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Physics[Vectors][DirectionalDiff] - the directional derivative
Calling Sequence
DirectionalDiff(A, B_)
Parameters
A
-
any algebraic (vectorial or scalar) expression
B_
a vector
Description
DirectionalDiff(A, B_) computes the directional derivative of in the direction of , that is, the scalar product of a unitary vector in the direction of times Nabla - the differential operator - applied to the function A. Two cases can happen:
is not a vector. Hence
is a vector. Hence
The %DirectionalDiff is the inert form of DirectionalDiff, that is: it represents the same mathematical operation while holding the operation unperformed. To activate the operation use value.
Examples
The definition of directional derivative
Directional derivative in spherical coordinates
Directional derivative of a vector function
Note that, when the vector which defines the direction (the second argument) is projected over one coordinate system, the function being differentiated is expected to be expressed using the same coordinate system; otherwise an error interruption happens and a corresponding message is displayed
Error, (in Physics:-Vectors:-DirectionalDiff) vectors must be projected over one and the same base
For this example, correct input could be
See Also
Identify, Nabla, operations, Physics, Physics conventions, Physics examples, Student[MultivariateCalculus][DirectionalDerivative], tensor/directional_diff, VectorCalculus[DirectionalDiff]., Vectors, Vectors[`.`]
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