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
examples/binarytree: A demonstration of programming a Maple package, this worksheet implements a dictionary structure that uses binary trees.
examples/CodeCoverage: A demonstration of programming a Maple package, this worksheet creates a package for code coverage profiling.
examples/CommandTemplate: Template for top-level command help page.
examples/ContextMenu: Examples of context menu use.
examples/ContextMenu/PackageContextMenus: Examples of creating package-specific context menus.
examples/DefaultUnits: Using units in the default Maple environment.
examples/Domains: A tool for developing code for complicated algorithms.
examples/evalntype: One of the extensions to the Maple type system.
examples/FileTools: An overview of the FileTools package and selected examples.
examples/GenericGraphAlgorithms: Illustrates generic programming in an example using simple graph algorithms.
examples/GenericGroups: A demonstration of programming with Maple modules, using generic programming.
examples/GMP: An introduction to the GNU Multiple Precision (GMP) integer library and Maple exact arbitrary-precision integer arithmetic.
examples/lexical: An explanation of lexical scoping in Maple.
examples/LinearAlgebraMigration: An overview of converting worksheets that use the superseded linalg package to use the LinearAlgebra and VectorCalculus packages.
examples/LinkedListPackage: A demonstration of programming a Maple package, this worksheet implements a linked list structure and operations on the pairs.
examples/matlab: A demonstration of the Matlab package.
examples/memo: Using modules to implement memoization.
examples/NaturalUnits: Using units in the Natural Units environment.
examples/PackageCommandTemplate: Template for package command help page.
examples/PackageOverviewTemplate: Template for package overview help page.
examples/PriorityQueues: A demonstration implementing priority queues using Maple modules.
examples/QuotientFields: A generic quotient field implementation using generic programming.
examples/SearchEngine: Construct a simple search engine using Maple.
examples/SimpleUnits: Use units in the Simple Units environment.
examples/spread: A package for programmatically manipulating spreadsheets.
examples/StandardUnits: Using units in the Standard Units environment.
examples/string: Using strings in Maple.
examples/SymbolicDifferentiator: Illustrates various module concepts in a symbolic differentiator example.
examples/Task: Examples using the Task Programming Model for multithreaded programming.
examples/Threads: An overview of the Threads package.
examples/WorksheetPackage: An introduction to programmatic worksheet access with the Worksheet package.
Connectivity
examples/CodeGeneration: An introduction to the Maple package that controls the translation of Maple code to other languages.
examples/DatabaseGrades: An example of creating and modifying a database.
examples/ExternalCalling: An introduction to the use of external compiled code.
examples/ExternalCode: Sample command lines for building an OpenMaple application.
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
examples/Calculus1Derivatives: Differentiation in the visualization component of the Student[Calculus1] package.
examples/Calculus1DiffApps: Differentiation applications in the visualization component of the Student[Calculus1] package.
examples/Calculus1IntApps: Integration applications in the visualization component of the Student[Calculus1] package.
examples/Calculus1Integration: Integration in the visualization component of the Student[Calculus1] package.
examples/Calculus1SingleStepping: An overview of single-step problem solving in the Student[Calculus1] package.
examples/Calculus1Tangents: Tangents, function inverses, and plotting by sampling in the visualization component of the Student[Calculus1] package.
examples/Calculus1Theorems: Differentiation theorems in the visualization component of the Student[Calculus1] package.
examples/Calculus1Visualization: An overview of visualization in the Student[Calculus1] package.
examples/MultivariateCalculus: An overview of the Student[MultivariateCalculus] package.
examples/moreStudentMultivariateCalculus: Additional examples for the Student[MultivariateCalculus] package.
examples/StudentPrecalculus: An overview of the Student[Precalculus] package.
examples/StudentVectorCalculus: An overview of the Student[VectorCalculus] package.
examples/VectorCalculus: An overview of vector calculus package.
