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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.

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 non-ideal response using commands.

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

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applications/BandpassFilter: An application to investigate the frequency response for a Bandpass filter.

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applications/BeamDistributedPointLoad: An application that derives an expression for the deflection of a beam with a distributed load and a point load.

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

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applications/BivariatePolynomialRegression: Example to find the surface of best fit for a 3-D data set.

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applications/BlackScholes: Example to compute the option price using three different methods.

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applications/BoltGroupCoefficient: An application that calculates the bolt coefficient for eccentrically loaded bolt groups.

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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/CatalyticCrackingOfEthane: An application that calculates the equilibrium composition of the catalytic cracking of ethane.

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applications/ChemicalKineticsParameterEstimation: An application that estimates the rate parameters for a reversible chemical reaction.

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applications/CountercurrentHeatExchanger: An application that models the temperature dynamics of a countercurrent double-pipe heat exchanger.

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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/DigitalFilterDesign: An application that demonstrates the design and analysis of a discrete filter.

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applications/EconomicPipeSizing: An application that minimizes the total cost of pipework across the lifetime of a plant.

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applications/FFTOptionPricing: An application that calculates an option price using FFTs.

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applications/FilteringAudioApp: An application that lets you apply filters to a WAV file.

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applications/FilteringFrequencyDomainNoise: An application that demonstrates frequency filtering.

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applications/FitHeadFlowRateData: An application that fits head-flow rate data to a pump curve.

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applications/FrequencyDomainSystemIdentification: Example of determining the parameters of a model when its structure is known.

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applications/FuelPod: An application for optimizing the design of a fuel pod.

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applications/GasOrifice: An application that calculates the flow rate through a large-diameter orifice.

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applications/HarmonicOscillator: An application that illustrates a second order harmonic oscillator under different control strategies.

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applications/ImageProcessing: An application that tests the effectiveness of image processing algorithms.

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applications/InteractingTanks: An application that models liquid flow between three tanks connected by two pipes.

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applications/InterauralTimeDelay: An application that introduces a delay in one channel of a sound to change the characteristics of the output.

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applications/InvertedPendulum: An application that simulates the dynamics of an inverted pendulum on a cart.

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applications/MaxFlowRatePartiallyFilledPipe: An application that finds the maximum flow rate in a partially filled circular pipe.

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applications/MaxPressureSurge: An application that finds the excess pressure generated by water hammer due to instantaneous valve closure.

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applications/MOSFETParameterEstimation: An application that estimates the KP and VTO SPICE parameters for an n-channel enhancement mode MOSFET.

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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 model-predicted and actual concentrations of paint produced.

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applications/PumpPower: An application that calculates the pump power for flow between two reservoirs.

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applications/PyramidalHorn: An application that calculates the optimum design parameters for an X-band pyramidal horn.

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

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applications/RobotArm: An application that models a robot arm with three degrees of freedom.

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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/SettlingVelocity: Find the terminal velocity of a particle settling in a fluid.

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applications/SignalGeneration: Example that demonstrates how to efficiently generate signals.

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applications/SimplySupportedBeam: An application that performs a design analysis on a simply supported beam with torsional loading.

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applications/SingleStubMatching: An application that calculates the position of a load impedance on a transmission line, terminated by a short circuit.

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

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applications/SunspotPeriodicity: An application that finds the period of sunspots using FFTs as well as autocorrelation.

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applications/TheGreeks: An application that computes various measurements of risk in mathematical finance.

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applications/ThreeReservoirProblem: An application that calculates the flow rates, flow directions, and head at the common junction connecting three reservoirs.

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applications/TunedMassDamper: An application that finds the optimum spring and damping constant for a tuned mass damper.

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applications/VehicleRide: An application that analyzes vehicle ride and handling.

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applications/WaterHammer: An example of how differential equations can model pressure dynamics at a water valve.

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applications/WaveHeight: An application that fits wave height data to a probability distribution.

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DataFrame/Guide: A guide to working with data frames.

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

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examples/addtable: Extending the power of the integral transforms in Maple.

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examples/AdvancedMapletsLayout: An example Maplet application providing detailed information on how Maplet layouts work.

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examples/AirPassengers: An example of forecasting future air passenger data using TimeSeriesAnalysis.

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

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examples/algcurve: A package for working with algebraic curves.

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examples/applyrl: Rule-based symbolic programming.

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examples/archi: Archimedean solids.

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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/Calculus1Derivatives: Differentiation in the visualization component of the Student[Calculus1] package.

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examples/Calculus1DiffApps: Differentiation applications in the visualization component of the Student[Calculus1] package.

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examples/Calculus1IntApps: Integration applications in the visualization component of the Student[Calculus1] package.

