http://www.maplesoft.com/applications en-us 2012 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 16 May 2012 21:38:09 GMT Wed, 16 May 2012 21:38:09 GMT The latest content added to the Application Center http://www.mapleprimes.com/images/mapleapps.gif http://www.maplesoft.com/applications http://www.maplesoft.com/applications/view.aspx?SID=134198&ref=Feed The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion. <img src="/view.aspx?si=134198/thumb.jpg" alt="Classroom Tips and Techniques: Fourier Series and an Orthogonal Expansions Package" align="left"/>The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion. 134198 Mon, 14 May 2012 04:00:00 Z Dr. Robert Lopez Dr. Robert Lopez http://www.maplesoft.com/applications/view.aspx?SID=133288&ref=Feed The application is an example of minimal size implementation of the freeware chess game Maple wrapper. The file smartchess.maplet has been created using Maple 15.01 working with 64-bit Windows 7. <img src="/applications/images/app_image_blank_lg.jpg" alt="Maple Chess Game Wrapper" align="left"/>The application is an example of minimal size implementation of the freeware chess game Maple wrapper. The file smartchess.maplet has been created using Maple 15.01 working with 64-bit Windows 7. 133288 Mon, 23 Apr 2012 04:00:00 Z Czeslaw Koscielny Czeslaw Koscielny http://www.maplesoft.com/applications/view.aspx?SID=133128&ref=Feed <p>It is shown in the application how to implement a Maple wrapper<br />for the freeware Rubik game (<a href="http://sites.google.com/site/kubrub/rubikscube">http://sites.google.com/site/kubrub/rubikscube</a>).</p> <img src="/applications/images/app_image_blank_lg.jpg" alt="Versatile Rubik's Cube" align="left"/><p>It is shown in the application how to implement a Maple wrapper<br />for the freeware Rubik game (<a href="http://sites.google.com/site/kubrub/rubikscube">http://sites.google.com/site/kubrub/rubikscube</a>).</p> 133128 Wed, 18 Apr 2012 04:00:00 Z Czeslaw Koscielny Czeslaw Koscielny http://www.maplesoft.com/applications/view.aspx?SID=132914&ref=Feed New in Maple 16, the Custom palette is a palette added to Maple by the user. It is populated with task templates that are already in the Task Browser Table of Contents. A separate Tasks palette can be populated with task templates created by the "Create Task" option in the Context Menu for any selection in a worksheet. This article sheds light on these new functionalities, and gives an example of a Custom palette developed to capture part of the geom3d package in task templates. <img src="/view.aspx?si=132914/thumb.jpg" alt="Classroom Tips and Techniques: Custom and Task Palettes" align="left"/>New in Maple 16, the Custom palette is a palette added to Maple by the user. It is populated with task templates that are already in the Task Browser Table of Contents. A separate Tasks palette can be populated with task templates created by the "Create Task" option in the Context Menu for any selection in a worksheet. This article sheds light on these new functionalities, and gives an example of a Custom palette developed to capture part of the geom3d package in task templates. 132914 Thu, 12 Apr 2012 04:00:00 Z Dr. Robert Lopez Dr. Robert Lopez http://www.maplesoft.com/applications/view.aspx?SID=132896&ref=Feed <p><em><span>definition:</span></em></p> <p><strong>un dossier est un dossier qui contient des feuilles * ou des dossiers.<span>Un dossier contient au moins 2 &eacute;l&eacute;ments.</span></strong><br />Si on d&eacute;marre cette proc&eacute;dure r&eacute;currente &agrave; partir d'un dossier D et qu'au final on a r&eacute;ussit &agrave; placer n feuilles ,on dit que le dossier D est un <strong>classement des n feuilles</strong><br />classement(n) donne tous les classements de n feuilles.</p> <p><br />un dossier est repr&eacute;sent&eacute; par une matrice:la premiere ligne est le nom du dossier qui correspond au nombre d'&eacute;l&eacute;ments qu'il contient,la deuxieme ligne est le contenu du dossier.</p> <p>voir image ci-contre: tous les classements de 3 feuilles.</p> <p>le document donne aussi plusieures de mes proc&eacute;dures de combinatoire.</p> <p>NB:Ce document est la version corrig&eacute;e de l'ancien.</p> <img src="/view.aspx?si=132896/classt3.JPG" alt="combinatoire et classements" align="left"/><p><em><span>definition:</span></em></p> <p><strong>un dossier est un dossier qui contient des feuilles * ou des dossiers.