New Tips & Techniques
http://www.maplesoft.com/applications/TipsAndTechniques
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 19 Feb 2017 18:54:06 GMTSun, 19 Feb 2017 18:54:06 GMTThe latest Tips & Techniques applications added to the Application Centerhttp://www.mapleprimes.com/images/mapleapps.gifNew Tips & Techniques
http://www.maplesoft.com/applications/TipsAndTechniques
Classroom Tips and Techniques: Norm of a Matrix
http://www.maplesoft.com/applications/view.aspx?SID=1430&ref=Feed
The greatest benefits from bringing Maple into the classroom are realized when the static pedagogy of a printed textbook is enlivened by the interplay of symbolic, graphic, and numeric calculations made possible by technology. Getting Maple to compute the correct answer is just the first step. Using Maple to bring insights not easily realized with by-hand calculations should be the goal of everyone who sets a hand to improving the learning experiences of students. In this article we will show how Maple can be used to gain insight on what the norm of a matrix means.<img src="/view.aspx?si=1430/thumb.jpg" alt="Classroom Tips and Techniques: Norm of a Matrix" align="left"/>The greatest benefits from bringing Maple into the classroom are realized when the static pedagogy of a printed textbook is enlivened by the interplay of symbolic, graphic, and numeric calculations made possible by technology. Getting Maple to compute the correct answer is just the first step. Using Maple to bring insights not easily realized with by-hand calculations should be the goal of everyone who sets a hand to improving the learning experiences of students. In this article we will show how Maple can be used to gain insight on what the norm of a matrix means.1430Mon, 13 Feb 2017 05:00:00 ZDr. Robert LopezDr. Robert LopezVisualizing Multiple Datasets with BubblePlot
http://www.maplesoft.com/applications/view.aspx?SID=154178&ref=Feed
The BubblePlot command can convey information about three dimensions of a multi-dimensional dataset using the horizontal axis, the vertical axis, and point (bubble) size. Moreover, if a dataset is a time series, BubblePlot can generate an animation that shows the movement of data points over a common period of time.
In the following example, datasets containing information on Gross Domestic Product at Power Purchasing Parity, Life Expectancy, and Population are retrieved for selected countries and visualized.<img src="/view.aspx?si=154178/BubblePlot.png" alt="Visualizing Multiple Datasets with BubblePlot" align="left"/>The BubblePlot command can convey information about three dimensions of a multi-dimensional dataset using the horizontal axis, the vertical axis, and point (bubble) size. Moreover, if a dataset is a time series, BubblePlot can generate an animation that shows the movement of data points over a common period of time.
In the following example, datasets containing information on Gross Domestic Product at Power Purchasing Parity, Life Expectancy, and Population are retrieved for selected countries and visualized.154178Mon, 17 Oct 2016 04:00:00 ZDaniel SkoogDaniel SkoogWorking with Thermophysical Data: Dew-Point and Wet-Bulb Temperature of Air
http://www.maplesoft.com/applications/view.aspx?SID=154054&ref=Feed
Maple can perform calculations and generate visualizations involving thermophysical properties of pure fluids, humid air, and mixtures. Using the dew-point and web-bulb temperature of air as an example, this Tips and Techniques application demonstrates how to access thermophysical properties data, perform calculations that include units, and visualize the results on a psychrometric chart.
<BR><BR>
Atmospheric air contains varying levels of water vapor. Weather reports often quantify the water content of air with its relative humidity; this is the amount of water in air, divided by the maximum amount of water air can hold at the same temperature.
<BR><BR>
Given the temperature and the relative humidity of air, you can calculate:
<UL>
<LI>the temperature below which water condenses out of air - this is known as the dew-point
<LI>the coldest temperature you can achieve through evaporative cooling - this is known as the wet-bulb temperature
</UL><img src="/view.aspx?si=154054/webbulb.PNG" alt="Working with Thermophysical Data: Dew-Point and Wet-Bulb Temperature of Air" align="left"/>Maple can perform calculations and generate visualizations involving thermophysical properties of pure fluids, humid air, and mixtures. Using the dew-point and web-bulb temperature of air as an example, this Tips and Techniques application demonstrates how to access thermophysical properties data, perform calculations that include units, and visualize the results on a psychrometric chart.
