Dear all;

Some of you will have heard of the new open access (and free of page charges) journal Maple Transactions https://mapletransactions.org which is intended to publish expositions on topics of interest to the Maple community. What you might not have noticed is that it is possible to publish your papers as Maple documents or as Maple workbooks.  The actual publication is on Maple Cloud, so that even people who don't have Maple can read the papers.

Two examples: one by Jürgen Gerhard, https://mapletransactions.org/index.php/maple/article/view/14038 on Fibonacci numbers

and one by me, https://mapletransactions.org/index.php/maple/article/view/14039 on Bohemian Matrices (my profile picture here is a Bohemian matrix eigenvalue image).

I invite you to read those papers (and the others in the journal) and to think about contributing.  You can also contribute a video, if you'd rather.

I look forward to seeing your submissions.

Rob Corless, Editor-in-Chief, Maple Transactions

Dear all,

Recently we learned that the idea of "anti-secularity" in perturbation methods was known to Mathieu already by 1868, predating Lindstedt by several years.  The Maple worksheet linked below recapitulates Mathieu's computations:

https://github.com/rcorless/MathieuPerturbationMethod

Nic Fillion and I wrote a more general introduction to perturbation methods using Maple and you can find that paper at 

https://arxiv.org/abs/1609.01321

and the supporting Maple code in a workbook at 

https://github.com/rcorless/Perturbation-Methods-in-Maple

For instance, one of the problems solved is the lengthening pendulum and when we do so taking proper account of anti-secularity (we use renormalization for that one, I seem to remember) we get an error curve that is bounded over time.

Hope that some of you find this useful.

Welcome to Maplesoft Orientation Week!  We know what a difference math software can make when it comes to enhancing student learning, but we also know that everyone is very busy at the beginning of the school year! So our goal for this week is to make it easier for high school and university students to select the best math tool for their needs, and help them get on track for a great math year.  The week’s activities include free training on Maple and Maple Learn, discounts on Student Maple, live events with some of your favorite math TikTok personalities, and even the chance to win an iPad Air!  Check out all the activities now, and plan your week or tell your students.

Orientation week runs Mon. Sept. 20 – Fri. Sept. 24.

As most Maple Primes readers have hopefully seen, Maplesoft is having our Maple Conference again this fall. This year we decided to add a space to the conference to showcase creative and artistic work that would be interesting to our Maple Community. The conference organizers asked me if I would coordinate and curate this exhibition of creative uses of Math and Maple, and I agreed. So now, I am asking the Maple community to send us your most creative work related to or using Maple.

The obvious thing to submit would be a beautiful digital plot or animation with an interesting mathematical story and of course, we are really interested to see those. But, we would are especially excited to see some art created with physcial media. I would love to see your knitting or needle point project that is inspired by a mathematical theme or was created with the help of Maple.

The full announcement can be found at the Maple Conference Art Gallery page. We would like to have all submissions by October 12th so that can review and finalize the gallery before the conference begins November 1st.

Oh yeah, there will also be prizes.

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

Hi everyone! It's been a remarkably long time since I posted on MaplePrimes -- I should probably briefly reintroduce myself to the community here. My name is Erik Postma. I manage the mathematical software group at Maplesoft: the team that writes most of the Maple-language code in the Maple product, also known as the math library. You can find a longer introduction at this link.

One of my tasks at Maplesoft is the following. When a request for tech support comes in, our tech support team can usually answer the request by themselves. But no single person can know everything, and when specialized knowledge of Maple's mathematical library is needed, they ask my team for help. I screen such requests, answer what I can by myself, and send the even more specialized requests to the experts responsible for the appropriate part of the library.

Yesterday I received a request from a user asking how to unwrap angles occurring in an expression. This is the general idea of taking the fact that , and similarly for the other trig functions; and using it to modify an expression of the form  to make it look "nicer" by adding or subtracting a multiple of  to the angle. For a constant, real value of  you would simply make the result be as close to 0 as possible; this is discussed in e.g. this MaplePrimes question, but the expressions that this user was interested in had arguments for the trig functions that involved variables, too.

