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Laplacian

The Laplace-operator is a differential operator given by the divergence of the gradient of a function f on Euclidean space

 


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 n coordinates

 


Additional information

The French mathematician Pierre-Simon Laplace (1749 - 1827) has proposed this technique.

 


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