Grad

Grad[f,{x1,,xn}]
gives the gradient .

Grad[f,{x1,,xn},chart]
gives the gradient in the coordinates chart.

DetailsDetails

  • Grad[f,x] can be input as . The character can be typed as EscdelEsc or \[Del]. The list of variables is entered as a subscript.
  • An empty template can be entered as EscgradEsc, and Tab moves the cursor from the subscript to the main body.
  • All quantities that do not explicitly depend on the variables given are taken to have zero partial derivative.
  • If f is an array of dimensions , then Grad[f,{x1,,xm}] yields an array of dimensions .
  • If f is a scalar, Grad[f,{x1,x2,,xn},chart] returns a vector in the orthonormal basis associated with chart.
  • In Grad[f,{x1,,xn},chart], if f is an array, it must have dimensions . The components of f are interpreted as being in the orthonormal basis associated with chart.
  • Coordinate charts in the third argument of Grad 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.
  • Grad works with SparseArray and StructuredArray objects.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

The gradient in three-dimensional Cartesian coordinates:

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The gradient using an orthonormal basis for three-dimensional cylindrical coordinates:

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The gradient in two dimensions:

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Use EscdelEsc to enter and Ctrl+- to enter the list of subscripted variables:

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Use EscgradEsc to enter the template ; press Tab to move between inputs:

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Introduced in 2012
(9.0)
| Updated in 2014
(10.0)