A Monge patch is a patch of the form
(1)

where is an open set in and is a differentiable function. The coefficients of the first fundamental form are given by
(2)
 
(3)
 
(4)

and the second fundamental form by
(5)
 
(6)
 
(7)

For a Monge patch, the Gaussian curvature and mean curvature are
(8)
 
(9)
