VectorCalculus - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Vector Calculus : VectorCalculus/Gradient

VectorCalculus

  

Gradient

  

compute the gradient of a function from R^n to R

  

Del

  

Vector differential operator

  

Nabla

  

Vector differential operator

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Gradient(f, c)

Del(f, c)

Nabla(f, c)

Gradient()

Del()

Nabla()

Parameters

f

-

algebraic expression

c

-

(optional) list(name) or name[name, name, ...]; specify the list of variable names or coordinate system indexed by coordinate names

Description

• 

The Gradient(f, c) command computes the gradient of the expression f.  The result is a vector field.

• 

If c is a list of names, the gradient is taken in the current default coordinate system by using the names in c as the coordinate names.  If the number of given names is not compatible with this coordinate system, an error is raised.

  

If c is a name indexed by other names, the gradient is computed in this coordinate system by using the indices as the coordinate names.  If the number of names is not compatible with the coordinate system, an error is raised.

  

If c is not specified, the current default coordinates are used. The default coordinates must be indexed by coordinate names, otherwise an error is raised.

• 

The command Del(f, c) is just a synonym for Gradient(f, c). However, Del is also recognized as the Vector differential operator that is used with DotProduct and CrossProduct as shortcuts for Curl, Divergence, Gradient, and Laplacian.

• 

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

  

Nabla is a synonym for Del.

Examples

withVectorCalculus:

g1Gradientx2+y2,x,y

g1:=2xe_x+2ye_y

(1)

attributesg1

vectorfield,coords=cartesianx,y

(2)

g2Gradientr2,'polar'r,θ

g2:=2re_r

(3)

attributesg2

vectorfield,coords=polarr,θ

(4)

SetCoordinates'spherical'r,φ,θ

sphericalr,φ,θ

(5)

g3Gradientr2φ

g3:=2rφe_r+re_φ

(6)

attributesg3

vectorfield,coords=sphericalr,φ,θ

(7)

Delr2φ

2rφe_r+re_φ

(8)

Gradient

rSF r,φ,θe_r+φSF r,φ,θre_φ+θSF r,φ,θrsinφe_θ

(9)

SetCoordinates'cartesian'x,y,z

cartesianx,y,z

(10)

Delx2+y2+z2

2xe_x+2ye_y+2ze_z

(11)

n1Nablax2+y2+z2

n1:=2xe_x+2ye_y+2ze_z

(12)

Del.n1

6

(13)

Del &x VectorFieldy,x,0

2e_z

(14)

LVectorFieldx,y,z &x Del

L:=e→VectorCalculus:-&xVector(3, {(1) = x, (2) = y, (3) = z}, attributes = [vectorfield, coords = cartesian[x, y, z]]),VectorCalculus:-Gradiente

(15)

Lsinxyz

y2xcosxyzz2xcosxyze_x+x2ycosxyz+z2ycosxyze_y+x2zcosxyzy2zcosxyze_z

(16)

LDel &x Del

L:=VectorCalculus:-Curl@VectorCalculus:-Gradient

(17)

Lfx,y,z

0e_x

(18)

See Also

attributes

plots[gradplot3d]

plots[gradplot]

Student[MultivariateCalculus][Gradient]

Student[VectorCalculus][Gradient]

VectorCalculus

VectorCalculus[Curl]

VectorCalculus[Divergence]

VectorCalculus[Laplacian]

VectorCalculus[SetCoordinates]

VectorCalculus[Vector]

VectorCalculus[VectorField]

Vectors/Gradient

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam