UNIVERSIDAD AUTÓNOMA METROPOLITANA
UNIDAD XOCHIMILCO

15º Foro de Investigación de las Matemáticas Aplicadas a las Ciencias Sociales "Reflexiones sobre Educación y Matemáticas”,

"Learning of mathematical functions using applications with Maple, for students of Social Sciences"

The students of the first cycles have a low level of learning in the subject of functions, and the arrival of the pandemic worsened the understanding of this content. Increasing the use of ICT in great magnitude improving learning.
To determine the relationship between learning and mathematical functions using applications with Maple, for students of Social Sciences. The experimental method was used using the scientific software Maple applied to students of Social Sciences.

In Spanish.

Lenin Araujo Casillo

Ambassador of Maple

Following the previous post on The Electromagnetic Field of Moving Charges, this is another non-trivial exercise, the derivation of 4-dimensional relativistic Lorentz transformations,  a problem of a 3rd-year undergraduate course on Special Relativity whose solution requires "tensor & matrix" manipulation techniques. At the end, there is a link to the Maple document, so that the computation below can be reproduced, and a link to a corresponding PDF file with all the sections open.

Download Deriving_the_mathematical_form_of_Lorentz_transformations.mw

Deriving_the_mathematical_form_of_Lorentz_transformations.pdf

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

We've just released Maple Flow 2022.1. We've squeezed in a few new features as requested by our users - I'll describe them below.

Before we get to that, I'd like to give everyone an open invitation to grab a Maple Flow trial - I'd love to know what you think. I'm fanatically devoted to making Flow better, but I can only do that if you give me your feedback.

You can specify if you want your results to be globally displayed using engineering, scientific, or fixed notation

Supporting images can be cut and pasted from another source directly into Maple Flow using standard clipboard operations.

You can now insert a time stamp in headers and footers. And you can optionally place a border around the header, footer or body of the page.

New content in the help system makes it easier to get started with advanced features, including techniques for optimization and signal processing.

Go here to learn more...and don't forget to grab a trial.

Yes, you read that right! Steps documents are a feature in Maple Learn that we wanted to highlight this week, as they can provide great use in understanding concepts and solving problems. Within them, they can show all steps to solve a problem, including reminders of any formulas used! They can be found at the homepage for steps documents. A list of all can be found below the image, with links.

All steps documents:

• Calculus
  • Derivative Steps
  • Limit Steps
• Algebra and Equations Steps
  • Expansion Steps
  • Simplification Steps
  • Solving Equation Steps
  • Factoring Steps
• Matrix Steps
  • Determinant Steps
  • Eigenvector Steps
  • Inverse Steps
  • Gauss-Jordan Elimination Steps
  • Gaussian Elimination Steps

All of our documents follow the same format, which I’ll show you using 3 different documents: Derivatives Steps, Factoring Steps, and Matrix Determinant Steps. They will be shown from left to right in that order, so you can see the different steps and how they work.

The first thing you’ll see on any steps document is the place to enter the equation. Each equation can be entered in the appropriate box, in different styles to fit your needs and the problem asked.

Then, you click on the show steps button, which is the same for all of the documents:

This is where the magic happens. The steps will appear line by line, in great detail. The actual steps are generated by Maple, and presented in Maple Learn through scripting. Because of this, please don’t click off the group the steps appear in, or they’ll appear in the new group as well!

There are many other steps documents than the ones we have here, and will be adding more as time goes on. Please keep an eye out, and enjoy the updates! We hope this was helpful to you all, and let us know if there are any other steps you’d like to see.

According to Wikipedia

"In computing, a programming language reference or language reference manual is
part of the documentation associated with most mainstream programming languages. It is
written for users and developers, and describes the basic elements of the language and how
to use them in a program. For a command-based language, for example, this will include details
of every available command and of the syntax for using it.

The reference manual is usually separate and distinct from a more detailed
 programming language specification meant for implementors of the language rather than those who simply use it to accomplish some processing task."

