Examples and Applications Index
This worksheet provides access to the example worksheets and applications that are available through the help system. The worksheets have been organized into topical sections, with a complete alphabetical listing of all example worksheets at the end. Click the box to the left of a section name to expand the section and display the list of examples. Click the appropriate hyperlink in a section to open the corresponding worksheet.
Example worksheets and workbooks are also installed with the Maple software. Example worksheets can be found in the examples directory of your Maple installation. Sample workbooks can be found in the data/Workbook directory of your Maple installation.
For additional applications and other free resources, visit the Maple Application Center.

Language and System


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examples/binarytree: A demonstration of programming a Maple package, this worksheet implements a dictionary structure that uses binary trees.

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examples/CodeCoverage: A demonstration of programming a Maple package, this worksheet creates a package for code coverage profiling.

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examples/GMP: An introduction to the GNU Multiple Precision (GMP) integer library and Maple exact arbitraryprecision integer arithmetic.

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examples/LinearAlgebraMigration: An overview of converting worksheets that use the superseded linalg package to use the LinearAlgebra and VectorCalculus packages.

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examples/LinkedListPackage: A demonstration of programming a Maple package, this worksheet implements a linked list structure and operations on the pairs.

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examples/Task: Examples using the Task Programming Model for multithreaded programming.



Connectivity


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examples/CodeGeneration: An introduction to the Maple package that controls the translation of Maple code to other languages.

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examples/Quiz: An introduction to generating interactive tests using the Grading package. If desired, you can create a quiz that can then be exported as a Maple T.A. course module.



Calculus


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examples/Calculus1Tangents: Tangents, function inverses, and plotting by sampling in the visualization component of the Student[Calculus1] package.



Statistics


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examples/IrisData: Examples of using summary statistics and principal component analysis on the Iris data set.

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examples/RobustStatistics: An overview of the Statistics package commands for describing data sets that have noisy measurements.

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examples/StatisticsEstimation: An overview of the Statistics package commands for statistical estimation, including maximum likelihood estimation.



App Authoring


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examples/Explore: Examples using the Explore command to construct and insert a collection of embedded components used to explore an expression or a plot.



Maplet Applications


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examples/AlertMaplet: An example Maplet application providing advanced information for the Alert example Maplet application.

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examples/BezoutMatrixMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra BezoutMatrix Maplet application.

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examples/ConditionNumberMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra ConditionNumber Maplet application.

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examples/ConfirmMaplet: An example Maplet application providing advanced information for the example Confirm Maplet application.

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examples/GetColorMaplet: An example Maplet application providing advanced information for the GetColor example Maplet application.

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examples/GetEquationMaplet: An example Maplet application providing advanced information for the GetEquation example Maplet application.

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examples/GetExpressionMaplet: An example Maplet application providing advanced information for the GetExpression example Maplet application.

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examples/GetFileMaplet: An example Maplet application providing advanced information for the GetFile example Maplet application.

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examples/GetInputMaplet: An example Maplet application providing advanced information for the GetInput example Maplet application.

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examples/HilbertMatrixMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra HilbertMatrix Maplet application.

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examples/IntegrationMaplet: An example Maplet application providing advanced information for the advanced Integration Maplet application.

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examples/MatrixNormMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra MatrixNorm Maplet application.

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examples/MessageMaplet: An example Maplet application providing advanced information for the Message example Maplet application.

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examples/QRDecompositionMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra QRDecomposition Maplet application.

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examples/QuestionMaplet: An example Maplet application providing advanced information for the Question example Maplet application.

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examples/SelectionMaplet: An example Maplet application providing advanced information for the Selection example Maplet application.

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examples/ShowTableMaplet: An example Maplet application providing advanced information for the advanced ShowTable Maplet application.

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examples/SingularValuesMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra SingularValues Maplet application.

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examples/VectorNormMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra VectorNorm Maplet application.



Algebra


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examples/LinearAlgebraMigration: An overview of converting worksheets that use the superseded linalg package to use the LinearAlgebra and VectorCalculus packages.



