You are teaching linear algebra, or perhaps a differential equations course that contains a unit on first-order linear systems. You need to get across the notion of the eigenpair of a matrix, that is, eigenvalues and eigenvectors, what they mean, how are they found, for what are they useful.

Of course, Maple's Context Menu can, with a click or two of the mouse, return both eigenvalues and eigenvectors. But that does not satisfy the needs of the student: an answer has been given but nothing has been learned. So, of what use is Maple in this pedagogical task? How can Maple enhance the lessons devoted to finding and using eigenpairs of a matrix?

In this webinar I am going to demonstrate how Maple can be used to get across the concept of the eigenpair, to show its meaning, to relate this concept to the by-hand algorithms taught in textbooks.

Ah, but it's not enough just to do the calculations - they also have to be easy to implement so that the implementation does not cloud the pedagogic goal. So, an essential element of this webinar will be its Clickable format, free of the encumbrance of commands and their related syntax. I'll use a syntax-free paradigm to keep the technology as simple as possible while achieving the didactic goal.

Notes added on July 7, 2015:

• This live webinar has already been presented and you can view the recording here: http://www.maplesoft.com/webinars/recorded/featured.aspx?id=922
  
  
• For one reaction to a point made in the webinar, see this post.

The question of colorbars for plots comes up now and then.

One particular theme involves creating an associated 2D plot as the colorbar, using the data within the given 3D plot. But the issue arises of how to easily display the pair together. I'll mention that Maple 2015.1 (the point-release update) provides quite a simple way to accomplish the display of a 3D plot and an associated 2D colorbar side-by-side.

I'm just going to use the example of the latest Question on this topic. There are two parts to here. The first part involves creating a suitable colorbar as a 2D plot, based on the data in the given 3D plot. The second part involves displaying both together.

Here's the 3D plot used for motivating example, for which in this initial experiment I'll apply shading by using the z-value for hue shading. There are a few ways to do that, and a more complete treatment of the first part below would be to detect the shading scheme and compute the colorbar appropriately.

Some of the code below requires update release Maple 2015.1 in order to work. The colors look much better in the actual Maple Standard GUI than they do in this mapleprimes post (rendered by MapleNet).

f := 1.7+1.3*r^2-7.9*r^4+16*r^6:

P := plot3d([r, theta, f],
            r=0..1, theta=0..2*Pi, coords=cylindrical,
            color=[f,1,1,colortype=HSV]):

P;

Now for the first part. I'll construct two variants, one for a vertical colorbar and one for a horizontal colorbar.

I'll use the minimal and maximal z-values in the data of 3D plot P. This is one of several aspects that needs to be handled according to what's actually inside the 3D plot's data structure.

zmin,zmax := [min,max](op([1,1],P)[..,..,3])[]:

verthuebar := plots:-densityplot(z, dummy=0..1, z=zmin..zmax, grid=[2,49],
                                 size=[90,260], colorstyle=HUE,
                                 style=surface, axes=frame, labels=[``,``],
                                 axis[1]=[tickmarks=[]]):

horizhuebar := plots:-densityplot(z, z=zmin..zmax, dummy=0..1, grid=[49,2],
                                  size=[300,90], colorstyle=HUE,
                                  style=surface, axes=frame, labels=[``,``],
                                  axis[2]=[tickmarks=[]]):

Now we can approach the second part, to display the 3D plot and its colorbar together.

An idea which is quite old is to use a GUI Table for this. Before Maple 2015 that could be done by calling plots:-display on an Array containing the plots. But that involves manual interation to fix it up to look nice: the Table occupies the full width of the worksheet's window and must be resized with the mouse cursor, the relative widths of the columns are not right and must be manually adjusted, the Table borders are all visible and (if unwanted) must be hidden using context-menu changes on the Table, etc. And also the rendering of 2D plots in the display of the generated _PLOTARRAY doesn't respect the size option if applied when creating 2D plots.

I initially thought that I'd have to use several of the commands for programmatic content generation (new in Maple 2015) to build the GUI Table. But in the point-release Maple 2015.1 the size option on 2D plots is respected when using the DocumentTools:-Tabulate command (also new to Maple 2015). So the insertion and display is now possible with that single command.

