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Vector Analysis Package Symbol

Laplacian

Laplacian[f]
gives the Laplacian,

²f, of the scalar function or vector field f in the default coordinate system.

Laplacian[f, coordsys]
gives the Laplacian of f in the coordinate system coordsys.

To use Laplacian, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].

Needs["VectorAnalysis`"]

Laplacian of a function in Cartesian coordinates:

Needs["VectorAnalysis`"]

Verify that a function is harmonic:

Needs["VectorAnalysis`"]

Expression for the Laplacian in cylindrical coordinates: