MaplePrimes Posts

MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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    The Bohemian Matrix Calendar 2022 is up!  You may find it at https://rcorless.github.io/ (four versions: letter/A4 paper, Sunday/Monday start to the week).

    It prints quite well (with proper equipment).  I wish you all the best for 2022.

     

    Since the start of the pandemic, I have been involved in online mathematics tutoring. I tried many different applications to best communicate with my students, and ended up sticking with Maple Learn. Here’s my setup, and why I chose Maple Learn.

     

    My Setup

    When I have an online tutoring session, I join a scheduled video call to “see” my students. I then open a blank Maple Learn document, and share my screen. I explain whatever I need to explain, while writing key information on the Maple Learn document. When I don’t want Learn to interpret what I write, I go into text mode; when I do (e.g. when I want to graph a function), I stay in math mode. When the class is over, I send the document’s sharelink to my students by email, so that they can access it. 

    Here is an example of a Maple Learn document (pictured below) that I created while teaching trigonometry to a student. Keep in mind that I typed this while on call with the student, so the document is very simple - it only uses the most basic features of Maple Learn.

     

    Why I Chose Maple Learn

    My main student wants me to teach him trigonometry ahead of it being taught to him at school. For this, I need to be able to write lots of text and math easily, while on video call with him. 

    Microsoft Word is not good enough for this: the equation editor is too clumsy. I also tried drawing tools where you can move your mouse to draw on the screen, but they make it too hard to write text. I even tried pointing a camera at my desk and writing the notes by hand, but my handwriting is terrible, and I could never find the right position for the camera. That’s the main reason why I chose Maple Learn: it lets me write both text and math quickly and simply, unlike many other applications.

    There are some other benefits to using Maple Learn. I like that I can organize what I write in a visually appealing manner on the canvas, by moving groups around. I like that I can graph functions within Maple Learn, without having to open a graphing calculator in a separate tab. Finally, I find the sharelink feature convenient for sending the notes to my students after class.

     

    Disclaimer: I discovered Maple Learn while working at Maplesoft during a co-op term.

     

    As always, it's just about drawings.
    The parametric equation of a circle has 3 variables and two equations. In 3-dimensional space, a circle is a spiral, but we only need one projection of this spiral into 2-dimensional space, and we also know how  the rest 2 it's projections on flat space look.
    If we look at the equation of the sphere in parametric form, we will see that these are 3 equations and 5 variables:
    x1 = sin(x4)*cos(x5); 
    x2 = sin(x4)*sin(x5); 
    x3 = cos(x4);
    And so I wanted to see how the remaining 9 projections of the sphere onto 3-dimensional space look. It is very easy to do this with Maple.
    SPHERE.mw

    Are you teaching a calculus course? Then use Maple Learn, Maplesoft’s free online product, to do so.

    Below are some examples of calculus documents you can create in Maple Learn.

     

    1. Documents Explaining Concepts with Interactive Visuals

    Example: Visualizing the Formal Definition of the Derivative

     

    2. Interactive Quizzes

    Example: The Product Rule: Practice Questions

     

    3. Documents Using Maple to Perform Complex Operations

    Example: Taylor Series Approximation Calculator

     

    Maplesoft’s learn content team has already created about 200 Maple Learn calculus documents! The full list is here. You can modify these documents easily, and use them to teach your calculus class as well.

    Is there a possibility for maple ambassadors to purchase the new maple version now?

    It would be great if maplesoft come forward to help maple ambassadors have the ease to access latest version for mutual growth and benefits.

    Cheers.

    RK

    A user wonders if there is a straightforward way to show US states with names using the WorldMap Data Set in Maple

    We suggest something like the attached: map-of-us-with-states.mw

     

    restart; with(DataSets:-Builtin); r := Reference("GeoNames"); states := r[[Country = "United States", Type = "first-order administrative division"]]; w := WorldMap(); w:-AddPoints(w, states); Display(w, mapdata = fine, style = polygonoutline, size = [2000, 1500])

     

     

    I ask a lot of question on MaplePrimes.

    I can get  a list of all my question. 

    I like to search in this list to people on the forum who has answered my questions

    Is this possible to add this functionality in MaplePrimes?

    Jan

    I've said it before, and I'll say it again, at Maplesoft, I have the privilege of working with some of the most talented and creative minds around. My colleagues are constantly pushing the boundaries of what we can build and what our products can do.Christmas Wreath in Maple Learn

    So to close out 2021, I wanted to share a video that one of our brilliant developers, Marek, sent the company. Marek emails a greeting every year wishing his Maplesoft colleagues a Happy Holiday.  Well, this year, he stepped it up a notch and created this superb video explaining "How to decorate for Christmas using Math", where he created a wreath using Maple Learn.

    Watching the video brought a smile to my face, and I know it did the same for others.

    I hope this video warms your heart as it did mine. On behalf of all of us at Maplesoft, Happy Holidays!

    Recently, the Maple Learn team hosted an internal Maple Learn day. The team encouraged Maplesoft employees to create Maple Learn content. A lot of art was created.