<BR><BR>
Atmospheric air contains varying levels of water vapor. Weather reports often quantify the water content of air with its relative humidity; this is the amount of water in air, divided by the maximum amount of water air can hold at the same temperature.
<BR><BR>
Given the temperature and the relative humidity of air, you can calculate:
<UL>
<LI>the temperature below which water condenses out of air - this is known as the dew-point
<LI>the coldest temperature you can achieve through evaporative cooling - this is known as the wet-bulb temperature
</UL>154054Wed, 09 Mar 2016 05:00:00 ZSamir KhanSamir KhanTips and Techniques: Working with Finitely Presented Groups in Maple
http://www.maplesoft.com/applications/view.aspx?SID=153852&ref=Feed
This Tips and Techniques article introduces Maple's facilities for working with finitely presented groups. A finitely presented group is a group defined by means of a finite number of generators, and a finite number of defining relations. It is one of the principal ways in which a group may be represented on the computer, and is virtually the only representation that effectively allows us to compute with many infinite groups.<img src="/view.aspx?si=153852/thumb.jpg" alt="Tips and Techniques: Working with Finitely Presented Groups in Maple" align="left"/>This Tips and Techniques article introduces Maple's facilities for working with finitely presented groups. A finitely presented group is a group defined by means of a finite number of generators, and a finite number of defining relations. It is one of the principal ways in which a group may be represented on the computer, and is virtually the only representation that effectively allows us to compute with many infinite groups.153852Tue, 25 Aug 2015 04:00:00 ZMaplesoftMaplesoftTime Series Analysis: Forecasting Average Global Temperatures
http://www.maplesoft.com/applications/view.aspx?SID=153791&ref=Feed
Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.<img src="/view.aspx?si=153791/thumb.jpg" alt="Time Series Analysis: Forecasting Average Global Temperatures" align="left"/>Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.153791Tue, 21 Apr 2015 04:00:00 ZDaniel SkoogDaniel SkoogTips and Techniques: 3-D Model Import/Export and Printing
http://www.maplesoft.com/applications/view.aspx?SID=153770&ref=Feed
Maple can import from and export to several popular graphics formats. In this tips and techniques, you’ll learn about importing and exporting 3-D graphics files. Examples include printing Maple graphics on 3-D printers.<img src="/view.aspx?si=153770/thumb.jpg" alt="Tips and Techniques: 3-D Model Import/Export and Printing" align="left"/>Maple can import from and export to several popular graphics formats. In this tips and techniques, you’ll learn about importing and exporting 3-D graphics files. Examples include printing Maple graphics on 3-D printers.153770Fri, 13 Mar 2015 04:00:00 ZStephen ForrestStephen ForrestClassroom Tips and Techniques: Real and Complex Derivatives of Some Elementary Functions
http://www.maplesoft.com/applications/view.aspx?SID=153726&ref=Feed
The elementary functions include the six trigonometric and hyperbolic functions and their inverses. For all but five of these 24 functions, Maple's derivative (correct on the complex plane) agrees with the real-variable form found in the standard calculus text. For these five exceptions, this article explores two issues: (1) Does Maple's derivative, restricted to the real domain, agree with the real-variable form; and (2), to what extent do both forms agree on the complex plane.<img src="/view.aspx?si=153726/thumb.jpg" alt="Classroom Tips and Techniques: Real and Complex Derivatives of Some Elementary Functions" align="left"/>The elementary functions include the six trigonometric and hyperbolic functions and their inverses. For all but five of these 24 functions, Maple's derivative (correct on the complex plane) agrees with the real-variable form found in the standard calculus text. For these five exceptions, this article explores two issues: (1) Does Maple's derivative, restricted to the real domain, agree with the real-variable form; and (2), to what extent do both forms agree on the complex plane.153726Wed, 10 Dec 2014 05:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Branch Cuts for a Product of Two Square-Roots
http://www.maplesoft.com/applications/view.aspx?SID=153697&ref=Feed
Naive simplification of f(z) = sqrt(z - 1) sqrt(z + 1) to F(z) = sqrt(z<sup>2</sup> - 1) results in a pair of functions that agree on only part of the complex plane. The enhanced ability of Maple 18 to find and display branch cuts of composite functions is used in this article to explore the branch cuts and regions of agreement/disagreement of f and F.<img src="/view.aspx?si=153697/thumb.jpg" alt="Classroom Tips and Techniques: Branch Cuts for a Product of Two Square-Roots" align="left"/>Naive simplification of f(z) = sqrt(z - 1) sqrt(z + 1) to F(z) = sqrt(z<sup>2</sup> - 1) results in a pair of functions that agree on only part of the complex plane. The enhanced ability of Maple 18 to find and display branch cuts of composite functions is used in this article to explore the branch cuts and regions of agreement/disagreement of f and F.153697Tue, 11 Nov 2014 05:00:00 ZDr. Robert LopezDr. Robert LopezGroebner Bases: What are They and What are They Useful For?
