VectorAnalysis`
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

Examples

Basic Examples  (3)

Laplacian of a function in Cartesian coordinates:

Verify that a function is harmonic:

Expression for the Laplacian in cylindrical coordinates: