A surface parameterization is a map from a two-dimensional parameter domain with coordinates 
and 
to a surface in 3-space, given by
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
If a surface is parameterized as above, then the tangent vectors
 |
(4)
|
 |
(5)
|
are useful in computing the surface area and surface integral.