<span>Un dossier contient au moins 2 &eacute;l&eacute;ments.</span></strong><br />Si on d&eacute;marre cette proc&eacute;dure r&eacute;currente &agrave; partir d'un dossier D et qu'au final on a r&eacute;ussit &agrave; placer n feuilles ,on dit que le dossier D est un <strong>classement des n feuilles</strong><br />classement(n) donne tous les classements de n feuilles.</p> <p><br />un dossier est repr&eacute;sent&eacute; par une matrice:la premiere ligne est le nom du dossier qui correspond au nombre d'&eacute;l&eacute;ments qu'il contient,la deuxieme ligne est le contenu du dossier.</p> <p>voir image ci-contre: tous les classements de 3 feuilles.</p> <p>le document donne aussi plusieures de mes proc&eacute;dures de combinatoire.</p> <p>NB:Ce document est la version corrig&eacute;e de l'ancien.</p> 132896 Wed, 11 Apr 2012 04:00:00 Z xavier cormier xavier cormier http://www.maplesoft.com/applications/view.aspx?SID=132195&ref=Feed 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. <img src="/view.aspx?si=132195/thumb.jpg" alt="Statistics Enhancements in Maple 16" align="left"/>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. 132195 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132199&ref=Feed 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. <img src="/view.aspx?si=132199/thumb.jpg" alt="Object-Oriented Programming in Maple 16" align="left"/>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. 132199 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132208&ref=Feed 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. <img src="/view.aspx?si=132208/thumb.jpg" alt="Polynomial System Solving in Maple 16" align="left"/>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. 132208 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132209&ref=Feed 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. <img src="/view.aspx?si=132209/thumb.jpg" alt="Physics in Maple 16" align="left"/>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. 132209 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132220&ref=Feed 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. <img src="/applications/images/app_image_blank_lg.jpg" alt="Math Apps in Maple 16" align="left"/>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. 132220 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132223&ref=Feed 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. <img src="/view.aspx?si=132223/thumb.jpg" alt="Interpolation and Smoothing" align="left"/>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. 132223 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132224&ref=Feed 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. <img src="/view.aspx?si=132224/thumb.jpg" alt="Differential Geometry in Maple 16" align="left"/>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. 132224 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132225&ref=Feed 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. <img src="/view.aspx?si=132225/thumb2.jpg" alt="Differential Equations in Maple 16" align="left"/>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. 132225 Tue, 27 Mar 2012 04:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=132143&ref=Feed <p>Some years ago I have written a Maple document ( already on Maple's online) on the subject of animating a simple pendulum for large angles of oscillation. This gave me the chance to test Maple command JacobiSN(time, k). I was very much pleased to see Maple do a wonderful job in getting these Jacobi's elliptic functions without a glitch.<br />Today I am back to these same functions for a similar purpose though much more sophisticated than the previous one.<br />The idea is:<br />1- to get the differential equations of motion for the Spherical Pendulum (SP),<br />2- to solve them,<br />3- to use&nbsp; Maple for finding the inverse of these Elliptic Integrals i.e. finding the displacement z as function of time,<br />4- to get a set of coordinates [x, y, z] for the positions of the bob at different times for plotting,<br />5- finally to work out the necessary steps for the purpose of animation.<br />It turns out that even with only 3 oscillations where each is defined with only 20 positions of the bob for a total of 60 points on the graph, the animation is so overwhelming that Maple reports:<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; " the length of the output exceeds 1 million".