A very important operator in mathematical physics. Basically, it is the summation of the second derivatives of a function with respect to each of its independent variables. Now suppose we have a function u(x,y) in two dimensions, the Laplacian Operator is expressed as follows:

∇² = δ²/δx² + δ²/δy².

For the function u(x, y, z) in three dimensions, the Laplacian Operator is expressed as follows:

∇² = δ² /δx² + δ²/δy² + δ²/δz².

The Laplacian Operatoris used to compare the value of a function at a point with its value at neighbouring points.