Geometry




Discrete Mathematics


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Combinatorial Structures Package, Sample Structures: A simple collection of combstruct examples showing how to generate random trees, investigate the distribution of height by simulation, enumerate functional graphs, alcohols, necklaces, expression trees, and more.

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Wavelet Transforms: An introduction to the mathematical concepts behind the wavelet transforms available, and the ways in which you would implement such concepts in Maple.



Number Theory




Integration




Integral Transforms




Differential Equations


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examples/deplot: Special facilities for plotting solutions of differential equations.

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examples/deplot3d: Plotting solutions of differential equations in three dimensions.



DifferentialAlgebraic Equations




Symbolic Calculations


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examples/define: Using the Maple define command to specify a function by its behavior.



Numeric Calculations


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examples/Optimization: Overview of using the Optimization package to find local optima. It includes linear programming, quadratic programming, nonlinear programming, and least squares examples.



Mathematical Visualization


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examples/BranchCuts: A visual exploration of branches and branch cuts for the inverse trig and hyperbolic functions.

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examples/Calculus1Tangents: Tangents, function inverses, and plotting by sampling in the visualization component of the Student[Calculus1] package.

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examples/deplot: Special facilities for plotting solutions of differential equations.

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examples/deplot3d: Plotting solutions of differential equations in three dimensions.

See the Plotting Guide for other sample graphs.


Finance




Grading and Assessment


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examples/Quiz: An introduction to generating interactive tests using the Grading package. If desired, you can create a quiz that can then be exported as a Maple T.A. course module.



Science and Engineering


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applications/AntennaArray: An application that calculates the array factor and directivity for a uniform linear antenna array.

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applications/AmplifierGain: An application that plots the gain of an amplifier circuit for both ideal and nonideal response using commands.

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applications/AmplifierGainApp: An application that plots the gain of an amplifier circuit for both ideal and nonideal response using sliders and input fields.

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applications/BinaryDistillation: An application that finds the required number of stages for separating two liquid components by using the McCabeThiele method.

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applications/BouncingBall: Example on how event modeling in the dsolve
command can be used to model a ball bouncing on a hilly terrain.

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applications/DCMotor: Example to obtain the transfer function and state space model of a system, and then design a LQR controller.

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applications/PaintProcess: An application that illustrates how Maple was used to identify and subsequently correct the source of error between the modelpredicted and actual concentrations of paint produced.

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applications/RadiatorDesign: An application that demonstrates the use of Maple's connectivity to CAD systems, and presents a typical usecase, for the design of a radiator assembly.

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applications/ReactionSpontaneity: An application that calculates the temperature at which the reaction of oxygen and nitrogen to form nitrogen monoxide becomes spontaneous.

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applications/StabilityAnalysis: An application that shows how Maple can be used to control the reentry path of a space shuttle by examining the boundaries of constant gain and phase margins.

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ElCentroEarthquakeAnalysis: An application that analyzes accelerometer data from the 1940 El Centro earthquake.

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examples/SignalProcessing: Examples of frequency domain analysis, windowing, filtering, and signal analysis using the Signal Processing package.

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Thermal Engineering with Maple: A collection of applications related to thermal engineering.

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Thermal Engineering/Heat Transfer/Energy Needed to Vaporize Ethanol: An application that calculates the energy needed to vaporize liquid ethanol at an initial temperature and pressure.

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Thermal Engineering/Heat Transfer/Heat Transfer Coefficient across Flat Plate: An application that calculates the heat transfer coefficient of air flowing across a flat plate.

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Thermal Engineering/Misc/Particle Falling through Air: An application that models a particle falling through air.

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Thermal Engineering/Psychrometric Modeling/Adiabatic Mixing of Air: An application that mixes humid air and plots the thermodynamic process on a psychrometric chart.

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Thermal Engineering/Psychrometric Modeling/Human Comfort Zone: An application that conditions air into the human comfort zone and plots the thermodynamic process on a psychrometric chart.

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Thermal Engineering/Misc/Saturation Temperature of Fluids: An application that plots the saturation temperature, or boiling point, of a userselected fluid as a function of pressure.

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Thermal Engineering/Refrigeration/Flow through an Expansion Valve: An application that models the thermodynamics of flow through an expansion valve.