In such cases, the easiest solution is usually to write a small piece of custom code that the user can use. You might think that we should just add all these bits and pieces to the Maple product, so that everyone can use them -- but there are several reasons why that's not usually a good idea:

• Such code is often too specialized for general use.
• Sometimes it is reliable enough to use if we can communicate a particular caveat to the user -- "this will not work if condition XYZ occurs" -- but if it's part of the Maple library, an unsuspecting user might try it under condition XYZ and maybe get a wrong answer.
• This type of code code generally doesn't undergo the careful interface design, the testing process, and the documentation effort that we apply to the code that we ship as part of the product; to bring it up to the standards required for shipping it as part of Maple might increase the time spent from, say, 15 minutes, to several days.

That said, I thought this case was interesting enough to post on MaplePrimes, so that the community can take a look - maybe there is something here that can help you with your own code.

So here is the concrete question from the user. They have expressions coming from an inverse Laplace transform, such as:

with(inttrans):
F := -0.3000*(-1 + exp(-s))*s/(0.0500*s^2 + 0.1*s + 125);
f := invlaplace(F, s, t)*u(t);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t-
#         49.98999900)-357.*cos(49.98999900*t-49.98999900))+.1680672269e-1*(-7.141428429*sin
#         (49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

I interpreted their request for unwrapping these angles as replacing the expressions of the form  with versions where the constant term was unwrapped. Thinking a bit about how to be safe if unexpected expressions show up, I came up with the following solution:

unwrap_trig_functions := module()
local ModuleApply := proc(expr :: algebraic, $)
  return evalindets(expr, ':-trig', process_trig);
end proc;

local process_trig := proc(expr :: trig, $)
  local terms := convert(op(expr), ':-list', ':-`+`');
  local const, nonconst;
  const, nonconst := selectremove(type, terms, ':-complexcons');
  const := add(const);
  local result := add(nonconst) + (
    if is(const = 0) then
      0;
    else
      const := evalf(const);
      if type(const, ':-float') then
        frem(const, 2.*Pi);
      else
        frem(Re(const), 2.*Pi) + I*Im(const);
      end if;
    end if);
  return op(0, expr)(result);
end proc;
end module;

# To use this, with f defined as above:
f2 := unwrap_trig_functions(f);
# result: (.1680672269e-1*exp(1.-1.*t)*Heaviside(t-1.)*(7.141428429*sin(49.98999900*t+
#         .27548346)-357.*cos(49.98999900*t+.27548346))+.1680672269e-1*(-7.141428429*sin(
#         49.98999900*t)+357.*cos(49.98999900*t))*exp(-1.*t))*u(t)

Exercise for the reader, in case you expect to encounter very large constant terms: replace the calls to frem above with the code that Alec Mihailovs wrote in the question linked above!

Mathematics for Chemistry with Symbolic Computation

J. F. Ogilvie

            This interactive electronic textbook, in the form of Maple worksheets, is released in its sixth edition, 2021 August.  This book has two major divisions, mathematics for chemistry -- the mathematics that any instructor of a course in chemistry would wish a student thereof to understand and to be able to implement, and mathematics of chemistry, in the sense of the classic volumes by Margenau and Murphy -- mathematical treatments of particular topics in chemistry from an introductory post-secondary level to a post-graduate level. The content, which includes not only chapters in previous editions that have been revised but also additional chapters on quantum mechanics, molecular spectrometry and advanced chemical kinetics, has been collected during two decades, with many contributions from other authors, acknowledged in particular locations.  Each chapter includes not only explanatory treatments but also illuminating examples and exercises with chemical applications where practicable.