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examples/Calculus1Integration: Integration in the visualization component of the Student[Calculus1] package.

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examples/Calculus1SingleStepping: An overview of single-step problem solving in the Student[Calculus1] package.

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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/Calculus1Theorems: Differentiation theorems in the visualization component of the Student[Calculus1] package.

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examples/Calculus1Visualization: An overview of visualization in 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/CommandTemplate: Template for top-level command help page.

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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/ContextMenu: Examples of context menu use.

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examples/ContextMenu/PackageContextMenus: Examples of creating package-specific context menus.

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examples/ConvexHull: Examples of Convex Hulls in ComputationalGeometry and PolyhedralSets.

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examples/CurveFitting: The CurveFitting package.

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examples/DatabaseGrades: An example of creating and modifying a database.

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examples/DataFrame/Statistics: Examples of using commands from Statistics on data frames.

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examples/DataFrame/Subsets: Examples of finding subsets for data frames.

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examples/DataSets/BubblePlot: Example of visualizing multiple data sets using BubblePlot.

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examples/DataSets/Choropleth/CustomData: Example of visualizing custom data using choropleth maps.

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examples/DefaultUnits: Using units in the default Maple environment.

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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/DEplotSystems: Describes the default models for the DEplot[interactive] differential system tool.

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examples/DifferentialThomas: A package for differential elimination using Thomas decomposition.

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examples/diffop: A subpackage (of DEtools) for differential operators.

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examples/Domains: A tool for developing code for complicated algorithms.

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examples/dsolve_numeric_NewErrorControl: An introduction to error control methods for numerical ODE solutions.

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examples/dual: Duality of polyhedra.

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examples/DynamicSystems: Examples of creating, manipulating, simulating, and plotting linear systems models.

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examples/elliptic: Elliptic integrals examples.

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examples/elliptic2: Elliptic integrals examples.

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examples/EmbeddedComponents/ExploreApp: Building an application with Explore.

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examples/EmbeddedComponents/NumberLine: Building an interactive number line.

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examples/evalntype: One of the extensions to the Maple type system.

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examples/ExampleMaplets: An overview of example Maplet applications.

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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/ExternalCalling: An introduction to the use of external compiled code.

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examples/ExternalCode: Sample command lines for building an OpenMaple application.

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examples/FileTools: An overview of the FileTools package and selected examples.

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examples/finance: Examples of calculations for personal finance.

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examples/fourier: An illustration of the Fourier transform in Maple.

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examples/functionaloperators: Defining and using various forms of functional operators.

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examples/GaussInt: Examples on working with Gaussian Integers.

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examples/GenericGraphAlgorithms: Illustrates generic programming in an example using simple graph algorithms.

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examples/GenericGroups: A demonstration of programming with Maple modules, using generic programming.

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examples/geometry: The Maple geometry package.

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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/GlobalTemperature: An example of forecasting future average global temperature data using TimeSeriesAnalysis.

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

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examples/GraphTheory: An overview of the GraphTheory package.

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examples/hankel: The Hankel transform.

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examples/hilbert: The Hilbert transform.

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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/Interpolation_and_Smoothing: An introduction to interpolation and smoothing of given two-dimensional and three-dimensional data in Maple.

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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/knots: Examples for visualizing various knots.

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examples/LA_Linear_Solve: Using the LinearAlgebra package to solve systems.

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examples/LA_NAG: Using the LinearAlgebra package with NAG routines.

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examples/LA_options: LinearAlgebra package options.

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examples/LA_Syntax_Shortcuts: LinearAlgebra package shortcuts.

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examples/laplace: The Laplace transform.

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examples/lexical: An explanation of lexical scoping in Maple.

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examples/LinearAlgebraComputation: An overview of matrix and vector computations in the Student[LinearAlgebra] package.

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examples/LinearAlgebraInteractive: An overview of the Maplet interface routines in the Student[LinearAlgebra] package.

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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/LinearAlgebraVisualization1: An overview of visualization for vector, plane, and linear system problems in the Student[LinearAlgebra] package.

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examples/LinearAlgebraVisualization2: An overview of visualization for least squares approximation and eigenvector problems in the Student[LinearAlgebra] package.

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examples/linearode: Examples of determining closed-form solutions using dsolve.

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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/MapletBuilder: An introduction to creating Maplets using Maplet Builder.

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examples/MapletBuilderAdvanced: An introduction to creating Advanced Maplets using Maplet Builder.

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examples/MapletsLayout: An introduction to Maplet application layout and design.

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examples/MapletsStyleGuide: A list of guidelines for writing readable Maplet application code.

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examples/MapletsTutorial: An introduction to writing Maplet applications.

