Div

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

Div[f]

gives the divergence, ∇·f, of the vector field f in the default coordinate system.

Div[f,coordsys]

gives the divergence of f in the coordinate system coordsys.

Details and Options

To use Div, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
The vector field f should be a 3-element list where each element is a function of the coordinates of the appropriate coordinate system.

Wolfram Language code: Needs["VectorAnalysis`"]

Compute the divergence of a vector field:

Wolfram Language code: v := {Xx ^ 2 + Zz, Yy * Sin[Xx], E ^ (3Zz)}

Wolfram Language code: Div[v]

Verify that the divergence of the curl of a vector field is 0:

Wolfram Language code: w := {f[Xx, Yy, Zz], g[Xx, Yy, Zz], h[Xx, Yy, Zz]}

Wolfram Language code: Div[Curl[w]]

Top