http://www.maplesoft.com/applications/view.aspx?SID=153693&ref=Feed
Since they were first introduced in 1965, Groebner bases have proven to be an invaluable contribution to mathematics and computer science. All general purpose computer algebra systems like Maple have Groebner basis implementations. But what is a Groebner basis? And what applications do Groebner bases have? In this Tips and Techniques article, I’ll give some examples of the main application of Groebner bases, which is to solve systems of polynomial equations.<img src="/view.aspx?si=153693/thumb.jpg" alt="Groebner Bases: What are They and What are They Useful For?" align="left"/>Since they were first introduced in 1965, Groebner bases have proven to be an invaluable contribution to mathematics and computer science. All general purpose computer algebra systems like Maple have Groebner basis implementations. But what is a Groebner basis? And what applications do Groebner bases have? In this Tips and Techniques article, I’ll give some examples of the main application of Groebner bases, which is to solve systems of polynomial equations.153693Fri, 17 Oct 2014 04:00:00 ZProf. Michael MonaganProf. Michael MonaganComputational Performance with evalhf and Compile: A Newton Fractal Case Study
http://www.maplesoft.com/applications/view.aspx?SID=153683&ref=Feed
<p>This Tips and Techniques article focuses on the relative performance of Maple's various modes for floating-point computations. The example used here is the computation of a particular Newton fractal, which is easily parallelizable. We compute an image representation for this fractal under several computational modes, using both serial and multithreaded computation schemes.</p>
<p>This article is a follow up to a previous Tips and Techniques, <a href="http://www.maplesoft.com/applications/view.aspx?SID=153645">evalhf, Compile, hfloat and all that</a>, which discusses functionality differences amongst Maple's the different floating-point computation modes available in Maple.</p><img src="/view.aspx?si=153683/thumb.jpg" alt="Computational Performance with evalhf and Compile: A Newton Fractal Case Study" align="left"/><p>This Tips and Techniques article focuses on the relative performance of Maple's various modes for floating-point computations. The example used here is the computation of a particular Newton fractal, which is easily parallelizable. We compute an image representation for this fractal under several computational modes, using both serial and multithreaded computation schemes.</p>
<p>This article is a follow up to a previous Tips and Techniques, <a href="http://www.maplesoft.com/applications/view.aspx?SID=153645">evalhf, Compile, hfloat and all that</a>, which discusses functionality differences amongst Maple's the different floating-point computation modes available in Maple.</p>153683Fri, 26 Sep 2014 04:00:00 ZDave LinderDave LinderGenerating random numbers efficiently
http://www.maplesoft.com/applications/view.aspx?SID=153662&ref=Feed
Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.<img src="/view.aspx?si=153662/thumb.jpg" alt="Generating random numbers efficiently" align="left"/>Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.153662Mon, 18 Aug 2014 04:00:00 ZDr. Erik PostmaDr. Erik Postmaevalhf, Compile, hfloat and all that
http://www.maplesoft.com/applications/view.aspx?SID=153645&ref=Feed
Users sometimes ask how to make their floating-point (numeric) computations perform faster in Maple. The answers often include references to special terms such as evalhf, the Compiler, and option hfloat. A difficulty for the non-expert lies in knowing which of these can be used, and when. This Tips and Techniques attempts to clear up some of the mystery of these terms, by discussion and functionality comparison.<img src="/applications/images/app_image_blank_lg.jpg" alt="evalhf, Compile, hfloat and all that" align="left"/>Users sometimes ask how to make their floating-point (numeric) computations perform faster in Maple. The answers often include references to special terms such as evalhf, the Compiler, and option hfloat. A difficulty for the non-expert lies in knowing which of these can be used, and when. This Tips and Techniques attempts to clear up some of the mystery of these terms, by discussion and functionality comparison.153645Tue, 22 Jul 2014 04:00:00 ZDave LinderDave LinderCustom Plot Sizing and Shading