Mathematics for chemistry      0  introduction to Maple commands

                                                 1  numbers, symbols and elementary functions

                                                 2  plotting, geometry, trigonometry and functions

                                                 3  differential calculus

                                                 4  integral calculus

                                                 5  multivariate calculus

                                                 6  linear algebra

                                                 7  differential and integral equations

                                                 8  probability, statistics, regression and optimisation

Mathematics of chemistry       9  chemical equilibrium

                                                10  group theory

                                                11  graph theory

                                                12  quantum mechanics in three parts -- models, atoms and molecules

                                                13  molecular spectrometry

                                                14  Fourier transforms

                                                15  advanced chemical kinetics

                                                16  dielectric and magnetic properties

The content freely available at https://www.maplesoft.com/applications/view.aspx?SID=154267 includes also a published report on teaching mathematics with symbolic software and an interactive periodic chart that yields information about particular chemical elements and their isotopic variants.

            The nature of this electronic interactive textbook makes it applicable with an instructor in a traditional setting, or computer laboratory, for which the material of mathematics for chemistry could be reasonably covered in three or four semesters, but even for self study.  The chapters on quantum mechanics and Fourier transforms are available as separate textbooks in the same format.

We had the exciting opportunity to interview Dr Trefor Bazett, a math professor at the University of Victoria who also regularly posts videos to his YouTube channel explaining a wide variety of math concepts, from cool math facts to full university courses. You may also recognize him from the recent webinar he did on effective interactive learning! If you’re a teacher, and particularly if you’re trying to find ways to keep your students engaged when teaching math online, read on for some great advice and perspective from someone who’s already built a significant online following. If you’re not a teacher, read on anyways! We may not all be teachers, but we’ve all been (or are!) students. And as students, we probably all have some opinions on how things should be taught! Read on for a new perspective, and maybe even some new ways to approach your learning in the future.

What are some unique challenges presented by teaching math online, and how do you overcome them?

Teaching online I work a lot harder to keep students truly engaged. I’m a big believer in active learning, which means that students are actively taking part in their learning through solving problems, asking questions, and making connections themselves. This might seem a bit strange coming from a YouTuber since watching a video is one of the most passive ways to learn! When it is an in-person class, the social pressures of that environment make it easier to create a supportive learning environment that fosters active engagement. When I teach online, I try to scaffold interactive activities and learning opportunities around my videos, but for me at least it is challenging! I find it easier in many ways to think of the passive components of my teaching like creating a video that introduces a topic but designing learning activities around those videos where students are engaged and feel like they are part of a supportive community is crucial. 

Do you think the experience of teaching online has led to any positive trends in education that will live on once students are back in the classroom?

Absolutely. Whether we wanted to or not, teachers now have experience and skills integrating technology into their learning because so many of us had to figure out how to teach online. The big question is how do we leverage these new technological tools and experiences and resources we have created for when we return to the physical classroom? Can we reincorporate in a new way, for instance, the videos we created for the pandemic? We have so many amazing tech tools – and of course I have to shout out Maple Learn as one of those! – that made it possible for students to engage in interactive learning in the online space, but now we can think about all the ways to leverage these tools in face-to-face learning whether as part of a classroom demo, in-class student activities, or outside-of-class activities.

How do you think the influx of math educators on social media, such as yourself, has changed and will change the shape of math education?

I’m so proud of the math education community on YouTube and other platforms, the quality and diversity of math education online is truly incredible. Having universal access to free high quality education materials can really help level the playing field. But there is still a crucial role to the classroom as well, whether it is in person or online. Just watching YouTube videos on a math channel isn’t going to be enough for most people. You need to be actively practicing math in a supportive environment, receiving feedback on your progress, and getting help when you need it. I feel there is a lot of opportunities for teachers to leverage online materials for instance by linking students to excellent expository content while in class teachers are focusing on designing engaging active learning activities.

What made you decide to create a YouTube channel? Do you have any tips for others wanting to do the same?

My first online course was designed asynchronously and so I needed a place to host the videos for that course. Why not YouTube? I only had twenty students in the course, and never imagined anyone else would actually watch them, let along millions of them! But when I noticed my first math video that got picked up by the YouTube search algorithm and I kept getting comment after comment thanking me I realized there really was a big appetite for quality math education content on YouTube.

