compute the divergence of a vector field - Maple Help

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VectorCalculus[Divergence] - compute the divergence of a vector field

Calling Sequence

Divergence(F)

Parameters

F

-

(optional) vector field or a Vector valued procedure; specify the components of the vector field

Description

• 

The Divergence(F) command computes the divergence  of the vector field F.  This is a synonym for Del.F or DotProduct(Del, F).

• 

If F is a Vector valued procedure, the default coordinate system is used, and it must be indexed by the coordinate names.  Otherwise, F must be a Vector with the vectorfield attribute set, and it must have a coordinate system attribute that is indexed by the coordinate names.

• 

If F is a procedure, the returned object is a procedure. Otherwise, the returned object is an expression.

• 

The Divergence() command returns the differential form of the divergence operator in the current coordinate system.  For more information, see SetCoordinates.

Examples

withVectorCalculus:

SetCoordinates'cartesian'x,y,z

cartesianx,y,z

(1)

F:=VectorFieldx2,y2,z2

F:=x2e_x+y2e_y+z2e_z

(2)

DivergenceF

2x+2y+2z

(3)

Divergence

xVF 1x,y,z+yVF 2x,y,z+zVF 3x,y,z

(4)

Del.F

2x+2y+2z

(5)

Nabla.F

2x+2y+2z

(6)

DotProductDel,F

2x+2y+2z

(7)

Divergencex,y,z→PositionVectorsinx,cosy,tanz

x,y,z→cosxsiny+1+tanz2

(8)

SetCoordinates'polar'r,θ

polarr,θ

(9)

Divergencer,θ→fr,θ,gr,θ

r,θ→fr,θ+rrfr,θ+θgr,θr

(10)

See Also

VectorCalculus, VectorCalculus[Curl], VectorCalculus[Del], VectorCalculus[DotProduct], VectorCalculus[Gradient], VectorCalculus[Laplacian], VectorCalculus[SetCoordinates], VectorCalculus[Vector], VectorCalculus[VectorField], Vectors/Divergence


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