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<<Calculus`VectorAnalysis`

The syntax of the vectors analysis commands can be found in the help browser. First, we can set the default coordinate system:

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SetCoordinates[Cartesian[x, y, z]] ;

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f[x_, y_, z_] = 1/(x^2 + y^2 + z^2)^(1/2) ;

G[x_, y_, z_] = {x^2 + y, y + z, z x} ;

The nabla symbol is typed Esc-del-Esc.

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Print["∇f(x,y,z) = ", Grad[f[x, y, z]]]

Print["∇·G(x,y,z) = ", Div[G[x, y, z]]]

Print["∇G(x,y,z) = ", Curl[G[x, y, z]]]

∇f(x,y,z) =  {-x/(x^2 + y^2 + z^2)^(3/2), -y/(x^2 + y^2 + z^2)^(3/2), -z/(x^2 + y^2 + z^2)^(3/2)}

∇·G(x,y,z) = 1 + 3 x

∇G(x,y,z) =  {-1, -z, -1}

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