Overview of the VectorCalculus Package - Maple Programming Help

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Overview of the VectorCalculus Package

 

Basic Functionality

Interfaces to the VectorCalculus Package

Essential VectorCalculus Package Commands

Examples

Details

Basic Functionality

Description

• 

The VectorCalculus package is a collection of commands that perform multivariate and vector calculus operations.

  

Multivariate calculus refers to the calculus of functions from Rn to R. Vector calculus refers to the calculus of functions from Rn to Rm, where 1<m.

• 

The VectorCalculus package contains a large set of predefined coordinate systems. All computations in the package can be performed in any of these coordinate systems.  By default, the Cartesian coordinate system is used.  The basic objects on which the commands in the VectorCalculus package operate are Vectors, vector fields, and scalar functions.

• 

For a complete list of the routines in the VectorCalculus package and advanced information on the capabilities of this package, see the Details of the Vector Calculus package help page.

Interfaces to the VectorCalculus Package

Commands

• 

Each command in the VectorCalculus package can be accessed by using either the long form or the short form of the command name in the command calling sequence.  For more information, see the Using Packages help page.

  

Long form

VectorCalculus[CrossProduct](<a, b, c>, <d, e, f>);

  

Short form

with(VectorCalculus):

CrossProduct(<a, b, c>, <d, e, f>);

Tasks

• 

Some routines in the VectorCalculus package come with a task template to step you through the process of solving a vector calculus problem. For more information, see the Using Tasks help page.

  

 

Student[VectorCalculus] Package

• 

For students learning the concepts presented in an introductory vector calculus course, see the Student[VectorCalculus] help page.

  

 

Essential VectorCalculus Package Commands

About

returns information about a VectorCalculus object

CrossProduct

computes the cross product of Vectors and differential operators

Curl

compute the curl of a vector field in R^3

DirectionalDiff

computes the directional derivative of a scalar field in the direction given by a vector

evalVF

evaluate a vector field at a point

Flux

compute the flux of a vector field through a surface in R^3 or a curve in R^2

Laplacian

compute the Laplacian of functions from R^n to R, or of a vector field

LineInt

compute the line integral of a vector field in R^n

MapToBasis

converts Vectors and vector fields

Nabla

Vector differential operator

PlotPositionVector

plots a curve or surface

PositionVector

creates a position Vector with specified components

RadiusOfCurvature

compute the radius of curvature of a curve

RootedVector

creates a Vector rooted at a point with specified components

SetCoordinates

set the coordinate attribute on a free Vector

Torsion

compute the torsion of a curve in R^3

Vector

creates a free Vector with specified components

VectorField

creates a vector field

Examples

withVectorCalculus&colon;

Compute the cross product.

CrossProducta&comma;b&comma;c&comma;d&comma;e&comma;f

bfceex&plus;af&plus;cdey&plus;aebdez

(1)

Compute the radius of curvature.

RadiusOfCurvature2cost&comma;sintassumingt::real

123cost2&plus;43&sol;2

(2)

Integrate a function over R^2.

intx2&plus;y2&comma;x&comma;y&equals;Circle0&comma;0&comma;r

12&pi;r4

(3)

Change the coordinate system to cylindrical.

SetCoordinates&apos;cylindrical&apos;r&comma;&theta;&comma;z

cylindricalr&comma;&theta;&comma;z

(4)

Define a vector field.

FVectorFieldr3&comma;z&theta;&comma;r

Fr3e&lowbar;r&plus;z&theta;e&lowbar;&theta;&plus;re&lowbar;z

(5)

Compute the flux of a vector field through a specified surface.

FluxF&comma;Sphere0&comma;0&comma;0&comma;R

3215R5&pi;

(6)

Compute the Laplacian of a vector field.

simplifyLaplacianF

24r3&theta;2&plus;zr2&theta;2e&lowbar;rz&theta;22r2&theta;3e&lowbar;&theta;&plus;14r3&sol;2e&lowbar;z

(7)

Details

  

For more information including:

• 

a complete list of the routines in the VectorCalculus package, see the Details of the Vector Calculus Package help page.

• 

a complete list of the supported coordinate systems, see the Coordinates help page.

See Also

examples/VectorCalculus

LinearAlgebra

 


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