    Below is a link to an example of Maple Learn art, and a picture relating to it. The document is interactive, so open it to see what it does.

    Christmas Art, by Marek Krzeminski - Senior Architect at Maplesoft

    If you too like to combine math and art, use Maple Learn here to create artwork yourself, and share it with us in the comments.


     

    Recently I decided to compare continuity, related notions, and differentiability. Can a function be differentiable, but not continuous? What about uniformly continuous, but not differentiable? I used Maplesoft's new online product, Maple Learn (free to use at learn.maplesoft.com), to explore.

    Here is a Maple Learn document I created. It is an organizational diagram, as shown below. Each rectangle in the diagram corresponds to a different property that a function may satisfy. Within each rectangle, examples are provided of functions satisfying the appropriate properties.

    If you click on an example, it will be selected, and the corresponding function will be plotted in Maple Learn's context panel. Try it!

    I've also created companion documents to explain certain concepts in greater detail. For instance, below is a snapshot of a document explaining uniform continuity, which you can access here.

    By using sliders in the document, you can move and resize the rectangle drawn in the graph. You should notice when doing this that the green function never touches the horizontal sides of the rectangle. This turns out to be the "reason" why the function is uniformly continuous.

    You can find a companion document on Lipschitz continuity here.

    I’ve learnt a lot about continuity in creating the documents shown. I hope that you too have learnt something from them!

    Although not mentioned in the documentation, the flexible beam component of MapleSim allows for simulation of large deflections.  

    In the animation, a flexible beam is loaded with a moment (red arrow) at its free end. Assuming a Euler-Bernoulli beam and slow loading (i.e., no dynamic forces), the beam should deform to an arc of constant radiusNot only the deformation of the beam can be described analytically, also the path (red trace) of the free end follows an analytical curve.

     

    I used this test case to get a better understanding of nonlinearities observed in an oscillating system using flexible beams (https://www.mapleprimes.com/posts/215718-Mode-Coupling-With-Flexible-Beams-). The system required tuning of the structure to develop mode coupling. This could not be explained by linear theory. It was unclear whether the large deflections (nonlinear kinematics of the beam) themselves or the implementation of the flexible beam component were responsible for that.  

     

    What I have learned so far with the test case using only default settings: 

    • For moderate deflections there is no difference to textbook formulas.
    • Up to 15 degrees rotation of the end frame, the difference between observed displacement and the Bernoulli beam stays bellow 5%.  
    • Up to 30 degrees rotation of the end frame (as in the mode coupling example) the trace of the end frame conforms well with the analytical path.
    • To simulate verry large deflections beyond 45 degrees rotation, the beam needs to be segmented to closely follow the analytical path.  

    For those that are unsure about the fidelity of their models, I can suggest increasing the numbers of flexible beam components and to compare. I did this in the case of the mode coupling example and noticed no difference. So, the component was not responsible for the nonlinearities. It were the kinematics.

    It's unclear whether this good performance in large deflections was intended or is a byproduct of the sophisticated multibody dynamics under the hood.  Maybe an expert can tell more.

    Overall, to what I have seen the (static) performance was very satisfying. Judging dynamic is performance is much more difficult. Has anyone experience to share with that?

    Flexible_beams_const_moment_curve_MP.mw

    Flexible_beams_const_Moment_single_beam_MP.msim

    Flexible_beams_const_Moment_7_beams_MP.msim

    is what I have used.

    December and Maple 2021.2 have both arrived, which means that we can look forward to year 2022 and Maple 2022.

            What should we like to find new in Maple 2022?  Here follow a few suggestions, to which readers of Maple Primes can add.

            In my opinion the weakest feature of Maple 2021 is the solution of integral equations.  Even when this package was first introduced into Maple, a couple of decades ago, it was weak, applicable to only linear such equations.  A quarter century earlier, David Stoutemyer (a true genius and entrepreneur, originator of Mu-Math, Mu-Lisp, Derive and computer-algebra capabilities incorporated in calculators of Texas Instruments) had published code for non-linear integral equations, based on Reduce.  There is a Handbook of Integral Equations by Polyanin and Manzhirov that lists about 2000 solutions of integral equations.  Let Maple 2022 be the basis of a boast by Maplesoft for Maple to be able to solve 96 per cent of those equations, in the same way that Edgardo Cheb-Terrab can (rightfully) boast that Maple can solve 96 per cent of differential equations in a standard compilation.  Any differential equation can, apparently, be converted to an integral equation, whereas the converse is not true.  For this reason alone, the development of solution of integral equations should become a priority to assist users of Maple.

            Another area worthy of expansion and enhancement is the solution of differential equations in terms of Heun functions; that capability is already present, but working with those functions in their present form is difficult and slow.  The inclusion of related functions, such as Lame functions, into Maple is long overdue.  Although efforts have been devoted to the development of the physics package in recent years, culminating in a tremendous achievement of capability, only a few physicists in the world can appreciate that luxury, whereas the solution of differential, and integral, equations permeates all science and engineering. 

              What items are on your list of wishes for Maple 2022?

