BUILT-IN MATHEMATICA SYMBOL

# Curl

Curl[{f1, f2}, {x1, x2}]
gives the curl .

Curl[{f1, f2, f3}, {x1, x2, x3}]
gives the curl .

Curl[f, {x1, ..., xn}]
gives the curl of the ××...× array f with respect to the -dimensional vector .

Curl[f, x, chart]
gives the curl in the coordinates chart.

## DetailsDetails

• All quantities that do not explicitly depend on the variables given are taken to have zero partial derivative.
• In Curl[f, {x1, ..., xn}], if f is an array with depth , it must have dimensions , and the resulting curl is an array with depth of dimensions .
• If f is a scalar, Curl[f, {x1, ..., xn}, chart] returns an array of depth n-1 in the orthonormal basis associated with chart.
• In Curl[f, {x1, ..., xn}, chart], if f is an array, the components of f are interpreted as being in the orthonormal basis associated with chart.
• Coordinate charts in the third argument of Curl can be specified as triples in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
• Curl works with SparseArray and StructuredArray objects.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Curl of a vector field in Cartesian coordinates:

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Curl of a vector field in cylindrical coordinates:

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Rotational in two dimensions:

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