And no, Maple's Programming guide is not a Language reference manual. This is a guide to how to program in Maple. But it is not reference manual for the language itself. i.e. description of the Language itself.

Examples of Language reference manuals are

C

Original C++ 

Python

Ada

Fortran 77

and so on.

Why is there no LRM for Maple? Should there be one? I find Maple semantics sometime confusing, and many times I find how things work by trial and error. Having a reference to look at will be good. 

I know for a language as large as Maple, this is not easy to do. But it will good for Maplesoft to invest into making one.

Registration for Maple Conference 2022 is now open! Please go to our conference home page and click on the "Register Now" button.

A tentative schedule has also been posted on the conference agenda page.

The call for participation has closed but please keep in mind that you still have until September 22 to submit creative works.

We hope to see you at the conference!

Have you ever heard of a matrix kernel or nullspace? If not, or you’d like a refresher on the topic, keep reading! We’re doing a Maple Learn document walkthrough today on Fundamental Subspaces.

The document starts by defining the nullspace/kernel and nullity of a matrix. Nullity is defined as the number of vectors in the basis of the kernel for the given matrix. This makes sense, as nullspace is defined as:

This may still not make sense to you, and that’s okay! We have an example for a reason, where we try to find a basis for Null(A) and state the dimension of the subspace (nullity).

I won’t go through the solution here, as trying it yourself is always important. But one hint! If you get really stuck, you can find the Reduced Row Echelon Form (RREF) and the kernel using Maple Learn’s context panel, or check out the rest of our Matrices collection for other helpful documents on this topic.

Please let us know what you thought of this walkthrough or if there are any specific documents or topics you’d like to see in the comments below this post. I hope you enjoyed this walkthrough!

We’ve decided to start a new series of blog posts, where we take a closer look at the collections available in Maple Learn. What collection are we looking at first, you ask? Our largest, the Calculus collection! This collection has around 250 documents, and was one of the first to be added to the Maple Learn document gallery.

Because it’s so big, we can’t talk about it all in one post. Instead, we’re going to break it up into three posts: Limits (this one!), Derivatives, and Integration. Keep an eye out for those other ones!

Let’s dive into it. If you’re learning limits for the first time, the first document you’ll want to take a look at is our document on the formal definition of limits.

And of course, just as the document title says, we start with the formal definition of a limit:

From there, like many of our other documents, there’s a visualization to the left, and an explanation to the right. Seems fairly simple, right?

Well, what if you wanted to dig further into the topic?

That’s what the rest of this collection is for! We have documents on many topics relating to limits, such as The Squeeze Theorem, or The Fundamental Trig Limit (don’t forget to use the slider!). We also have a steps document, to help you solve any limits problems you’ve created or found.

We can’t wait to see you another time for when we dive into Derivative documents. Let us know if after the Calculus collection showcase, if you have another collection you’d like to see summarized!

Today I’m here with a document walkthrough under the subject of graph theory! Do you know what an Eulerian path is? Have you ever tried to find one?

An Eulerian path is a path that uses every edge in the graph exactly once. Vertices can be revisited, just not the edges. There are mathematical ways to find an Eulerian path, but at the level of math I’m at, I just use my eyes!

In the document Eulerian Paths Quiz, we focus on trying to find an Eulerian path. This document, created using Maple scripting, uses the click on plot feature, allowing you to click on the edges and check your answer. When an edge is clicked, it turns red, and feedback is given.

If you make a mistake, there are a few options. If the most recent edge chosen is the mistake, you can simply click on it again to undo the selection. However, if the mistake is several edges back, or you need to undo the whole thing, you can click the blue reset button.

Once you’ve done one, you might want to try another graph. That’s why we have a try another button, to give you another random new graph.

We hope you enjoy this document! If you’re curious about how this document was scripted, you can see our script HERE. Please let us know if there are any specific documents you’d like as a walkthrough in the comments below, and check out our other graph theory documents.

