VectorAnalysis`

Laplacian

As of Version 9.0, vector analysis functionality is built into the Wolfram Language »

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.

Details and Options

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

Laplacian of a function in Cartesian coordinates:

Verify that a function is harmonic:

Expression for the Laplacian in cylindrical coordinates:

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