New Editor's Choice Applications

Statistics Enhancements in Maple 16

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

Statistical computations in Maple combine the ease of working in a high-level, interactive environment with a very large and powerful set of algorithms. Large data sets can be handled efficiently with 35 built-in statistical distributions, sampling, estimations, data smoothing, hypothesis testing, and visualization algorithms. In addition, integration with the Maple symbolic engine means that you can easily specify custom distributions by combining existing distributions or simply by giving a formula for the probability or cumulative distribution function. These examples illustrate the use of the Statistics package, with emphasis on enhancements in Maple 16.

Object-Oriented Programming in Maple 16

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

The Maple language is a full programming language designed for mathematical computation, combining the best principles from procedural, functional, and object-oriented programming. Maple 16 adds support for light-weight objects for enhanced object-oriented programming. Such objects integrate closely with Maple using operator overloading, making your objects almost indistinguishable from built-in Maple types. This example illustrates the use of light-weight objects.

Polynomial System Solving in Maple 16

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

Computing and manipulating the real solutions of a polynomial system is a requirement for many application areas, such as biological modeling, robotics, program verification, and control design, to name just a few. For example, an important problem in computational biology is to study the stability of the equilibria (or steady states) of biological systems. This question can often be reduced to solving a parametric system of polynomial equations and inequalities. In this application, these techniques are used to perform stability analysis of a parametric dynamical system and verify mathematical identities through branch cut analysis.

Physics in Maple 16

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

Maple 16 provides the most significant evolution of the Physics package since its introduction in Maple 11, underscoring Maple's goal of having a state-of-the-art environment for algebraic computations in physics. The Physics package in Maple 16 includes 17 new commands that extend its functionality in vector and tensor analysis, general relativity, and quantum fields. In addition, a vast number of changes were introduced to support the goal of making the computational experience as natural as possible, resembling the paper-and-pencil way of doing computations and providing textbook-quality display of results. This application illustrates some of the new features in the Physics package.

Math Apps in Maple 16

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains four of the over 100 new Math Apps that have been added to Maple 16.

Interpolation and Smoothing

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

These examples illustrate 3-D interpolation and smoothing. It shows the use of a smoothing algorithm to create a smooth surface that approximates your noisy data 3-D data, and interpolation methods that generate a surface that matches your data exactly, regardless of whether the data points lie on a uniform or non-uniform grid. Many of these techniques are new in Maple 16.

Differential Geometry in Maple 16

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

With over 250 commands, the DifferentialGeometry package allows sophisticated computations from basic jet calculus to the realm of the mathematics behind general relativity. In addition, 19 differential geometry lessons, from beginner to advanced level, and 6 tutorials illustrate the use of the package in applications. This applications demonstrates some of the new functionality in Maple 16 for working with abstractly defined differential forms, general relativity, and Lie algebras.

Differential Equations in Maple 16

Maplesoft — Tue, 27 Mar 2012 04:00:00 Z

Maple 16 continues to push the frontiers in differential equation solving and extends its lead in computing closed-form solutions to differential equations, adding in even more classes of problems that can be handled. The numeric ODE, DAE, and PDE solvers also continue to evolve. Maple 16 shows significant performance improvements for these solvers, as well as enhanced event handling. This application illustrates many of these improvements.

Parameterizing Motion along a Curve

Shawn Hedman — Wed, 08 Feb 2012 05:00:00 Z

We use the Euler-Lagrange equation to parameterize the motion of a bead on a parabola, a helix, and a piecewise defined combination of the two.

Shoot the Ball

Dr. Gilbert Lai — Fri, 27 Jan 2012 05:00:00 Z

This model stimulates a ball being shot with an initial speed and initial angle (relative to the ground) and determines if the ball hits one of the three predefined targets.

This application is related to a blog post on MaplePrimes: Rebound Rumble: MapleSim Ball Shooting Model for FIRST Robotics 2012

Flow Dynamics in Connected Liquid Tanks

Maplesoft — Mon, 09 Jan 2012 05:00:00 Z

This models investigates the flow dynamics between three liquid tanks connected by two pipes (the first pipe connecting Tank 1 and 2, and the second pipe connecting Tank 2 and 3).

The liquid level in each tank oscillates due to the flow inertia in each pipe. Flow inertia is damped by pipe friction, and eventually the liquid height in each tank reaches an equilibrium.

A Maple worksheet that models the system from a first-principle momentum balance is also attached (see Project > Attachments > Documents > OscillatingTanks.mw). In the Maple worksheet, differential equations that describe a momentum balance and the dynamic change in liquid height in each tank are solved numerically.

The results of the MapleSim model and Maple worksheet agree.

