The Gradient(f) calling sequence computes the gradient of the expression f in the current coordinate system.  If no coordinate system has been explicitly specified, the command will assume a cartesian system with coordinates the variables which appear in the expression f.

The Gradient(f,c) calling sequence computes the gradient of the expression f in the coordinate system specified by the parameter c, which can be given as:

* an indexed name, e.g., ${\mathrm{spherical}}_{r,\mathrm{\phi },\mathrm{\theta }}$

* a name, e.g., spherical; default coordinate names will be used

* a list of names, e.g., $\left[r\,\mathrm{\phi }\,\mathrm{\theta }\right]$; the current coordinate system will be used, with these as the coordinate names

For more information on coordinate systems, see SetCoordinates.

The Gradient(c) calling sequence returns the differential form of the gradient operator in the coordinate system specified by the parameter c.

The Gradient() calling sequence returns the differential form of the gradient operator in the current coordinate system.  If no coordinate system has been set (by a call to SetCoordinates), cartesian coordinates are assumed.

In all cases, the result is a vector field.

Nabla and Del are both synonyms for Gradient.

However, you can also use the Del or Nabla commands (as the Vector differential operator) with . (DotProduct) and &x (CrossProduct) as synonyms for the Curl, Divergence, and Laplacian commands.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right)\:$

$\mathrm{Gradient}\left(x^2+y^2\right)$

$\mathrm{Del}\left(u^2+a{v}^2\,\left[u\,v\right]\right)$

$\nabla \left(x^2+y^2\right)$

$\mathrm{Gradient}\left(r^2\mathrm{\phi }\,\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$

$\mathrm{SetCoordinates}\left(\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$

${\mathrm{spherical}}_{r,\mathrm{\phi },\mathrm{\theta }}$

$\mathrm{Del}\left(r^2\mathrm{\phi }\right)$

$\mathrm{Gradient}\left(\right)$

$\mathrm{Gradient}\left(\mathrm{polar}\left[r,\mathrm{\theta }\right]\right)$

$\mathrm{SetCoordinates}\left(\mathrm{cartesian}\left[x,y,z\right]\right)$

${\mathrm{cartesian}}_{x,y,z}$

$\mathrm{Divergence}\left(\mathrm{VectorField}\left(⟨y\,-x\,0⟩\right)\right)$

$0$

$\mathrm{Del}·\mathrm{VectorField}\left(⟨y\,-x\,0⟩\right)$

$0$

$\mathrm{Curl}\left(\mathrm{VectorField}\left(⟨y\,-x\,0⟩\right)\right)$

$\nabla \&x\mathrm{VectorField}\left(⟨y\,-x\,0⟩\right)$

$\mathrm{SetCoordinates}\left(\mathrm{spherical}\left[r,\mathrm{\phi },\mathrm{\theta }\right]\right)$

${\mathrm{spherical}}_{r,\mathrm{\phi },\mathrm{\theta }}$

$\mathrm{Laplacian}\left(r\sin \left(\mathrm{\theta }\right)\right)$

$\frac{2r\sin \left(\mathrm{\phi }\right)\sin \left(\mathrm{\theta }\right)-\frac{r\sin \left(\mathrm{\theta }\right)}{\sin \left(\mathrm{\phi }\right)}}{r^2\sin \left(\mathrm{\phi }\right)}$

$\mathrm{Del}·\mathrm{Del}\left(r\sin \left(\mathrm{\theta }\right)\right)$

$\frac{2r\sin \left(\mathrm{\phi }\right)\sin \left(\mathrm{\theta }\right)-\frac{r\sin \left(\mathrm{\theta }\right)}{\sin \left(\mathrm{\phi }\right)}}{r^2\sin \left(\mathrm{\phi }\right)}$