Statistics
DataFrame/Guide: A guide to working with data frames.
examples/AirPassengers: An example of forecasting future air passenger data using TimeSeriesAnalysis.
examples/DataFrame/Statistics: Examples of using commands from Statistics on data frames.
examples/DataFrame/Subsets: Examples of finding subsets for data frames.
examples/DataSets/BubblePlot: Example of visualizing multiple data sets using BubblePlot.
examples/DataSets/Choropleth/CustomData: Example of visualizing custom data using choropleth maps.
examples/GlobalTemperature: An example of forecasting future average global temperature data using TimeSeriesAnalysis.
examples/IrisData: Examples of using summary statistics and principal component analysis on the Iris data set.
examples/RobustStatistics: An overview of the Statistics package commands for describing data sets that have noisy measurements.
examples/StatisticsDataSmoothing: An overview of the Statistics package commands for performing data smoothing.
examples/StatisticsEstimation: An overview of the Statistics package commands for statistical estimation, including maximum likelihood estimation.
examples/StatisticsHypothesisTesting: An overview of the Statistics package commands for hypothesis testing and inference.
examples/StatisticsProbabilityDistributions: An overview of the Statistics package commands for statistical distributions and manipulating random variables.
examples/SteadyStateMarkovChain: Compute the steady-state vector of a Markov chain.
examples/Student/Statistics: A selection of examples covering material in a introductory statistics course.
examples/Student/Statistics,DescriptiveStatisticsQuiz: An example worksheet showing how to create quizzes for descriptive statistics.
App Authoring
examples/EmbeddedComponents/ExploreApp: Building an application with Explore.
examples/EmbeddedComponents/NumberLine: Building an interactive number line.
examples/Explore: Examples using the Explore command to construct and insert a collection of embedded components used to explore an expression or a plot.
examples/ProgrammaticContentGeneration: Examples for programmatically generating worksheet content.
Maplet Applications
examples/AdvancedMapletsLayout: An example Maplet application providing detailed information on how Maplet layouts work.
examples/AlertMaplet: An example Maplet application providing advanced information for the Alert example Maplet application.
examples/BezoutMatrixMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra BezoutMatrix Maplet application.
examples/ConditionNumberMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra ConditionNumber Maplet application.
examples/ConfirmMaplet: An example Maplet application providing advanced information for the example Confirm Maplet application.
examples/ExampleMaplets: An overview of example Maplet applications.
examples/GetColorMaplet: An example Maplet application providing advanced information for the GetColor example Maplet application.
examples/GetEquationMaplet: An example Maplet application providing advanced information for the GetEquation example Maplet application.
examples/GetExpressionMaplet: An example Maplet application providing advanced information for the GetExpression example Maplet application.
examples/GetFileMaplet: An example Maplet application providing advanced information for the GetFile example Maplet application.
examples/GetInputMaplet: An example Maplet application providing advanced information for the GetInput example Maplet application.
examples/HilbertMatrixMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra HilbertMatrix Maplet application.
examples/IntegrationMaplet: An example Maplet application providing advanced information for the advanced Integration Maplet application.
examples/MapletBuilder: An introduction to creating Maplets using Maplet Builder.
examples/MapletBuilderAdvanced: An introduction to creating Advanced Maplets using Maplet Builder.
examples/MapletsLayout: An introduction to Maplet application layout and design.
examples/MapletsStyleGuide: A list of guidelines for writing readable Maplet application code.
examples/MapletsTutorial: An introduction to writing Maplet applications.
examples/MatrixNormMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra MatrixNorm Maplet application.
examples/MessageMaplet: An example Maplet application providing advanced information for the Message example Maplet application.
examples/QRDecompositionMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra QRDecomposition Maplet application.
examples/QuestionMaplet: An example Maplet application providing advanced information for the Question example Maplet application.
examples/SelectionMaplet: An example Maplet application providing advanced information for the Selection example Maplet application.
examples/ShowTableMaplet: An example Maplet application providing advanced information for the advanced ShowTable Maplet application.
examples/SingularValuesMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra SingularValues Maplet application.
examples/VectorNormMaplet: An example Maplet application providing advanced information for the advanced LinearAlgebra VectorNorm Maplet application.
Algebra
examples/LA_Linear_Solve: Using the LinearAlgebra package to solve systems.
examples/LA_NAG: Using the LinearAlgebra package with NAG routines.
examples/LA_options: LinearAlgebra package options.
examples/LA_Syntax_Shortcuts: LinearAlgebra package shortcuts.
examples/LinearAlgebraComputation: An overview of matrix and vector computations in the Student[LinearAlgebra] package.
examples/LinearAlgebraInteractive: An overview of the Maplet interface routines in the Student[LinearAlgebra] package.
examples/LinearAlgebraVisualization1: An overview of visualization for vector, plane, and linear system problems in the Student[LinearAlgebra] package.
examples/LinearAlgebraVisualization2: An overview of visualization for least squares approximation and eigenvector problems in the Student[LinearAlgebra] package.
examples/StudentLinearAlgebra: A selection of examples illustrating the use of Student[LinearAlgebra] package commands.
examples/Ore_algebra: The Ore algebras package.
examples/PolynomialIdeals: Overview of the PolynomialIdeals package.
examples/QuantifierElimination: An overview of the QuantifierElimination package.
examples/RegularChains: Studying and solving polynomial systems with the RegularChains library.