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Thermal Engineering/Refrigeration/Refrigeration Cycle Analysis 1: An application that analyzes a vaporcompression refrigeration cycle.

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Thermal Engineering/Thermodynamic Cycles/Optimize a Rankine Cycle: An application that optimizes the efficiency of a regenerative Rankine cycle.

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Thermal Engineering/Thermodynamic Cycles/Organic Rankine Cycle: An application that analyzes a subcritical organic Rankine cycle.



Alphabetical Listing of all Examples and Applications


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applications/AntennaArray: An application that calculates the array factor and directivity for a uniform linear antenna array.

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applications/AmplifierGain: An application that plots the gain of an amplifier circuit for both ideal and nonideal response using commands.

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applications/AmplifierGainApp: An application that plots the gain of an amplifier circuit for both ideal and nonideal response using sliders and input fields.

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applications/BinaryDistillation: An application that finds the required number of stages for separating two liquid components by using the McCabeThiele method.

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applications/BouncingBall: Example on how event modeling in the dsolve
command can be used to model a ball bouncing on a hilly terrain.

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applications/DCMotor: Example to obtain the transfer function and state space model of a system, and then design a LQR controller.

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applications/PaintProcess: An application that illustrates how Maple was used to identify and subsequently correct the source of error between the modelpredicted and actual concentrations of paint produced.

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applications/RadiatorDesign: An application that demonstrates the use of Maple's connectivity to CAD systems, and presents a typical usecase, for the design of a radiator assembly.

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applications/ReactionSpontaneity: An application that calculates the temperature at which the reaction of oxygen and nitrogen to form nitrogen monoxide becomes spontaneous.

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applications/StabilityAnalysis: An application that shows how Maple can be used to control the reentry path of a space shuttle by examining the boundaries of constant gain and phase margins.

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ElCentroEarthquakeAnalysis: An application that analyzes accelerometer data from the 1940 El Centro earthquake.

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examples/AlertMaplet: An example Maplet application providing advanced information for the Alert example Maplet application.

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examples/BezoutMatrixMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra BezoutMatrix Maplet application.

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examples/binarytree: A demonstration of programming a Maple package, this worksheet implements a dictionary structure that uses binary trees.

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examples/BranchCuts: A visual exploration of branches and branch cuts for the inverse trig and hyperbolic functions.

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examples/Calculus1Tangents: Tangents, function inverses, and plotting by sampling in the visualization component of the Student[Calculus1] package.

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examples/CodeCoverage: A demonstration of programming a Maple package, this worksheet creates a package for code coverage profiling.

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examples/CodeGeneration: An introduction to the Maple package that controls the translation of Maple code to other languages.

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examples/combstruct_attributes: Attribute grammars are a way to express recursively defined properties of structures. They are available in the combstruct package.

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examples/combstruct_gen_funcs: It is possible to produce generating function equations and to solve some of them. Also, there is the allstructs function which performs exhaustive structure generation.

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examples/combstruct_grammars: An introduction to combstruct. Learn the basics of specifications, how to get counting sequences, and how to use predefined structures (including subsets, permutations, and combinations).

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examples/combstruct_sample_structs: A simple collection of combstruct examples showing how to generate random trees, investigate the distribution of height by simulation, enumerate functional graphs, alcohols, necklaces, expression trees, and more.

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examples/ConditionNumberMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra ConditionNumber Maplet application.

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examples/ConfirmMaplet: An example Maplet application providing advanced information for the example Confirm Maplet application.

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examples/define: Using the Maple define command to specify a function by its behavior.

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examples/deplot: Special facilities for plotting solutions of differential equations.

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examples/deplot3d: Plotting solutions of differential equations in three dimensions.

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examples/Explore: Examples using the Explore command to construct and insert a collection of embedded components used to explore an expression or a plot.

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examples/GetColorMaplet: An example Maplet application providing advanced information for the GetColor example Maplet application.

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examples/GetEquationMaplet: An example Maplet application providing advanced information for the GetEquation example Maplet application.

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examples/GetExpressionMaplet: An example Maplet application providing advanced information for the GetExpression example Maplet application.

