Biharmonic

As of version 9.0, vector analysis functionality is built into Mathematica

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


gives the biharmonic of f in the coordinate system coordsys.

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

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基本范例 (2)基本范例 (2)

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Biharmonic of a function in the default Cartesian coordinate system:

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Expression for the biharmonic in cylindrical coordinates:

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