    We’ve been busy! We have just released the 2021.2 updates for Maple, Maple Flow, and MapleSim. Here’s a quick overview. These updates are freely available to all customers who have the 2021 version of these products.

    Maple

    The Maple update includes a variety of corrections and improvements to the math engine and interface. It is available through Tools>Check for Updates in Maple, and is also available from the Maple 2021 download page, where you can also find more details.

    In particular, this update includes fixes to the bug in the combine command when working with double summations, and the problems when performing context menu operations on values with units while in Document mode, both of which were reported on MaplePrimes. As always, we appreciate the feedback!

    Maple Flow

    The Maple Flow 2021.2 update offers a richer range of formatting features for creating professional-looking engineering documents, which have been requested by customers. Highlights include sections, controlling the display of commands, annotating images, and disabling automatic evaluation while making a series of changes.  This update is available from the Maple Flow 2021.2 download page, which also contains more details.

    MapleSim

    Lots of good stuff here that makes it easier to build and analyze models, including productivity features that speed up the creation of models that use hydraulics, support for the latest CAD file formats in the MapleSim CAD toolbox, the ability to model drift conditions with the MapleSim Tire Library, tools for simulating 3-D winding effects with the MapleSim Ropes and Pulleys Library, and a new MapleSim Web Handling Library add-on (which, I am sad to say, has nothing to do with Spiderman). See What’s New in MapleSim for details, and the MapleSim 2021.2 download page for instruction on how to obtain your update.

    Some years ago I taught a calculus course for especially talented students. I made up the following problem as an interesting challenge.

    Take a circular disk made of paper. Cut out a sector of some angle α from the disk. Roll each of the resulting two pieces into cones. Let V(α) be the sum of the volumes of the two cones. Find the α that maximizes V(α).

    Here is an animated statement of the problem, produced in Maple.

     

    The most frequent question I get asked when presenting Maple Learn is: “How is Maple Learn different from Desmos?”  The second most frequent question is: “How is Maple Learn different from GeoGebra?”. And they are great questions! Why invest time in learning and introducing students to something new if it works and behaves exactly like something you already use? I certainly wouldn’t bother, and I can’t imagine that anyone else would either. So, in this post, I will do my best to articulate the differences as succinctly as possible, and we’ll be happy to arrange a demo for anyone who is interested in learning more.  Are you ready for another top 3 list!?

    Disclaimer: Before we dive in, I’d like to start by saying that Desmos and GeoGebra are great tools. This post is not intended to disparage them. Rather my goal is to highlight the things that make Maple Learn unique.

    So without further ado:

    1. Maple Learn is the equivalent to doing math on paper, just better!

    Maple Learn is akin to a digital math notebook. The canvas gives students the same feeling as solving a math problem on paper – the ability to work through a problem line by line, with explanations, notes, and additional calculations wherever they want them on the page – only with extras. Students can also use Maple Learn to perform tedious intermediate steps, see a graph to get a better sense of the problem, vary parameters to explore the effect on graphs and results, do a quick side calculation to double-check an individual step, and verify the final result.

    2. Maple Learn takes a more holistic approach to learning

    Where other tools focus predominately on visualization and getting the final answer, the Maple Learn environment supports much more of the teaching and learning experience.  Students can articulate their thought processes and mathematical reasoning using a combination of text, math, plots and images that can be placed anywhere on the canvas. Teachers can devise lessons in Maple Learn that focus not just on solving problems, but on developing skills in mathematical thinking, communication, and all the competencies and standards outlined in the curriculum. For example, instead of having your students work through the minutia of solving for x from two equations, you can create a document that focuses on having them set up the problem correctly, and then let them use the content panel to get the solution. Or you can use interactive supports, such as Algebra Tiles, to allow them to explain the concept of Completing the Square. Or give them an equation, and ask them to jot down features of the equation. The questions you can pose and the discussion that arises as a result is what sets Maple Learn apart from the rest. Because ultimately, the study of mathematics and science is about understanding, not the final answer.

    3. Maple Learn is about math not commands

    Maple Learn is an environment for learning math and math-based subjects, not about learning commands. So how do you perform an operation in Maple Learn? Easy! Maple Learn’s intelligent context-sensitive panel offers students a list of relevant operations to choose from, based on the mathematical equation or expression in question. This feature was first introduced in Maple over two decades ago, and it’s one of the most beloved features of students, teachers, and new Maple users, so of course we included it in Maple Learn. The context panel means that you and your students can focus on learning math not commands.

    And here’s a bonus for making it all the way through:

    4. You can pull math into Maple Learn really easily using the Maple Calculator

    Let’s face it, for now at least, there will always be students who will feel more comfortable doing math on paper. It’s like tomato soup and grilled cheese – some things are meant to go together. So to make the transition from paper to digital easier, students can take a picture of their problem, or even their completed handwritten solution and bring them into Maple Learn instantly. That way, they can have the comfort of paper, AND the advantages of the digital environment. (I’d say something about having their cake and eating it too, but all this talk of food is making me hungry!)

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