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examples/GetFileMaplet: An example Maplet application providing advanced information for the GetFile example Maplet application.

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examples/GetInputMaplet: An example Maplet application providing advanced information for the GetInput example Maplet application.

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examples/GMP: An introduction to the GNU Multiple Precision (GMP) integer library and Maple exact arbitraryprecision integer arithmetic.

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examples/HilbertMatrixMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra HilbertMatrix Maplet application.

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examples/IntegrationMaplet: An example Maplet application providing advanced information for the advanced Integration Maplet application.

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examples/IrisData: Examples of using summary statistics and principal component analysis on the Iris data set.

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examples/LinearAlgebraMigration: An overview of converting worksheets that use the superseded linalg package to use the LinearAlgebra and VectorCalculus packages.

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examples/LinkedListPackage: A demonstration of programming a Maple package, this worksheet implements a linked list structure and operations on the pairs.

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examples/MatrixNormMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra MatrixNorm Maplet application.

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examples/MessageMaplet: An example Maplet application providing advanced information for the Message example Maplet application.

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examples/Optimization: Overview of using the Optimization package to find local optima. It includes linear programming, quadratic programming, nonlinear programming, and least squares examples.

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examples/QRDecompositionMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra QRDecomposition Maplet application.

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examples/QuestionMaplet: An example Maplet application providing advanced information for the Question example Maplet application.

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examples/Quiz: An introduction to generating interactive tests using the Grading package. If desired, you can create a quiz that can then be exported as a Maple T.A. course module.

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examples/RobustStatistics: An overview of the Statistics package commands for describing data sets that have noisy measurements.

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examples/SelectionMaplet: An example Maplet application providing advanced information for the Selection example Maplet application.

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examples/ShowTableMaplet: An example Maplet application providing advanced information for the advanced ShowTable Maplet application.

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examples/SignalProcessing: Examples of frequency domain analysis, windowing, filtering, and signal analysis using the Signal Processing package.

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examples/SingularValuesMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra SingularValues Maplet application.

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examples/spread: A package for programmatically manipulating spreadsheets.

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examples/StatisticsEstimation: An overview of the Statistics package commands for statistical estimation, including maximum likelihood estimation.

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examples/Task: Examples using the Task Programming Model for multithreaded programming.

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examples/VectorNormMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra VectorNorm Maplet application.

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examples/Wavelets: An introduction to the mathematical concepts behind the wavelet transforms available, and the ways in which you would implement such concepts in Maple.

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Thermal Engineering with Maple: A collection of applications related to thermal engineering.

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Thermal Engineering/Heat Transfer/Energy Needed to Vaporize Ethanol: An application that calculates the energy needed to vaporize liquid ethanol at an initial temperature and pressure.

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Thermal Engineering/Heat Transfer/Heat Transfer Coefficient across Flat Plate: An application that calculates the heat transfer coefficient of air flowing across a flat plate.

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Thermal Engineering/Misc/Particle Falling through Air: An application that models a particle falling through air.

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Thermal Engineering/Psychrometric Modeling/Adiabatic Mixing of Air: An application that mixes humid air and plots the thermodynamic process on a psychrometric chart.

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Thermal Engineering/Psychrometric Modeling/Human Comfort Zone: An application that conditions air into the human comfort zone and plots the thermodynamic process on a psychrometric chart.

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Thermal Engineering/Misc/Saturation Temperature of Fluids: An application that plots the saturation temperature, or boiling point, of a userselected fluid as a function of pressure.

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Thermal Engineering/Refrigeration/Flow through an Expansion Valve: An application that models the thermodynamics of flow through an expansion valve.

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Thermal Engineering/Refrigeration/Refrigeration Cycle Analysis 1: An application that analyzes a vaporcompression refrigeration cycle.

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Thermal Engineering/Thermodynamic Cycles/Optimize a Rankine Cycle: An application that optimizes the efficiency of a regenerative Rankine cycle.

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Thermal Engineering/Thermodynamic Cycles/Organic Rankine Cycle: An application that analyzes a subcritical organic Rankine cycle.