My biggest tip is just to get started! Your first video isn’t (probably!) going to be the one that gets picked up by the YouTube algorithm, but it is the one that starts you on that path and builds up your skills at telling math stories, speaking to the camera, using the technology, and so forth.  Don’t worry about that first video being completely perfect or mimicking the “style” of other YouTubers, use it as a chance to build from. If you want to know more about my process for making videos, I share a lot of my process here.

What do you think is the best way for students to approach homework problems?

Homework is often perceived, rather understandably, as a burdensome chore you frustratingly have to do. If that is the perception, then it is also understandable that students would take behaviours that might help them get points on the homework but aren’t very effective for learning. However, if you think about homework as both an opportunity to learn and an opportunity to get feedback on how effective your learning is, now you can engage in much more effective behaviours.

My suggestion is to always genuinely try the problem on your own first. If I’m completely stuck, I really like to write down everything I do know about the problem such as the definitions of the math words involved in the problem. This makes it so much easier to see all the pieces and figure out how to assemble them a bit like a jig-saw puzzle.

I’m a big believer in self-regulated learning, where you are identifying precisely what you know and what you don’t know, and then adapting you learning to zero in on the parts that are challenging. Technology tools like Maple Learn that provide step-by-step solutions to many types of math manipulations can help with this self-regulation, for instance by verifying that you correctly did some cumbersome algebra or precisely where the mistake is at.

Even if you have solved the problem, you can still learn more from it! You can imagine how the instructor could modify that question on a test and if so how would you respond? You can map out how this problem connects to other problems. You can write down a concept map of the larger picture and where this problem fits in it. I have a whole video with a bunch more strategies for approaching homework problems beyond just getting the answer here.

As a teacher, what is your opinion on providing students with step-by-step solutions?

Step-by-step solutions definitely have a role. To master math, you need to master a lot of little details, and then the deeper connections between ideas can start to form. Step-by-step solutions can really help support students mastering all those little details because they can identify the precise location of their confusion as opposed to just noting they got the wrong answer and not be able to identify where exactly their confusion lies. I think they can also help lower math anxiety as students can be confident they will have the tools to understand the problem.

However, it is important to use step-by-step solutions appropriately so that students use them as a supportive learning tool and not a crutch. Sometimes students try to learn math by mimicking the steps of some process without deeply understanding why or when to apply the steps. There can be a big gap between following a solution by someone else and being able to come up with it yourself. This is where teachers have an important role to play. We need to both be clear in our messaging to students about how to use these supports effectively, as well as to consistently be asking formative questions that encourage students to reflect on the mathematics they are doing and provide opportunities for students to creatively solve problems. 

You spoke a bit in your webinar about the “flipped classroom” model. Do you have any tips for educators who want to move more towards a flipped classroom where in-class time is focused on discussion and exploration?

I really love flipped classroom approaches. The big idea here is that students established foundational content knowledge before class, for instance by watching my pre-class videos, so they are empowered to do more collaborative active learning in class. The social supports of class are thus focused on the higher-level learning objectives. However, as much as I love this approach, it is just one of really an entire spectrum of options that start to shift towards student-centered learning. My main tip is to start small, perhaps just adding in one five-minute collaborative problem to each class before jumping all the way to a flipped classroom pedagogy. For myself, it took a few years where I kept adding more and more active learning elements to my classroom and each time I did that I felt it worked so well I added a bit more. One positive consequence from the pandemic-induced shift to online learning is there is now a tremendous amount of high-quality content available for free, so it is easier today to start embracing a fully flipped classroom than it has ever been.

What are some ways teachers can let students take their learning into their own hands?

