Vector Derivative

Author

Eric W. Weisstein
April 15, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/VectorDerivative.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/VectorDerivative.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Calculus`VectorAnalysis`

Curl

?Curl

Cartesian

FullSimplify[Curl[{x,0,0},Cartesian[x,y,z]]]

FullSimplify[Curl[{1,0,0},Cartesian[x,y,z]]]

Spherical

Curl[{r,0,0},Spherical[r,ϕ,θ]]

Curl[{1,0,0},Spherical[r,ϕ,θ]]

Divergence

?Div

Cartesian

FullSimplify[Div[{x,0,0},Cartesian[x,y,z]]]

FullSimplify[Div[{1,0,0},Cartesian[x,y,z]]]

Spherical

Div[{r,0,0},Spherical[r,ϕ,θ]]

Div[{1,0,0},Spherical[r,ϕ,θ]]

Gradient

?Grad

Cartesian

FullSimplify[Grad[x,Cartesian[x,y,z]]]

Spherical

Grad[r,Spherical[r,ϕ,θ]]