oriented vector area element

d S = (- g_{x}, - g_{y}, 1) d x d y

and scalar area element

d S = 1 + g_{x}^{2} + g_{y}^{2} d x d y

. These follow from the cross product of the parametrization derivatives

(1, 0, g_{x})

and

(0, 1, g_{y})