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examples/Mathieu: An overview of the Mathieu mathematical functions in Maple.

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examples/matlab: A demonstration of the Matlab package.

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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/mellin: The Mellin transform.

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examples/memo: Using modules to implement memoization.

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

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examples/minimize: Using the Maple minimize command.

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examples/moreStudentMultivariateCalculus: Additional examples for the Student[MultivariateCalculus] package.

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examples/MultivariateCalculus: An overview of the Student[MultivariateCalculus] package.

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examples/NaturalUnits: Using units in the Natural Units environment.

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examples/NumericDDEs: Examples of numeric differential equations with delay.

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examples/NumberTheory/ArithmeticFunctions: Selected examples on arithmetic functions.

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examples/NumberTheory/Divisibility: Selected examples on divisibility.

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examples/NumberTheory/MersennePrimes: Overview of commands relating to Mersenne primes.

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examples/NumberTheory/PrimeNumbers: Overview of working with prime numbers.

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examples/numeric_DAE: Overview of using numeric differential-algebraic equation solvers.

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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/OptimizationLPSolve: Examples of using the Optimization:-LPSolve command and a brief explanation of the algorithms used.

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examples/OptimizationMatrixForm: Overview of using the matrix-form calling sequences in the Optimization package.

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examples/Ore_algebra: The Ore algebras package.

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examples/PackageCommandTemplate: Template for package command help page.

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examples/PackageOverviewTemplate: Template for package overview help page.

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examples/patmatch: How to use the Maple pattern-matching algorithms.

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examples/Physics: Examples for the Physics package.

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examples/piecewise: Using the piecewise function.

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examples/poincare: A package for Hamiltonian equations.

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examples/PolynomialIdeals: Overview of the PolynomialIdeals package.

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examples/PriorityQueues: A demonstration implementing priority queues using Maple modules.

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examples/ProgrammaticContentGeneration: Examples for programmatically generating worksheet content.

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examples/QDifferenceEquations: An overview of the QDifferenceEquations package.

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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/QuotientFields: A generic quotient field implementation using generic programming.

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examples/regular: Regular polygons.

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examples/RegularChains: Studying and solving polynomial systems with the RegularChains library.

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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/RootOf: Using the RootOf function.

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examples/SCApps: Applications of the ScientificConstants package.

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examples/SEAApps: Applications of the ScientificErrorAnalysis package.

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examples/SearchEngine: Construct a simple search engine using Maple.

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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/SimpleUnits: Use units in the Simple Units environment.

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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/slode: The Slode package.

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examples/solve: The Maple equation solver.

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examples/specfcn: Illustrations of special functions available in Maple.

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examples/spread: A package for programmatically manipulating spreadsheets.

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examples/StandardUnits: Using units in the Standard Units environment.

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examples/StatisticsDataSmoothing: An overview of the Statistics package commands for performing data smoothing.

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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/StatisticsHypothesisTesting: An overview of the Statistics package commands for hypothesis testing and inference.

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examples/StatisticsProbabilityDistributions: An overview of the Statistics package commands for statistical distributions and manipulating random variables.

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examples/SteadyStateMarkovChain: Example of how to compute the steady-state vector of a Markov chain.

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examples/stellate: Stellated polyhedra.

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examples/string: Using strings in Maple.

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examples/StudentLinearAlgebra: A selection of examples illustrating the use of Student[LinearAlgebra] package commands.

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examples/StudentNumericalAnalysis: An overview of the Student[NumericalAnalysis] package.

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examples/StudentPrecalculus: An overview of the Student[Precalculus] package.

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examples/Student/Statistics: A selection of examples covering material in a introductory statistics course.

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examples/StudentVectorCalculus: An overview of the Student[VectorCalculus] package.

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examples/SuitcaseModel: An example of modeling a delay differential equation

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examples/SymbolicDifferentiator: Illustrates various module concepts in a symbolic differentiator example.

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

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examples/Threads: An overview of the Threads package.

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examples/transform: Geometric transformations.

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examples/UsefulMapleFunctions: An overview of some useful maple functions.

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examples/VectorCalculus: An overview of vector calculus package.

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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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examples/WorksheetPackage: An introduction to programmatic worksheet access with the Worksheet package.

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Finance/Examples/AsianOptions: Example pricing Asian options using the Finance package.

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Finance/Examples/CalendarsAndDayCounters: Introduction to day count conventions and working with calendars in the Finance package.

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Finance/Examples/EuropeanOptions: Example pricing European options using the Finance package.

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Finance/Examples/LocalVolatility: Example that computes local volatility and implied volatility using the Finance 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 user-selected 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 vapor-compression 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.