This is so important. Sometimes teaching can be too paternalistic, but I think we should trust our students more. Give students the time and space to try tackling interesting problems and it will happen! Our role as teachers is to create a supportive learning environment that is conducive to students learning. A few ingredients I think that can help are firstly to encourage students to collaborate and support each other. Mathematics is an inherently collaborative discipline in practice, but this can also be very helpful for learning. Secondly, we can provide effective scaffolding in problems that provide avenues for students to get started and making progress. Thirdly, tech tools like Maple Learn let us take some of the friction away from things like graphing, cumbersome algebra, and other procedural computations meaning we can instead focus our learning on developing conceptual understanding.

In your opinion, how can we motivate students to learn math?

Authenticity. Motivation is sometimes divided between intrinsic motivations (enjoyment of the subject itself) and extrinsic motivations (for instance wanting to get a good grade), and in general we learn more effectively and more deeply when we are intrinsically motivated. To capture intrinsic motivation, I always try to make my teaching and the problems I ask students to work on to feel authentic. That might mean the problem connects to real world challenges where students can see how the math relates to the world, but it doesn’t have to! A problem that stays in pure math but asks and answers interesting mathematical problems and delights the learner is also great for intrinsic motivation. If students are empowered to tackle authentic problems in a supportive learning environment, that motivation will naturally come.

What’s your favourite number, mathematical expression, or math factoid?

Somewhere on the surface of the earth, there is a spot that has the exact same temperature and pressure as the spot exactly opposite it on the other side of the earth. This is true no matter what possible weather patterns you have going on all around the earth! That this has to always be true is due to the Borsuk-Ulam theorem and if you want to know more about this theorem and its many consequences, I’ve done a whole video on it here.

Any parting thoughts?

At the start of every new school year, I read about dozens of cool ideas and am tempted to think “I want to try that!”. I suggest instead finding one thing to improve on the year before, one thing that you can really invest in that will make a difference for your students. You don’t need to reinvent the wheel every year!

This research work demonstrates the use of the MapleSim and Python scientific packages for the correct use of differential equations for engineering students, in the face of the pandemic generated by COVID-19. The main objective is to visualize the teaching and learning process of the subject presented. The methodology used is block diagrams using graphic programming and the one-dimensional symbolic structure. The results are totally optimal since automation was achieved in the differential equations applied to different engineering cases. The applications generated by the scientific software are fully upgradeable and available in the cloud.

Ponencia_CIMAC_2021.pdf

Lenin AC

Ambassador Maple

Another series of updates to Maple Learn? It’s almost like we’re constantly working on Maple Learn to add more features and improve based on your feedback! Wild, right? Anyways, here’s some of the latest features we’ve added to Maple Learn.

First, we’re very excited to present our new Example Gallery. Not only does it have a shiny new design, but there are now over 400 example documents in just about every area of mathematics you can think of.  These documents are perfect for seeing how Maple Learn can be used to teach and explore concepts, and you can easily modify them to suit your own needs. We’re still working hard on improving the Example Gallery and its content, so let us know what you want to see!

We’ve also got some shiny new features in Maple Learn itself. Do you ever look at a graph and think, “Wow, this is great and all, but I sure would love if it had fewer straight lines and more circles?” I know I do. Luckily for both of us, Maple Learn now supports polar coordinates! Just click the round globe icon to see your plots transformed to the circular form you’ve always wanted them to be.

Looking to enhance the text portion of your documents, rather than the graphs? We’ve got just the thing for you—Maple Learn now supports bullet lists! Take your pick of numerical lists, alphabetical, or your traditional bullet point. If you’re looking to augment your document with a step-by-step process, a list of your favourite mathematical expressions, or you’re just feeling tired of using pen and paper for grocery lists, Maple Learn now has what you need.

Speaking of improving the layout of your documents, we now have an option for horizontal tables. The vertical tables can get a bit a long, especially for a short document, but with horizontal tables you can keep all your documents cozy and compact.

And as always, this is just a taste of what we’ve been up to. We’ve also improved a variety of features (including our new steps feature!) and fixed an assortment of bugs. And remember, we couldn’t do this without you! Please continue to let us know what you’d like to see in Maple Learn, and someday it could be your request featured in our post!

