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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

Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.

• 

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

Important: The tensor package has been deprecated. Use the superseding packages DifferentialGeometry and Physics instead.

withtensor:

coord:=x,y,z:

f:=3xy+z

f:=3xy+z

(1)

V:=create1,arrayxy,yz,zx

V:=tableindex_char=1,compts=xyyzzx

(2)

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

directional_difff,V,coord

3xxzy2y+z2

(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):

U:=create1,arrayu1,u2,u3

U:=tableindex_char=1,compts=u1u2u3

(4)

directional_diffgx,y,z,U,coord

xgx,y,zu1+ygx,y,zu2+zgx,y,zu3

(5)

See Also

Physics[Vectors][DirectionalDiff], Student[MultivariateCalculus][DirectionalDerivative], tensor(deprecated), tensor(deprecated)/Lie_diff, tensor(deprecated)/partial_diff, tensor(deprecated)[simp], VectorCalculus[DirectionalDiff]


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