DocumentTools:-Tabulate([P,verthuebar],
                        exterior=none, interior=none,
                        weights=[100,25], widthmode=pixels, width=420);

DocumentTools:-Tabulate([[P],[horizhuebar]],
                        exterior=none, interior=none);

We may also with to restrict the view, vertically, and have the colorbar match the shades that are displayed.

DocumentTools:-Tabulate([plots:-display(P,view=2..5),
                         plots:-display(verthuebar,view=2..5)],
                        exterior=none, interior=none,
                        weights=[100,25], widthmode=pixels, width=420);

DocumentTools:-Tabulate([[plots:-display(P,view=2..5)],
                         [plots:-display(horizhuebar,view=[2..5,default])]],
                        exterior=none, interior=none);

I'd like to wrap both parts into either one or two procedures, and hopefully I'd find time to do that and post here as a followup comment.

Apart from considerations such as handling various kinds of 3D plot data (GRID vs MESH, etc, in the data structure) there are also the matters of detecting a view (VIEW) if specified when creating the 3D plot, handling custom shading schemes, and so on. And then there's the matter of what to do when multiple 3D surfaces (plots) have been merged together.

It's also possible that the construction of the 2D plot colorbar is the only part which requires decent programming as a procedure with special options. The Tabulate command already offers options to specify the placement, column weighting, Table borders, etc. Perhaps it's not necessary to roll both parts into a single command.

3dhuecolorbarA.mw

acer

In case anyone is interested, we recently posted a new application on the Application Center,

Time Series Analysis: Forecasting Average Global Temperatures

While interesting in itself (well, I think so, anyway), this application also provides tips and techniques for analyzing time series data in Maple, and shows how to access online data sets through the new data sets functionality in Maple 2015.

eithne

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Case Study: Transforming a University's Placement Testing Process

This webinar will feature the story of how the University of the Virgin Islands moved their placing testing process from paper and pen to using the Mathematical Association of America’s (MAA) placement tests offered through the Maple T.A. testing environment. Instructors at the university now handpick questions to create their own placement tests that best fit the course they are teaching. From there, they are able to analyze the data and craft lessons based on student performance. The end result is that students are more satisfied with the education they are receiving and instructors have made enormous gains with regards to efficiency and flexibility.

To join us for the live presentation with Dr. Celil Ekici from the University of the Virgin Islands, please click here to register.

Getting Started with Maple

This webinar is designed for the user who comes to Maple for the first time. It will demonstrate “how to get started” by clarifying the user interface and the ways math can be entered into Maple, and then “processed.” Coverage includes

• Entering mathematical expressions and interacting with them in a syntax-free way.
• The difference between input in mathematical notation and “linear” or text form.
• The role of the Context Sensitive Menu system for interacting with mathematical objects.
• Graphing and interacting with various types of graphs, including animations, surfaces, and implicit plots.
• Use of built-in tools such as Assistants, Tutors, and Task Templates.
• The Maple help system and the Maple Portal.
• Introduction to differential equations and matrix manipulations.

To join us for the live presentation, please click here to register.

The new Import and Export commands introduced in Maple 2015 provide a unified approach to all data import and export activities, replacing the need to use different commands in different situations. They can be used with many of the wide variety of file types supported by Maple, including 3-D graphics data, numeric and tabular data, images, audio files, special-purpose formats for mathematical objects such as graphs, and much more.

In the following example, you can see how to use these commands in order to bring 3-D models from the popular website Thingiverse and to export 3-D plots to a format suitable for 3-D printing.

Tips and Techniques: 3-D Model Import/Export and Printing

As you saw in the Maple 2015 What’s New, the MapleCloud is now online at maplecloud.maplesoft.com.  In addition to accessing MapleCloud content from within Maple, you can now use a web browser to view and interact with MapleCloud documents. The new online MapleCloud is based on HTML5 and works across a broad range of browsers. No plugins. No Java.

The MapleCloud was first introduced about five years ago, in Maple 14, and has allowed Maple users around the globe to share worksheets and Math Apps with fellow users. The Maple Cloud allows you to create groups in order to share content with specific people, as well as sharing them publicly.  Today we count over 1400 such groups that have been created for a class, a project or a workgroup, hosting tens of thousands of Maple worksheets, with thousands of worksheets being up- and down-loaded every month. Feedback has been tremendous, and clearly, this feature has hit a nerve with our user community and has attracted a strong following.