Water Hammer

Maplesoft — Mon, 09 Jan 2012 05:00:00 Z

When a valve at the end of a pipeline suddenly closes, a pressure surge hits the valve and travels along the pipeline. This process is modeled by two PDEs. The PDEs can be discretized along the spatial dimension to give a set of ODEs. This application, for a given set of parameters, solves the resulting ODEs numerically and plots the pressure dynamics at the valve.

Linear Algebra Example Generator

Jeff Knisley — Thu, 05 Jan 2012 05:00:00 Z

One of the challenges in Linear Algebra is in developing problems, projects, and exercises that are both larger dimensional and student-accessible. Indeed, round-off error, computational complexity, difficulty factoring characteristic polynomials of degree 3 or higher, and similar aspects often mean that any problems or applications of rank 3 or higher are approached solely via technology.

However, that same technology can be used to create student-accessible problems and applications of ranks 4 or 5 or even higher, even allowing the creation -- if desired -- of a technology-free course featuring only hand-calculable problems. In this presentation, we present a freely downloadable Maple worksheet that produces these types of problems. Moreover, it can be used to create hand-calculable applications of arbitrarily large rank involving stochastic matrices, eigenvalues and eigenvectors, Leslie matrix models, the simplex method, and several others.

Two files are included. The first is LinearAlgebraExamples and includes all the example generators. The second is LinearAlgebraExamplesApp and is stripped to only the main component interface of the first.

Street-fighting Math

Dr. Robert Israel — Thu, 29 Dec 2011 05:00:00 Z

This interactive Maple document contains a simple street-fighting game and performs a mathematical analysis of it, involving probability and game theory. The document is suitable for presentation in an undergraduate course on operations research, probability or linear programming. No knowledge of Maple is required.

Car Talk Puzzler

Dr. Robert Lopez — Thu, 15 Dec 2011 05:00:00 Z

National Public Radio in the USA carries Car Talk, a humorous phone-in program in which Tom and Ray Magliozzi (Click and Clack, the Tappet Brothers) diagnose and offer solutions for mysterious auto-related maladies. One of the program's segments is a weekly Puzzler, a logic (or other) mental puzzle begging for a solution. On May 21, 2011, their Puzzler caught my attention. Here’s the synopsis:

A six-digit odometer shows a palindromic number. The car it's in is driven no more than an hour, and again the odometer shows a palindromic number. How far was the car driven?

Intrigued, I decided to use Maple to solve the problem. I also wrote a blog post describing how I solved it.

Simple Harmonic Motion

Ali Abu Oam — Fri, 09 Dec 2011 05:00:00 Z

The aim of this topic is to visualize the motion of a simple pendulum which consist of a small mass m suspended by a light inextensible cord of length L from a fixed support.

Coriolis Effect

Pascal Thériault Lauzier — Fri, 09 Dec 2011 05:00:00 Z

The Coriolis effect is a force that modifies the trajectory of falling object on Earth. It is due to the rotation of the referential and, thereby, it is not a real force. The mathematical expression of this effect is obtained from the crossproduct of Earth's angular velocity (omega) with the object's linear velocity (v). The exact equation is F = 2m(v x omega). This worksheet demonstrates the action of the Coriolis effect on a projectile launched from our planet. It includes a graphic of the projectile's path as well as a procedure that determines how far the projectile will travel.

Lead Acid Battery

Maplesoft — Thu, 10 Nov 2011 05:00:00 Z

A model of a lead-acid battery powers a configurable reactive load. This equivalent-circuit battery model is implemented directly from governing equations. The model incorporates both electrical and thermal elements. In the model, the power from a lead-acid battery is used to drive a DC motor. The current sources are used to change the circuit switch from the battery driving the motor to the current sources driving the motor at the 6 hour mark. Then, the current sources drive the motor and recharge the battery at the 10 hour mark.

Quadski Turning and Actuation

Maplesoft — Wed, 09 Nov 2011 05:00:00 Z

A quadski actuation model, double wishbone front suspension and steering linkages for a small off-road vehicle are simulated. Suspension and steering are actuated to determine practical parameters, such as turning radius and bump steer. These multibody models can easily be incorporated into a larger system that includes powertrain, tires, and other elements.

Great Expectations

Dr. Robert Israel — Thu, 27 Oct 2011 04:00:00 Z

An investor is offered what appears to be a great investment opportunity. Unfortunately it doesn't turn out to be so great in the long run. This interactive Maple document explores the situation using simulation and analysis, and suggests a new strategy that would produce better results.

This is an example suitable for presentation in an undergraduate course on probability. No knowledge of Maple is required.