For a long time I could not understand how to make a kinematic analysis of this device based on the coupling equations (like here). The equations were drawn up relative to the ends of the grips (horns), that is, relative to the coordinates of 4 points. That's 12 equations. But then only a finite number of mechanism positions take place (as shown by RootFinding[Isolate]). It turns out that there is no continuous transition between these positions. Then it is natural to assume that the movement can be obtained with the help of a small deformation. It seemed that if we discard the condition of a constant distance between the midpoints of the horns (this is the f7 equation at the very beginning), then this will allow us to obtain minimal distortion during movement. In fact, the maximum distortion during the movement was in the second decimal place.
(It seemed that these guys came to a similar result, but analytically "Configuration analysis of the Schatz linkage" C-C Lee and J S Dai
Department of Tool and Die-Making Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan Department of Mechanical Engineering, King’s College, University of London, UK)
The left racks are input.


The first text is used to calculate the trajectory, and the other two show design options based on the data received.
For data transfer, a disk called E is used.
Schatz_mechanism_2_0.mw
OF_experimental_1_part_3_Barrel.mw
OF_experimental_1_part_3.mw

Highlights of the 2021 Maple Conference are now available. These include recordings of the keynote presentations, contributed sessions, and discussion panels, as well as the Art Gallery entries.

We encourage you to submit a presentation proposal or artwork to our 2022 Maple Conference by visiting the links below!
Call for Participation (proposals due July 18)
Call for Creative Works (submissions due September 22)

Maple Learn is an incredibly powerful tool for math and plotting, but it is made even more powerful when used in combination with Maple! Using scripting tools in Maple, we can make use of hundreds of commands that can solve complex problems for us. In the example of the Lagrange calculator, we are able to use the Maple command LagrangeMultipliers to generate a plot of the two functions and the critical points, even including text feedback about the points.

Something like this seems like it would take hours and a lot of coding knowledge to create, but a simple Maple command generates the entire plot for us! Then, all we had to do was use a button to update the plot. Give it a try yourself in Maple, run the following command with two functions f and g of your choosing:

That’s all there is to it! We now have a complex 3D plot showing the Lagrange problem, something that can be difficult to visualize in multivariate calculus. If we want detailed feedback about the Lagrange problem values, simply change output to detailed from plot:

Check out the entire Maple document (.mw file) to see how the Learn page was generated and to try things out for yourself. This entire document uses the LagrangeMultipliers command, but Maple has hundreds more to experiment with, so the possibilities are virtually limitless!

Share your creations here on MaplePrimes and tag us in your posts.

Maple Learn Document: https://learn.maplesoft.com/doc/lagrange-multipliers-calculator-1biue2ben9

Maple .mw file: https://maple.cloud/app/5998067190071296/LagrangeCalculatorCritical?key=54CE05EC89B34E47984BC61C329A6E759658927BED02458095DA1F576CD93DB9

Maple Learn has a new face! We’ve changed our homepage to the document gallery, which some of you may have already noticed. This is a huge change, and we’re excited for it, as it places content front and center: the goal of Maple Learn. Don’t worry, getting to a blank document is still easy. There is a large orange button on the top right of the document gallery which says “start creating now”. This button will take you to a blank Maple Learn Document.

The most important reason for this change is to help new users get started. Seeing a blank document can sometimes be terrifying! With this new homepage, users can immediately begin looking through premade content, and get inspiration for their own documents.

The first document collection a user sees in the document gallery is still the same: Our featured collection. From there, we have the Maple Learn how-to documents, and then it’s into documents sorted by the overarching subject. Two examples of overarching subjects are Functions and Biology. And, if a user is interested in some of the more artistic sides of Maple Learn, we have our art collection available as well. There’s something for everyone in our gallery!

