Overview of the Student NumericalAnalysis Subpackage
Calling SequenceDescriptionVisualizationInteractiveComputationGetting Help with a Command in the PackageDetails and Example WorksheetReferences
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Student:-NumericalAnalysis:-command(arguments)
command(arguments)
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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.
This subpackage has associated tutors. To access Student:-NumericalAnalysis tutors, select Tools>Tutors>NumericalAnalysis.
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.
The long form, Student:-NumericalAnalysis:-command, is always available. The short form can be used after loading the package.
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.
The Maple Command Completion facility is helpful for entering the names of Student package commands.
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.
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.
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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:
AdamsBashforthAdamsMoultonAdamsBashforthMoultonAdaptiveQuadratureBisectionDrawEulerFalsePositionFixedPointIterationInitialValueProblemIterativeApproximateModifiedNewtonNewtonQuadratureRootsRungeKuttaSecantSteffensenTaylor
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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:
EulerTutorInitialValueProblemTutorIterativeFormulaTutorMatrixDecompositionTutor
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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:
AbsoluteErrorAddPointApproximateExactUpperBoundApproximateValueBackSubstitutionBasisFunctionsCubicSplineDataPointsDistanceDividedDifferenceTableExactValueForwardSubstitutionFunctionInterpolantInterpolantRemainderTermIsConvergentIsMatrixShapeIterativeFormulaLeadingPrincipalSubmatrixLinearSolveLinearSystemMatrixConvergenceMatrixDecompositionNevilleTableNumberOfSignificantDigitsPolynomialInterpolationRateOfConvergenceRelativeErrorRemainderTermSpectralRadiusTaylorPolynomialUpperBoundOfRemainderTermVectorLimit
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To display the help page for a particular Student:-NumericalAnalysis command, see Getting Help with a Command in a Package.
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For details on how the commands in this package fall into the subject areas Interpolation, Quadrature, Root Finding, Numerical LinearAlgebra, Initial Value Problems, and more, see the Glossary of Commands.
For examples using the Student:-NumericalAnalysis subpackage, see Student:-NumericalAnalysis Example Worksheet.
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk5">References</Text-field>
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 AlsoGlossary of CommandsStudentStudent:-NumericalAnalysis Example WorksheetStudent[NumericalAnalysis][ComputationOverview]Student[NumericalAnalysis][InteractiveOverview]Student[NumericalAnalysis][VisualizationOverview]