Geometry
examples/algcurve: A package for working with algebraic curves.
examples/archi: Archimedean solids.
examples/ConvexHull: Examples of Convex Hulls in ComputationalGeometry and PolyhedralSets.
examples/dual: Duality of polyhedra.
examples/geometry: The Maple geometry package.
examples/regular: Regular polygons.
examples/stellate: Stellated polyhedra.
examples/transform: Geometric transformations.
Discrete Mathematics
Introduction to the Combinatorial Structures package: 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).
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.
The Combstruct Package, Generating Functions: 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.
Attribute Grammars and Combinatorics: Attribute grammars are a way to express recursively defined properties of structures. They are available in the combstruct package.
Q-Difference Equations: An overview of the QDifferenceEquations package.
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
examples/GaussInt: Examples on working with Gaussian Integers.
examples/NumberTheory/ArithmeticFunctions: Selected examples on arithmetic functions.
examples/NumberTheory/Divisibility: Selected examples on divisibility.
examples/NumberTheory/MersennePrimes: Overview of commands relating to Mersenne primes.
examples/NumberTheory/PrimeNumbers: Overview of working with prime numbers.
Integration
examples/elliptic: Elliptic Integration examples.
examples/elliptic2: More Elliptic Integration examples.
Integral Transforms
examples/addtable: Extending the power of the integral transforms in Maple.
examples/fourier: An illustration of the Fourier transform in Maple.
examples/hankel: The Hankel transform.
examples/hilbert: The Hilbert transform.
examples/laplace: The Laplace transform.
examples/mellin: The Mellin transform.
Differential Equations
examples/deplot: Special facilities for plotting solutions of differential equations.
examples/deplot3d: Plotting solutions of differential equations in three dimensions.
examples/DEplotSystems: Describes the default models for the DEplot[interactive] differential system tool.
examples/DifferentialThomas: A package for differential elimination using Thomas decomposition.
examples/diffop: A subpackage (of DEtools) for differential operators.
examples/linearode: Examples of determining closed-form solutions using dsolve.
examples/NumericDDEs: Examples of numeric differential equations with delay.
examples/pdsolve_boundaryconditions: Describes how pdsolve can adjust arbitrary functions and constants of PDE solutions, such that boundary conditions are satisfied.
examples/poincare: A package for Hamiltonian equations.
examples/slode: The Slode package.
examples/SuitcaseModel: An example of modeling a delay differential equation
Differential-Algebraic Equations
examples/numeric_DAE: Overview of using numeric differential-algebraic equation solvers.
Symbolic Calculations
examples/applyrl: Rule-based symbolic programming.
examples/define: Using the Maple define command to specify a function by its behavior.
examples/functionaloperators: Defining and using various forms of functional operators.
examples/Mathieu: An overview of the Mathieu mathematical functions in Maple.
examples/minimize: Using the Maple minimize command.
examples/patmatch: How to use the Maple pattern-matching algorithms.
examples/piecewise: Using the piecewise function.
examples/RootOf: Using the RootOf function.
examples/solve: The Maple equation solver.
examples/UsefulMapleFunctions: An overview of some useful maple functions.
Numeric Calculations
examples/Optimization: Overview of using the Optimization package to find local optima. It includes linear programming, quadratic programming, nonlinear programming, and least squares examples.
examples/OptimizationLPSolve: Examples of using the Optimization:-LPSolve command and a brief explanation of the algorithms used.
examples/OptimizationMatrixForm: Overview of using the matrix-form calling sequences in the Optimization package.
examples/specfcn: Illustrations of special functions available in Maple.
examples/StudentNumericalAnalysis: An overview of the Student[NumericalAnalysis] package.
Mathematical Visualization
examples/BranchCuts: A visual exploration of branches and branch cuts for the inverse trig and hyperbolic functions.
examples/CurveFitting: The CurveFitting package.
examples/Explore: Examples using the Explore command.
examples/GraphTheory: An overview of the GraphTheory package.
examples/Interpolation_and_Smoothing: An introduction to interpolation and smoothing of given two-dimensional and three-dimensional data in Maple.
examples/knots: Examples for visualizing various knots.
