compute the dot product of Vectors and differential operators - Maple Help

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Student[VectorCalculus][DotProduct] - compute the dot product of Vectors and differential operators

Calling Sequence

DotProduct(v1, v2)

v1 . v2

Parameters

v1

-

Vector or differential operator

v2

-

Vector or differential operator

Description

• 

The DotProduct(v1, v2) calling sequence computes the dot product ( scalar product ) of v1 and v2, where v1 and v2 can be Vectors, vector fields, Student[VectorCalculus]:-Del, or Student[VectorCalculus]:-Nabla.

• 

The Student[VectorCalculus] package has a `.` operator that you can use in place of the DotProduct command.  For example, DotProduct(v1, v2) is equivalent to v1.v2.

  

Also, Del.F is equivalent to Divergence(F).

Examples

withStudent[VectorCalculus]:

DotProducta,b,c,d

ac+bd

(1)

SetCoordinatespolarr,θ

polarr,θ

(2)

v:=RootedVectorroot=1,2,a,b

v:=ab

(3)

w:=RootedVectorroot=1,2,c,d

w:=cd

(4)

v.w

ac+bd

(5)

F:=VectorFieldr2,θ

F:=r2e_r+θe_θ

(6)

Del.F

3r2+1r

(7)

DivergenceF

3r2+1r

(8)

SetCoordinatescartesianx,y,z

cartesianx,y,z

(9)

L:=VectorFieldx,y,z.Delfx,y,z

L:=xxfx,y,z+yyfx,y,z+zzfx,y,z

(10)

See Also

combine, Student[VectorCalculus], Student[VectorCalculus][Del], Student[VectorCalculus][Divergence], Student[VectorCalculus][Laplacian], Student[VectorCalculus][Nabla], Student[VectorCalculus][SetCoordinates], Student[VectorCalculus][Vector], Student[VectorCalculus][VectorField]


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