< 1 >
Laplacian
The Laplace operator is a differential operator given by the divergence of the gradient of a function f on euclidean space
.gif){kind=small}
Explanation
It is a scalar operator that can be applied to either vector or scalar fields. For cartesian coordinate systems it is defined as
Example 1
In two-dimensional cartesian coordinates (plane), the laplacian of a function f is
and in three-dimensional coordinates
and in ℝn coordinates
 =.gif)
HistoryThe French mathematician Pierre-Simon Laplace (1749 - 1827) has proposed this technique. |