http://www.maplesoft.com/applications/view.aspx?SID=153606&ref=Feed
<p>If the number of Online Help queries per topic or the number of click-throughs on errors for a particular area of functionality is anything to go by, then plotting is hands down the most significant functionality in Maple. I saw some data on those recently, and what leapt out was just how much plotting dominated.</p>
<p>When functionality is introduced that affects most kinds of 2D or 3D plots, then it likely affects a great many Maple users in important ways. While there are help pages on the new 2D plot sizing and 3D plot shading options in Maple 18, I find myself using these new options so often I feel that its important to mention them as tips for visualization techniques.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Custom Plot Sizing and Shading" align="left"/><p>If the number of Online Help queries per topic or the number of click-throughs on errors for a particular area of functionality is anything to go by, then plotting is hands down the most significant functionality in Maple. I saw some data on those recently, and what leapt out was just how much plotting dominated.</p>
<p>When functionality is introduced that affects most kinds of 2D or 3D plots, then it likely affects a great many Maple users in important ways. While there are help pages on the new 2D plot sizing and 3D plot shading options in Maple 18, I find myself using these new options so often I feel that its important to mention them as tips for visualization techniques.</p>153606Mon, 16 Jun 2014 04:00:00 ZDave LinderDave LinderCustom Plot Sizing and Shading
http://www.maplesoft.com/applications/view.aspx?SID=153607&ref=Feed
Many Maple users, no matter what they are working on, make use of Maple’s plotting abilities, and so this Tips and Techniques highlights some small but useful new plotting features introduced in Maple 18. Maple 18 give you the ability to set the size of your plots, giving you more control over your document’s use of space, as well as the ability to set the colour gradients used in 3-D plots. In this Tips and Techniques, you will find a variety of example that show you how to take advantage of these new plot options.<img src="/view.aspx?si=153607/thumb.jpg" alt="Custom Plot Sizing and Shading" align="left"/>Many Maple users, no matter what they are working on, make use of Maple’s plotting abilities, and so this Tips and Techniques highlights some small but useful new plotting features introduced in Maple 18. Maple 18 give you the ability to set the size of your plots, giving you more control over your document’s use of space, as well as the ability to set the colour gradients used in 3-D plots. In this Tips and Techniques, you will find a variety of example that show you how to take advantage of these new plot options.153607Mon, 16 Jun 2014 04:00:00 ZDave LinderDave LinderClassroom Tips and Techniques: The Explore Command in Maple 18
http://www.maplesoft.com/applications/view.aspx?SID=153552&ref=Feed
The Explore functionality, which provides an interactive experience with parameter-dependent plots and expressions, has been significantly enhanced in Maple 18. In this Tips and Techniques article, I will focus on some key usage points of using the Explore command with plots, including explorations based on simple Maple plots as well as user-defined plotting procedures.<img src="/view.aspx?si=153552/thumb.jpg" alt="Classroom Tips and Techniques: The Explore Command in Maple 18" align="left"/>The Explore functionality, which provides an interactive experience with parameter-dependent plots and expressions, has been significantly enhanced in Maple 18. In this Tips and Techniques article, I will focus on some key usage points of using the Explore command with plots, including explorations based on simple Maple plots as well as user-defined plotting procedures.153552Wed, 16 Apr 2014 04:00:00 ZDave LinderDave LinderInternet Page Ranking Algorithms
