tensor/directional_diff

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tensor[directional_diff] - compute the directional derivative

	Calling Sequence
	directional_diff( f, V, coord)

Parameters

f	-	scalar field
V	-	contravariant vector field
coord	-	list of coordinate names

Description

•	The function directional_diff(f, V, coord) computes the directional derivative of the scalar field f with respect to the coordinates coord in the direction of the contravariant vector V.

•	f must be of type algebraic, and V must be a tensor_type with index character [1] (a contravariant vector field). The result is an algebraic expression.

•

Simplification: This routine uses the `tensor/directional_diff/simp` routine for simplification purposes. The simplification routine is applied to each component of the gradient of f (an intermediate calculation) and once to the contraction of this gradient with V (the result). By default, `tensor/directional_diff/simp` is initialized to the `tensor/simp` routine. It is recommended that the `tensor/directional_diff/simp` routine be customized to suit the needs of the particular problem.

Examples

(1)

(2)

Compute the directional derivative of f with respect to coord in the direction of V:

-3*x*(-y^2+z*x)/(y+z)^2

(3)

Compute the directional derivative of an arbitrary scalar field g(x,y,z) in the direction of an arbitrary vector field U = (u1, u2, u3):

(4)

(5)

	See Also
	Physics[Vectors][DirectionalDiff], Student[MultivariateCalculus][DirectionalDerivative], tensor, tensor/Lie_diff, tensor/partial_diff, tensor[simp], VectorCalculus[DirectionalDiff]