Now that we’ve explained the largest change, let’s talk about some smaller ones too. Tables now can have row and column headings, allowing for a greater range of data to be represented. Along with that, we’ve added a correlation command to the context panel. Some bugs have also been fixed: Special characters now appear properly in the French and German galleries and scrollbars work over 3D plots.

We hope you enjoy the changes we’ve made. Please continue to report bugs and telling us about features you’d like to see!

Hi Maple Users

As I hope you have already heard, Maplesoft is having our Maple Conference again this fall. And that means that

Last year we had many great submissions and you can still read about them in detail on the 2021 conference site. Some of the featured works were excellent Maple visualizations, including a special prize for a student contribution by Avek Dongol (center).

But we also featured a number of impressive physical works, including the people's choice winning wood carving by Paul DeMarco (left), and the judges' choice winning cross stitch by Bridjet Lee and Curtis Bright (right).

This year, we are again looking to fill our virtual exhibition with all types of mathematical art, ranging from computer graphics and animations, to needlework, geometrical sculptures, or almost anything you can come up with. Surprise us!

The full announcement can be found at the Maple Conference Art Gallery page. We would like to have all submissions by September 22nd so that we can review and finalize the gallery before the conference begins November 2nd.

I can't wait to see what everyone sends in this year!

MapleSim is a mature product. The rich component library leaves little room for improvement for wide range of applications. It is understandable that latest product releases focused on specialized toolboxes and performance improvements.

Here is what I think could be beneficial for many users, which is not related to performance, but can help improve the user experience:

1. Crossing connection lines: A view option to render a crossing connection line with an arc at the crossing point of two connection lines of the same type. Right-click on a connection line might be enough.
    
   
   -> To avoid misinterpretations of routing in crowded model diagrams
    
2. Parameters: An option to populate or reset changes in the parameter pane to the parameter default settings view and vice versa
   
   -> When testing or optimizing a model, sometimes changed parameters should become default values or be reset. Doing this manually is error prone and takes time.
    
3. Component flip: Selecting more than one component including connection lines and applying a flip to all of them
   
   -> When building a model, it can happen that a nicely laid out arrangement of components needs to be mirrored or rotated in its entirety. Doing this component by component and connection by connection is a lot of work that can be saved by this option.
    
4. Initial conditions: An option in the view menu to highlight components where ICs have been changed from ignore to treat as guess or to strictly enforce
    
   
   -> ICs are set for many purposes. In addition to defining ICs needed for simulations, this can include extracting equations, testing different model states, or temporarily "immobilizing" a model during assembly, to name a few. Undoing a tentative change can easily be forgotten. Combining existing models that work on their own into a new more complex model often results in an overly constrained model that either cannot be assembled or does not simulate.
   In debugging a model, ICs of all components must be individually inspected. This takes time. A quick overview that shows components where ICs are not set to ignore would be very helpful in debugging models.
    
5. Undo Create subsystem: A reverse operation that inserts the contents of a subsystem into a parent subsystem.
   
   -> With the evolution of a model it is sometimes useful to exclude or include existing components from or to a subsystem. For this purpose, an undo create subsystem operation should preserve existing connections. A time saver.
    
6. Subsystem ports: An option to align a subsystem port to the drawing grid to remove “micro” steps in connection lines
    
   
   -> For perfectionists who do not have the time to learn (and remember) how to fine-tune at the component level
   
   Update: MapleSim 2022.2 has subtantially improved on this. This item could be removed from the list.
    
7. A history or log function of user actions changing a model, its parametrization or internal state.
   
   -> Often a model does not simulate at all or as desired after modifications. Restoring to a configuration that worked by undo only goes back to the last simulation performed. In such a situation, only reloading the latest file version and redoing modifications may restore the desired model, parametrization, or state. This takes time and migth be unsuccessful. A record of user actions would be a great help.
   History or log information in file format could also help MapleSim support to reproduce an error.

For me personally, reducing errors (4. > 7. > 2.) would improve the use experience much more than layouting aids (3. > 1., 5., 6.).