Overview of the Student[NumericalAnalysis] Subpackage - Maple Help

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Overview of the Student[NumericalAnalysis] Subpackage

 

Calling Sequence

Description

Visualization

Interactive

Computation

Getting Help with a Command in the Package

Example Worksheets

References

Calling Sequence

Student[NumericalAnalysis][command](arguments)

command(arguments)

Description

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The Student[NumericalAnalysis] subpackage is designed to help teachers present and help students understand the basic material of a standard course in numerical analysis. There are three principal components to the subpackage: computation commands, visualization commands and interactive routines. These components are described in the following sections.

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This subpackage has associated tutors. To access Student[NumericalAnalysis] tutors, select Tools>Tutors>NumericalAnalysis.

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Each command in the Student[NumericalAnalysis] subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.

  

As the underlying implementation of the Student[NumericalAnalysis] subpackage is a module, it is also possible to use the form Student[NumericalAnalysis]:-command or Student:-NumericalAnalysis:-command to access a command. For more information, see Module Members.

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Many of the commands and tutors in the Student[NumericalAnalysis] package can be accessed through the context-menu. These commands are consolidated under the Student[NumericalAnalysis] name.

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The Maple Command Completion facility is helpful for entering the names of Student package commands.

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Note on boolean options: Many of the commands in the Student[NumericalAnalysis] subpackage take boolean options. That is, options of the form option_name = value, where value is true or false. These options are used, for example, to control which components are included in a plot. In all cases, the form option_name = true can be abbreviated as option_name.

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The commands in this subpackage that numerically solve initial value problems will sometimes display an exact result along with the approximated result.  The powerful Maple dsolve, numeric command is used to compute the exact result that is displayed.

Visualization

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The visualization commands in the Student[NumericalAnalysis] subpackage have the capability to return a plot illustrating relevant details of the approximation method. These commands still possess the ability to return a value rather than a plot. Visit each command's help page to see the default return value.

  

For more information on this functionality see Student[NumericalAnalysis][VisualizationOverview].

  

The visualization commands are:

AdamsBashforth

AdamsMoulton

AdamsBashforthMoulton

AdaptiveQuadrature

Bisection

Draw

Euler

FalsePosition

FixedPointIteration

InitialValueProblem

IterativeApproximate

ModifiedNewton

Newton

Quadrature

Roots

RungeKutta

Secant

Steffensen

Taylor

 

 

Interactive

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The interactive routines use Maplets to assist you to work through some of the standard problems of numerical analysis in a visually directed manner. Some of these Maplets display a plot and allow you to experiment by changing the approximation method being plotted. Other Maplets display key steps of the approximation method in an intuitive manner.

  

For more information on this functionality, see Student[NumericalAnalysis][InteractiveOverview].

  

The interactive routines are:

EulerTutor

InitialValueProblemTutor

 

IterativeFormulaTutor

MatrixDecompositionTutor

 

Computation

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The computation commands in the Student[NumericalAnalysis] subpackage implement standard numerical analysis operations.

  

For more information on this functionality, see Student[NumericalAnalysis][ComputationOverview].

  

The computation commands are:

AbsoluteError

AddPoint

ApproximateExactUpperBound

ApproximateValue

BackSubstitution

BasisFunctions

CubicSpline

DataPoints

Distance

DividedDifferenceTable

ExactValue

ForwardSubstitution

Function

Interpolant

InterpolantRemainderTerm

IsConvergent

IsMatrixShape

IterativeFormula

LeadingPrincipalSubmatrix

LinearSolve

LinearSystem

MatrixConvergence

MatrixDecomposition

NevilleTable

NumberOfSignificantDigits

PolynomialInterpolation

RateOfConvergence

RelativeError

RemainderTerm

SpectralRadius

TaylorPolynomial

UpperBoundOfRemainderTerm

VectorLimit

Getting Help with a Command in the Package

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To display the help page for a particular Student[NumericalAnalysis] command, see Getting Help with a Command in a Package.

Example Worksheets

  

For examples using the Student[NumericalAnalysis] subpackage, see Student[NumericalAnalysis] Example Worksheet.

References

  

Burden, R. L., and Faires, J. D., "Numerical Analysis", 8th edition, Thompson Brooks-Cole, 2005

  

Fausett, L. V., "Numerical Methods: Algorithms and Applications", Prentice-Hall, 2003

  

Golub, G. H., and Van Loan, C. F., "Matrix Computations", 3rd edition, Johns Hopkins University Press, 1996

See Also

Student

Student/NumericalAnalysis Example Worksheet

Student[NumericalAnalysis][ComputationOverview]

Student[NumericalAnalysis][InteractiveOverview]

Student[NumericalAnalysis][VisualizationOverview]

 


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