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Biharmonic

Biharmonic[f]

gives the biharmonic, , of the scalar function f in the default coordinate system.

Biharmonic[f,coordsys]

gives the biharmonic of f in the coordinate system coordsys.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
See Also
Tech Notes
Related Guides
VectorAnalysis`
VectorAnalysis`

Biharmonic

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

Biharmonic[f]

gives the biharmonic, , of the scalar function f in the default coordinate system.

Biharmonic[f,coordsys]

gives the biharmonic of f in the coordinate system coordsys.

Details and Options

  • To use Biharmonic, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
  • The biharmonic of f is the Laplacian of the Laplacian of f, .

Examples

Basic Examples  (2)

Wolfram Language code: Needs["VectorAnalysis`"]

Biharmonic of a function in the default Cartesian coordinate system:

Wolfram Language code: Biharmonic[Xx ^ 5 Zz + Sin[Yy Zz]]
Wolfram Language code: Needs["VectorAnalysis`"]

Expression for the biharmonic in cylindrical coordinates:

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