Calling all teachers! Have you ever sat wracking your brain on how to create an engaging lesson for students who aren’t so keen on math? Are you trying to help your students understand concepts on a deeper level? Well, Dr Trefor Bazett’s webinar “How to Design Effective Interactive Learning Activities” might have the answers you seek. Dr Trefor is professor at the University of Victoria who has risen to fame on the internet with his engaging YouTube math tutorials. He recently gave a great talk sharing some of the things he’s learned about teaching and how he structures his course content to maximize student learning and engagement. We wanted to take the time to highlight a few of the points he made.

One of the things Dr Trefor emphasized in his talk was the concept of active learning. Unusual as it may seem, math is a lot like juggling. You can learn all the theory of juggling and how it’s supposed to work, but when it comes down to it, if you want to learn how to juggle, you have to actually juggle! And as he describes, it’s the same for math. If you want to learn math, you have to actually do math. This means that educators need to find a way to make learning active for their students, and find ways for them to actually explore and use the concepts that are taught in class. There are many ways to approach this, and Dr Trefor has a few ideas in his talk that might help get you started! For example, he discusses a backwards model wherein teachers create their lectures based on the assessments and activities, rather than the other way around. That way, you can be sure that what you’re teaching is what the students need to know in order to complete the activities you’re giving them—and that in turn can make the activities more engaging for the students.

Another idea he talked about that I personally found quite appealing was the idea of incorporating storytelling into your teaching. Stories are always more interesting than just plain lectures. And you don’t even have to weave together a grand epic with elements of math being taught along the way (although that would be pretty cool!). It can be as simple as changing the way you explain a concept. “X is true, but, Y is also true! Therefore…” Doesn’t that seem a little more interesting? By tying together concepts with pseudo-narrative threads using ‘but’s and ‘therefore’s, you can create a lecture that students will want to listen to—after all, they’ll want to know what happens next.

Drawing from some of the science behind learning, Dr Trefor also discussed the idea of cognitive load. This is essentially the amount of stress the student is experiencing when they’re trying to learn. Concepts will always have a certain amount of intrinsic load to them—that is, when you’re trying to learn how to factor a quadratic equation, there’s going to be some amount of stress associated with factoring itself. The part educators can focus on reducing is the extrinsic load, which is the stress caused by outside factors. For example, your factoring lesson may be hindered by having to teach online instead of in-person, or by the fact that you keep thinking 2x3 is 5 (or maybe that’s just me!). Dr Trefor describes how online tools like Maple Learn can help to reduce this extrinsic load. With a way to show and explain a wide variety of concepts without pencil and paper, and to help perform those calculations that are muddying up the underlying concept, you can reduce the cognitive load and help your students learn.

This is just a taste of some of the ideas Dr Trefor talked about in his webinar. If we’ve piqued your interest, you can watch the full thing for yourself here, or by clicking the video below! Be sure to check out Dr Trefor’s channel as well if you want to see his dynamic teaching style in action.

 Pictures on the theme of Klein bottle.  Wikipedia article
KL_B_1.mw

KL_B_2.mw

Quantum Mechanics for Chemistry

J. F. Ogilvie

            This interactive electronic textbook, freely available from the Maple Application Centre [https://www.maplesoft.com/applications/view.aspx?SID=154768] in the form of three Maple worksheets comprises three extensive chapters, on model systems, atoms and molecules in turn.  As quantum mechanics is neither a chemical theory nor even a physical theory but a collection of methods, numbering at least thirteen, or algorithms, for calculations on systems of an atomic scale, it is appropriate that computer software combining both strong arithmetical and symbolic capabilities, i.e. Maple, be applied to implement this material.  The book includes calculations involving five of the known methods, and provides many examples and exercises for a reader to enhance understanding of the principles and practice. For the first and third chapters, a readable text as .pdf is also provided but the extent of the second chapter precludes this possibility.

