Overview of the Student VectorCalculus Subpackage
Getting Help with a Command in the Package
The Student:-VectorCalculus subpackage is a collection of commands that perform vector calculus operations.
The Student:-VectorCalculus subpackage is designed to help teachers present and students understand the basic concepts of vector calculus. For the purposes of this subpackage, vector calculus refers to the calculus of functions from Rn to Rm, where 1<m and, normally, n and m are at most 3.
For studying functions from Rn to R, see Student:-MultivariateCalculus.
The basic objects on which the commands in the Student:-VectorCalculus subpackage operate are Vectors, VectorFields (or Vector-valued functions), and scalar functions.
Vectors are the standard vectors of mathematics: they have magnitude and direction, but no position. (The name is capitalized in Maple documentation to distinguish an object built on the newer rtable data structure (introduced in Maple 6) -- Vector, Matrix, or Array -- from an object built on the older table data structure -- vector, matrix, or array.) There are also position Vectors, rooted Vectors, and VectorFields. For details on the differences between these Vectors see VectorCalculus,Details.
The commands in this subpackage keep track of the coordinate system in which Vectors are to be interpreted. You can change this coordinate system with the SetCoordinates command.
For more information on coordinates, see Coordinates.
A VectorField is a function that assigns a Vector to each point in its domain. You construct a VectorField using the VectorField command.
Note: A Vector that is not a VectorField is not interpreted as a constant VectorField by the Student:-VectorCalculus subpackage commands. VectorFields and the other Vectors cannot be used interchangeably.
By default, Vectors and VectorFields created by commands from the Student:-VectorCalculus subpackage are displayed using basis format, that is, as a sum of scalar multiples of basis vectors. VectorFields are visually distinguished in this format by displaying an overbar above each basis vector. For more information on Vector display formats, see BasisFormat.
The Student:-VectorCalculus subpackage has a set of predefined coordinate systems, and all computations in the package can be performed in any of these coordinate systems.
For a complete list of the predefined coordinate systems, see the Coordinates.
The Student:-VectorCalculus subpackage can be thought of as a simplified version of the full VectorCalculus package. The principal differences are (1) only a limited number of coordinate systems are supported; and (2) commands in the Student:-VectorCalculus subpackage often try to guess the intended coordinate system, or coordinate variable names, while the main VectorCalculus package is more strict about requiring that you provide these details.
Each command in the Student:-VectorCalculus subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.
The long form, Student:-VectorCalculus:-command, is always available. The short form can be used after loading the package.
The Maple Command Completion facility is helpful for entering the names of Student package commands.
Many of the commands in the Student:-VectorCalculus package can be accessed through the context panel. First, load the Student:-VectorCalculus package. Then, these commands are consolidated under the Student:-VectorCalculus name.
There are three main components of this subpackage: visualization, interactive and computation. These components are described in the following sections.
The visualization routines help with the understanding of the concepts and theorems of vector calculus by displaying plots illustrating the relevant details. These routines can optionally return computed values or formulas representing the underlying computations.
For more information on this functionality, see Student/VectorCalculus/VisualizationOverview.
The visualization commands are:
The interactive routines use the Maple Maplet technology to assist you to work through some of the standard problems of vector calculus in a visually directed manner. These Maplets display a plot and allow you to experiment by changing the function being plotted, display the effects of various different vector calculus operations or change underlying parameters.
For more information on this functionality, see Student/VectorCalculus/nteractiveOverview.
The interactive commands are:
The computation commands implement the standard operations of vector calculus. Note that the commands in this package generally assume that variables are real-valued, so, for example, a dot product computation does not use conjugates.
For more information on this functionality, see Student/VectorCalculus/ComputationOverview.
The computation commands are:
To display the help page for a particular Student:-VectorCalculus command, see Getting Help with a Command in a Package.
For examples using the Student:-VectorCalculus subpackage, including visualization and interactive features, see Student:-VectorCalculus Example Worksheet.
The VectorCalculus example worksheet offers a more detailed introduction to vector calculus using Maple. Most of the examples covered in that worksheet are also relevant to the Student:-VectorCalculus subpackage. See VectorCalculus Example Worksheet.
Student:-VectorCalculus Example Worksheet
VectorCalculus Example Worksheet
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