<br />Not withstanding this warning, Maple did a perfect job by getting the animation to my satisfaction. <br />Note that with only 60 positions of the bob, the present article length is equal to 11.3 MB! To be able to upload it, I have to save it without running the last command related to the animation. Doing so I reduced it to a mere 570 KB.<br /><br />It was tiring to get through a jumble of formulas, calculations and programming so I wonder why I have to go through all this trouble to get this animation and yet one can get the same thing with much better animation from the internet. I think the reason is the challenge to be able to do things that others have done before and secondly the idea of creating something form nothing then to see it working as expected, gives (at least to me) a great deal of pleasure and satisfaction.<br />This is beside the fact that, to my knowledge, no such animation for (SP) has been published on Maple online with detailed calculations &amp; programming as I did.<br /><br /></p> <img src="/view.aspx?si=132143/433082\Spherical_Pendulum_p.jpg" alt="Spherical Pendulum with Animation" align="left"/><p>Some years ago I have written a Maple document ( already on Maple's online) on the subject of animating a simple pendulum for large angles of oscillation. This gave me the chance to test Maple command JacobiSN(time, k). I was very much pleased to see Maple do a wonderful job in getting these Jacobi's elliptic functions without a glitch.<br />Today I am back to these same functions for a similar purpose though much more sophisticated than the previous one.<br />The idea is:<br />1- to get the differential equations of motion for the Spherical Pendulum (SP),<br />2- to solve them,<br />3- to use&nbsp; Maple for finding the inverse of these Elliptic Integrals i.e. finding the displacement z as function of time,<br />4- to get a set of coordinates [x, y, z] for the positions of the bob at different times for plotting,<br />5- finally to work out the necessary steps for the purpose of animation.<br />It turns out that even with only 3 oscillations where each is defined with only 20 positions of the bob for a total of 60 points on the graph, the animation is so overwhelming that Maple reports:<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; " the length of the output exceeds 1 million".<br />Not withstanding this warning, Maple did a perfect job by getting the animation to my satisfaction. <br />Note that with only 60 positions of the bob, the present article length is equal to 11.3 MB! To be able to upload it, I have to save it without running the last command related to the animation. Doing so I reduced it to a mere 570 KB.<br /><br />It was tiring to get through a jumble of formulas, calculations and programming so I wonder why I have to go through all this trouble to get this animation and yet one can get the same thing with much better animation from the internet. I think the reason is the challenge to be able to do things that others have done before and secondly the idea of creating something form nothing then to see it working as expected, gives (at least to me) a great deal of pleasure and satisfaction.<br />This is beside the fact that, to my knowledge, no such animation for (SP) has been published on Maple online with detailed calculations &amp; programming as I did.<br /><br /></p> 132143 Mon, 26 Mar 2012 04:00:00 Z Dr. Ahmed Baroudy Dr. Ahmed Baroudy http://www.maplesoft.com/applications/view.aspx?SID=131655&ref=Feed This article shows how to construct and visualize a <i>caustic</i>, the envelope of lines emanating from a fixed point, and reflecting off a plane curve. <img src="/view.aspx?si=131655/thumb.jpg" alt="Classroom Tips and Techniques: Caustics for a Plane Curve" align="left"/>This article shows how to construct and visualize a <i>caustic</i>, the envelope of lines emanating from a fixed point, and reflecting off a plane curve. 131655 Mon, 12 Mar 2012 04:00:00 Z Dr. Robert Lopez Dr. Robert Lopez http://www.maplesoft.com/applications/view.aspx?SID=131117&ref=Feed <p>In 1995, Boris Korsunsky published a collection of what he called "braintwisters" physics problems.&nbsp; In 2011, Norman Paris and Michael L. Broide presented a comprehensive analysis of one of the mechanics problems involving the coupled motion of two blocks.&nbsp; This worksheet demonstrates how to use Maple to derive the equations of motion using the calculus of variations, and to solve the differential equations numerically.