Grad

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

Grad[f]

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

Grad[f,coordsys]

gives the gradient of f in the coordinate system coordsys.

Details and Options

To use Grad, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].

Wolfram Language code: Needs["VectorAnalysis`"]

Gradient of a function in Cartesian coordinates:

Wolfram Language code: f = Xx ^ 2 + Yy E ^ (Zz);

Wolfram Language code: {v1, v2, v3} = Grad[f]

Wolfram Language code: Clear[f]

Recover the original function using DSolve:

Wolfram Language code: sol = DSolve[{D[f[Xx, Yy, Zz], Xx] == v1, D[f[Xx, Yy, Zz], Yy] == v2, D[f[Xx, Yy, Zz], Zz] == v3}, f, {Xx, Yy, Zz}]

Wolfram Language code: f[Xx, Yy, Zz] /. sol[[1]] /. {C[1] -> 0}

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