See the Plotting Guide for other sample graphs.
Finance
applications/BlackScholes: Example to compute the option price using three different methods.
applications/FFTOptionPricing: An application that calculates an option price using FFTs.
applications/TheGreeks: Compute various measurements of risk in mathematical finance.
examples/finance: Examples of calculations for personal finance.
Finance/Examples/AsianOptions: Example pricing Asian options using the Finance package.
Finance/Examples/CalendarsAndDayCounters: Introduction to day count conventions and working with calendars in the Finance package.
Finance/Examples/EuropeanOptions: Example pricing European options using the Finance package.
Finance/Examples/LocalVolatility: Example that computes local volatility and implied volatility using the Finance package.
Grading and Assessment
examples/Student/Statistics/DescriptiveStatisticsQuiz: An example worksheet showing how to create quizzes for descriptive statistics.
Science and Engineering
applications/AmplifierGain: An application that plots the gain of an amplifier circuit for both ideal and non-ideal response using commands.
applications/AmplifierGainApp: An application that plots the gain of an amplifier circuit for both ideal and non-ideal response using sliders and input fields.
applications/AntennaArray: An application that calculates the array factor and directivity for a uniform linear antenna array.
applications/BandpassFilter: An application to investigate the frequency response for a Bandpass filter.
applications/BeamDistributedPointLoad: An application that derives an expression for the deflection of a beam with a distributed load and a point load.
applications/BinaryDistillation: An application that finds the required number of stages for separating two liquid components by using the McCabe-Thiele method.
applications/BivariatePolynomialRegression: Example to find the surface of best fit for a 3-D data set.
applications/BoltGroupCoefficient: An application that calculates the bolt coefficient for eccentrically loaded bolt groups.
applications/BouncingBall: Example on how event modeling in the dsolve command can be used to model a ball bouncing on a hilly terrain.
applications/CatalyticCrackingOfEthane: An application that calculates the equilibrium composition of the catalytic cracking of ethane.
applications/ChemicalKineticsParameterEstimation: An application that estimates the rate parameters for a reversible chemical reaction.
applications/CountercurrentHeatExchanger: An application that models the temperature dynamics of a countercurrent double-pipe heat exchanger.
applications/DCMotor: Example to obtain the transfer function and state space model of a system, and then design a LQR controller.
applications/DigitalFilterDesign: An application that demonstrates the design and analysis of a discrete filter.
applications/EconomicPipeSizing: An application that minimizes the total cost of pipework across the lifetime of a plant.
applications/FilteringAudioApp: An application that lets you apply filters to a WAV file.
applications/FilteringFrequencyDomainNoise: An application that demonstrates frequency filtering.
applications/FitHeadFlowRateData: An application that fits head-flow rate data to a pump curve.
applications/FrequencyDomainSystemIdentification: Example of determining the parameters of a model when its structure is known.
applications/FuelPod: An application for optimizing the design of a fuel pod.
applications/GasOrifice: An application that calculates the flow rate through a large-diameter orifice.
applications/GibbsEnergyOfFormationOfEthanol: An application that calculates the Gibbs energy of formation of ethanol (C2H5OH) at any temperature, employing thermodynamic data.
applications/HarmonicOscillator: An application that illustrates a second order harmonic oscillator under different control strategies.
applications/HelicalSpring: An application that optimizes the design of a helical spring.
applications/ImageProcessing: An application that tests the effectiveness of image processing algorithms.
applications/InteractingTanks: An application that models liquid flow between three tanks connected by two pipes.
applications/InterauralTimeDelay: An application that introduces a delay in one channel of a sound to change the characteristics of the output.
applications/InvertedPendulum: An application that simulates the dynamics of an inverted pendulum on a cart.
applications/MaxFlowRatePartiallyFilledPipe: An application that finds the maximum flow rate in a partially filled circular pipe.
applications/MaxPressureSurge: An application that finds the excess pressure generated by water hammer due to instantaneous valve closure.
applications/MOSFETParameterEstimation: An application that estimates the KP and VTO SPICE parameters for an n-channel enhancement mode MOSFET.
