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`"].

Wolfram Language code: Needs["VectorAnalysis`"]

Laplacian of a function in Cartesian coordinates:

Wolfram Language code: Laplacian[Xx ^ 2 + Sin[Yy Zz]]

Wolfram Language code: Needs["VectorAnalysis`"]

Verify that a function is harmonic:

Wolfram Language code: Laplacian[Xx ^ 2 + 7Yy ^ 2 - 8 Zz ^ 2]

Wolfram Language code: Needs["VectorAnalysis`"]

Expression for the Laplacian in cylindrical coordinates:

Wolfram Language code: Laplacian[f[Rr, Ttheta, Zz], Cylindrical]//Simplify

Top