http://www.maplesoft.com/applications/view.aspx?SID=153532&ref=Feed
In this guest article in the Tips and Techniques series, Dr. Michael Monagan explains how internet pages are ranked.<img src="/view.aspx?si=153532/thumb.jpg" alt="Internet Page Ranking Algorithms" align="left"/>In this guest article in the Tips and Techniques series, Dr. Michael Monagan explains how internet pages are ranked.153532Thu, 20 Mar 2014 04:00:00 ZProf. Michael MonaganProf. Michael MonaganThe Mortgage Payment Problem: Approximating a Discrete Process with a Differential Equation
http://www.maplesoft.com/applications/view.aspx?SID=153511&ref=Feed
In this guest article in the Tips and Techniques series, Dr. Michael Monagan uses mortgage interest to test how well a differential equation models what is essentially a discrete process.<img src="/view.aspx?si=153511/thumb.jpg" alt="The Mortgage Payment Problem: Approximating a Discrete Process with a Differential Equation" align="left"/>In this guest article in the Tips and Techniques series, Dr. Michael Monagan uses mortgage interest to test how well a differential equation models what is essentially a discrete process.153511Thu, 20 Feb 2014 05:00:00 ZProf. Michael MonaganProf. Michael MonaganThe House Warming Model
http://www.maplesoft.com/applications/view.aspx?SID=153491&ref=Feed
In this guest article in the Tips and Techniques series, Dr. Michael Monagan discusses a model of heat-flow in a house, and shows how he uses this model in his class.<img src="/view.aspx?si=153491/thumb.jpg" alt="The House Warming Model" align="left"/>In this guest article in the Tips and Techniques series, Dr. Michael Monagan discusses a model of heat-flow in a house, and shows how he uses this model in his class.153491Wed, 22 Jan 2014 05:00:00 ZProf. Michael MonaganProf. Michael MonaganMeasuring Water Flow of Rivers
http://www.maplesoft.com/applications/view.aspx?SID=153480&ref=Feed
In this guest article in the Tips & Techniques series, Dr. Michael Monagan discusses the art and science of measuring the amount of water flowing in a river, and relates his personal experiences with this task to its morph into a project for his calculus classes.<img src="/view.aspx?si=153480/thumb.jpg" alt="Measuring Water Flow of Rivers" align="left"/>In this guest article in the Tips & Techniques series, Dr. Michael Monagan discusses the art and science of measuring the amount of water flowing in a river, and relates his personal experiences with this task to its morph into a project for his calculus classes.153480Fri, 13 Dec 2013 05:00:00 ZProf. Michael MonaganProf. Michael MonaganClassroom Tips and Techniques: Locus of Eigenvalues
http://www.maplesoft.com/applications/view.aspx?SID=153463&ref=Feed
If P(s) is a parameter-dependent square matrix, what is the locus of its eigenvalues as s varies from, say, 0 to 1? For a non-square P, the eigenvalues can become complex, so the loci could exist as curves in the real or complex planes. To avoid these difficulties, consider only real symmetric matrices for which the loci of eigenvalues are real curves, but curves that could intersect. What does it mean to trace an individual eigenvalue of P(0) to P(1) if the eigenvalue has algebraic multiplicity more than 1?<img src="/view.aspx?si=153463/thumb.jpg" alt="Classroom Tips and Techniques: Locus of Eigenvalues" align="left"/>If P(s) is a parameter-dependent square matrix, what is the locus of its eigenvalues as s varies from, say, 0 to 1? For a non-square P, the eigenvalues can become complex, so the loci could exist as curves in the real or complex planes. To avoid these difficulties, consider only real symmetric matrices for which the loci of eigenvalues are real curves, but curves that could intersect. What does it mean to trace an individual eigenvalue of P(0) to P(1) if the eigenvalue has algebraic multiplicity more than 1?153463Fri, 15 Nov 2013 05:00:00 ZDr. Robert LopezDr. Robert Lopez