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.
applications/PumpPower: An application that calculates the pump power for flow between two reservoirs.
applications/PyramidalHorn: An application that calculates the optimum design parameters for an X-band pyramidal horn.
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.
applications/ReactionSpontaneity: An application that calculates the temperature at which the reaction of oxygen and nitrogen to form nitrogen monoxide becomes spontaneous.
applications/RobotArm: An application that models a robot arm with three degrees of freedom.
applications/SettlingVelocity: An application that finds the terminal velocity of a particle settling in a fluid.
applications/SignalGeneration: Example that demonstrates how to efficiently generate signals.
applications/SimplySupportedBeam: An application that performs a design analysis on a simply supported beam with torsional loading.
applications/SingleStubMatching: An application that calculates the position of a load impedance on a transmission line, terminated by a short circuit.
applications/SunspotPeriodicity: An application that finds the period of sunspots using FFTs as well as autocorrelation.
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.
applications/ThreeReservoirProblem: An application that calculate the flow rates, flow directions, and head at the common junction connecting three reservoirs.
applications/TunedMassDamper: An application that finds the optimum spring and damping constant for a tuned mass damper.
applications/VehicleRide: Analyze vehicle ride and handling.
applications/WaterHammer: An example of how differential equations can model pressure dynamics at a water valve.
applications/WaveHeight: An application that fits wave height data to a probability distribution.
applications/WeldedBeam: An application that optimizes the design of a welded beam to minimize cost.
ElCentroEarthquakeAnalysis: An application that analyzes accelerometer data from the 1940 El Centro earthquake.
examples/DynamicSystems: Examples of creating, manipulating, simulating, and plotting linear systems models.
examples/Physics: Examples for the Physics package.
examples/SCApps: Applications of the ScientificConstants package.
examples/SEAApps: Applications of the ScientificErrorAnalysis package.
examples/SignalProcessing: Examples of frequency domain analysis, windowing, filtering, and signal analysis using the Signal Processing package.
Thermal Engineering with Maple: A collection of applications related to thermal engineering.
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.
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.
Thermal Engineering/Misc/Particle Falling through Air: An application that models a particle falling through air.
Thermal Engineering/Psychrometric Modeling/Adiabatic Mixing of Air: An application that mixes humid air and plots the thermodynamic process on a psychrometric chart.
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.
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.
Thermal Engineering/Refrigeration/Flow through an Expansion Valve: An application that models the thermodynamics of flow through an expansion valve.
Thermal Engineering/Refrigeration/Refrigeration Cycle Analysis 1: An application that analyzes a vapor-compression refrigeration cycle.
Thermal Engineering/Thermodynamic Cycles/Optimize a Rankine Cycle: An application that optimizes the efficiency of a regenerative Rankine cycle.
Thermal Engineering/Thermodynamic Cycles/Organic Rankine Cycle: An application that analyzes a subcritical organic Rankine cycle.
Alphabetical Listing of all Examples and Applications
applications/SettlingVelocity: Find the terminal velocity of a particle settling in a fluid.
applications/TheGreeks: An application that computes various measurements of risk in mathematical finance.
applications/ThreeReservoirProblem: An application that calculates the flow rates, flow directions, and head at the common junction connecting three reservoirs.
applications/VehicleRide: An application that analyzes vehicle ride and handling.
Canvas/ElementsAndLayout: Examples that illustrate the elements of a canvas in Maple and Maple Learn.
Example/DirectionFieldPlot: Visualization of direction field plots using the DocumentTools,Canvas package.
Example/FindPrimes: Using DocumentTools/Canvas to check whether user has input prime numbers, or not.
Example/NormalDistribution The histogram and density plot are computed for a list of student grades using the DocumentTools/Canvas subpackage.
Example/SolveFeedback: In this example, a user is asked to solve a linear equation. The DocumentTools/Canvas subpackage is used to check their work and provide feedback.
Example/WordProblem: Using DocumentTools/Canvas commands to create a word problem example.
examples/combstruct_attributes: Attribute grammars are a way to express recursively defined properties of structures. They are available in the combstruct package.
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.
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).
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.
examples/dsolve_numeric_NewErrorControl: An introduction to error control methods for numerical ODE solutions.
examples/elliptic: Elliptic integrals examples.
examples/elliptic2: Elliptic integrals examples.
examples/QDifferenceEquations: An overview of the QDifferenceEquations package.
examples/SteadyStateMarkovChain: Example of how to compute the steady-state vector of a Markov chain.
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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