&nbsp;</p> <img src="/view.aspx?si=131117/431266\a2709019060fd7fc58f2fcf404b072b7.gif" alt="Numerical Solution of a Mechanics Braintwister Problem" align="left"/><p>In 1995, Boris Korsunsky published a collection of what he called "braintwisters" physics problems.&nbsp; In 2011, Norman Paris and Michael L. Broide presented a comprehensive analysis of one of the mechanics problems involving the coupled motion of two blocks.&nbsp; This worksheet demonstrates how to use Maple to derive the equations of motion using the calculus of variations, and to solve the differential equations numerically.&nbsp;</p> 131117 Thu, 23 Feb 2012 05:00:00 Z Dr. Frank Wang Dr. Frank Wang http://www.maplesoft.com/applications/view.aspx?SID=131043&ref=Feed <p>Ce mod&egrave;le compare trois types de vitrage:</p> <ul> <li>un simple vitrage</li> <li>un double vitrage utilisant l'air comme isolant</li> <li>un double vitrage utilisant l'argon comme isolant</li> </ul> <p>This model compares three types of glazing:</p> <ul> <li>Single glazing</li> <li>Double glazing using air as insulation</li> <li>Double glazing using argon as insulation</li> </ul> <img src="/applications/images/app_image_blank_lg.jpg" alt="Double Vitrage (Double Glazed Windows)" align="left"/><p>Ce mod&egrave;le compare trois types de vitrage:</p> <ul> <li>un simple vitrage</li> <li>un double vitrage utilisant l'air comme isolant</li> <li>un double vitrage utilisant l'argon comme isolant</li> </ul> <p>This model compares three types of glazing:</p> <ul> <li>Single glazing</li> <li>Double glazing using air as insulation</li> <li>Double glazing using argon as insulation</li> </ul> 131043 Wed, 22 Feb 2012 05:00:00 Z Maplesoft Maplesoft http://www.maplesoft.com/applications/view.aspx?SID=130787&ref=Feed In this case, the launch angle is adjusted through a motor attached to the anchor pivot (located at the bottom of the red colored rods in the screenshots). As the support link (red) is rotated about the anchor pivot, the tip of the support link (red) will slide along the bottom of the shooter. Given a fixed length of the support link, the shooter angle will vary as the tip of the support link slides towards or away from the pivot point. <img src="/view.aspx?si=130787/thumb.jpg" alt="Pitching Mechanism with Slider Support" align="left"/>In this case, the launch angle is adjusted through a motor attached to the anchor pivot (located at the bottom of the red colored rods in the screenshots). As the support link (red) is rotated about the anchor pivot, the tip of the support link (red) will slide along the bottom of the shooter. Given a fixed length of the support link, the shooter angle will vary as the tip of the support link slides towards or away from the pivot point. 130787 Thu, 16 Feb 2012 05:00:00 Z Dr. Gilbert Lai Dr. Gilbert Lai http://www.maplesoft.com/applications/view.aspx?SID=130788&ref=Feed A mechanism for actively driving the shooter launch angle with the use of a threaded rod. The idea here is that a support link will be extended from the shooter pivot and attached to the thread of a threaded rod. As the rod rotates, the support connection collar will slide up and down the rod with the threads. This will then pitches the shooter up and down about the pivot. <img src="/view.aspx?si=130788/thumb.jpg" alt="Pitching Mechanism with Threaded Rod" align="left"/>A mechanism for actively driving the shooter launch angle with the use of a threaded rod. The idea here is that a support link will be extended from the shooter pivot and attached to the thread of a threaded rod. As the rod rotates, the support connection collar will slide up and down the rod with the threads. This will then pitches the shooter up and down about the pivot. 130788 Thu, 16 Feb 2012 05:00:00 Z Dr. Gilbert Lai Dr. Gilbert Lai http://www.maplesoft.com/applications/view.aspx?SID=130674&ref=Feed Methods for building slider-controlled graphs are explored, and used to show the variations in the limaçon. Then, the conchoid of a cubic is explored with the same set of tools. <img src="/view.aspx?si=130674/thumb.jpg" alt="Classroom Tips and Techniques: Sliders for Parameter-Dependent Curves" align="left"/>Methods for building slider-controlled graphs are explored, and used to show the variations in the limaçon. Then, the conchoid of a cubic is explored with the same set of tools. 130674 Tue, 14 Feb 2012 05:00:00 Z Dr. Robert Lopez Dr. Robert Lopez