            The objective of this textbook is to demonstrate how the principles of the varied methods become implemented in practical calculations. The chapter on model systems includes treatments of several oscillators that might serve as prototypical of features of diatomic molecules.  The chapter on atoms includes the most extensive treatment available on solutions of Schroedinger's equation for the hydrogen atom, in all four systems of coordinates in which the variables are separable, and also in momentum space.  The chapter on molecules includes an introduction to transparent quantum-chemical calculations, which enables a reader to understand each stage of a calculation on a simple atomic or molecular system leading to a self-consistent field and even to Moeller-Plesset perturbation theory of second order and application of density functionals, which can provide an excellent basis for a subsequent use of opaque numerical programs for calculation of molecular structures and properties.

            This textbook contains, with permission, contributions from several eminent chemists, mathematicians and physicists, acknowledged in the particular locations, that complement the explanatory descriptive text as a profound introduction to quantum mechanics in a context of chemical education.

Maple Learn is a great tool for checking the answer to your math problems, but what happens when your answer is wrong and you don’t know why? Knowing there’s a mistake doesn’t actually tell you what that mistake is. Luckily for you, Maple Learn’s newest feature is here to help you out: steps! Now, with the click of a button, you can see full, step-by-step solutions to a wide variety of problems. Instead of endlessly pouring over your work to find that one misplaced negative sign, you can check the steps to quickly and easily spot where you went wrong. Plus, if you’re having trouble figuring out how to approach a problem, you can sneak a peek at the first few steps to get the ball rolling. Full solutions are an invaluable learning tool, and we’re excited to be able to share them with our users.

Getting the steps is simple. When you perform an operation using the Context Panel, you’ll see a “Steps” button appear next to the solution when steps are available. Just click this button! This will take you to a new Maple Learn document showing you a full, detailed solution. Plus, if you want to bring the steps into another document, you can then click the “Copy to Clipboard” button. Checking your solution has never been easier!

What sorts of problems do we have steps for, you might ask? Good question! The answer is a resounding “most of them”. Are you a high schooler? We’ve got steps for factoring, expansion, and solving both equations and linear systems. Doing calculus? Derivatives, integrals, limits, and even solving differential equations all have full solutions available. How about linear algebra? Absolutely! We provide steps for Gauss-Jordan elimination, matrix inversion, finding eigenvalues and eigenvectors, and calculating the determinant! And that’s just a taste of what Maple Learn can do. We’re working constantly to expand our roster of steps, so let us know what you want to see!

I hear what some of you must be thinking: “But what about when I don’t have my computer with me? I never know when I’m going to need a step-by-step solution to a math problem!” If that’s you, then check out the Maple Calculator! The Maple Calculator provides full solutions just like Maple Learn, and you can carry it around in your pocket for math-on-the-go. With Maple Learn and the Maple Calculator on your side, no math problem can stop you now.

A manipulator, in which 3 degrees of freedom are provided by changing the length of the links and one degree of freedom, is provided by turning. Only 4 degrees of freedom. Solved using Draghilev's method. In one case, the length of the manipulator link could be expressed through the value of the 3rd coordinate. The lengths of the other two links are considered generalized coordinates. In this case, it is still obtained polynomial equations, as for the usual coordinates.
I was asked to make an example of the movement of such a manipulator using Maple. (Automatically, this is an example of solving an inverse kinematics problem.)
four_degrees_of_freedom_from_Sabina.mw

I am happy to announce that registration for Maple Conference 2021, to be held Nov. 2-5, is now open! The event is once again virtual and free this year. On our home page, you can find information about our keynote presentations. Our keynote speakers this year are Dr. Veselin Jungic, Dr. Evelyne Hubert and Dr. Laurent Bernardin.

The Agenda & Event Format page contains preliminary information about the event and will be updated as the agenda develops. This page describes two add-on workshops that are also free of charge: "Maple Programming: Beyond the Basics" and "Advanced Problem Solving with Regular Chains".

You can register for both the conference and the add-on workshops here: Maple Conference 2021. I hope to see you all in November!