A common use case is to set up a MapleCloud group for a class in order to exchange Maple material among students and instructors. Some teachers are using this as the primary mechanism for submitting and marking assignments. Just as common is to use the MapleCloud as a convenient way to exchange and review documents while working on a joint project. Many users also use the Cloud to store their own documents in a private online space so that they can access them from multiple computers and locations. Wherever they have access to Maple, they also have access to all their Maple documents.

Then, there are the public groups in the MapleCloud, where users around the world freely share applications and examples; it’s a treasure trove of material covering all sorts of topics from calculus to fractals.

Now online, the MapleCloud continues to be a great repository for Maple content, but in addition, there are also some new aspects. For starters, it is really easy to share a Maple worksheet or Math App with someone else by simply giving them a URL. Click on it and the Maple worksheet opens in your web browser and all interactive components and plots are live - you can change parameters, calculate new results and update plots. For example, you can try out a Password Security tool or explore the Vertex of a Parabola. Maple is not required for consuming content in this way. But if you do have Maple, another click downloads the document to your local copy of Maple, where you can modify and extend it.

The online MapleCloud is a great way to manage your documents and share Maple content with students and colleagues.  This, of course, is only one more step towards making all of our technology available online and you will see more unfold over the course of this year!

Maple T.A. 10 introduced two new question types: Sketch and Free Body Diagram. To assist users in learning the new question types, Maplesoft has created a few hundred samples to look at. These sample questions are already featured on the Maple T.A. Cloud, but you can also download the course modules below. 

Sketching Questions - This course module contains 309 sketch questions. Areas covered include: functions, exponential functions, inequalities, linear equations, logarithmic functions, piecewise functions, quadratic equations, systems of equations and transformations of functions.

Free Body Diagram Questions - This course module contains 118 free body diagram questions. Areas covered include: Electricity, Magnetism and Mechanics.

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on an upcoming webinar we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

See What’s New in Maple 2015 for Educators

Maple 2015 is a major new release of Maple, the technical computing software used for education, research, and development involving mathematics, engineering, and the sciences. With Maple 2015, Maplesoft offers important new abilities to both educators and researchers, particularly in the areas of data analysis, application development and statistics education. This webinar will provide a complete overview of these new features, including:

• A new interface to access, work with, and visualize millions of datasets in the areas of finance, economics, and demographics.
• New facilities for developing Math Apps, including a new microphone and speaker component.
• Advances in integration, differential equations, interactive maps, group theory, physics, and more.
• New Clickable Math tools, including palettes and 60 new interactive Math Apps.
• New tutors, palettes and Math Apps designed explicitly for teaching and learning statistics.
• And more!

To join us for the live presentation, please click here to register.

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Introduction to the Maple T.A. MAA Placement Test Suite – Part #2

This webinar will provide attendees with a more detailed guide to the Maple T.A. MAA Placement Test Suite. The presentation will go beyond the basics to introduce each type of placement test, including algorithmic tests, calculator-based tests, concept readiness tests, and more. A few topics will be explored in the context of each different test type. The presentation will conclude with an explanation of how to set cut-off scores for your institution, as well as how the placement tests were created and validated by the Mathematical Association of America.

To join us for the live presentation, please click here to register.

Creating Questions in Maple T.A. – Part #3

This presentation is the third installment of a series that explores question authoring in Maple T.A., Maplesoft’s testing and assessment solution for courses involving mathematics. This final webinar will focus on creating advanced Maple-graded questions using intuitive algorithms.

In case you missed them, the first webinar in the series provided an overview of the question repository and how to create various types of basic questions. The second webinar in the series focused on how to create better questions using the question designer, and introduced more advanced question types such as sketch and free body diagram. 

To join us for the live presentation, please click here to register.

Hey Everyone:

I was wondering what are your favorite and most useful code snippets that you often use. Maybe ones that are in your initialization code? Maybe ones that speed up something that you often do in maple? Maybe ones that you've seen on this and other websites and adopted for your own purposes?

For fun, I attach my init.mpl (.txt here, as .mpl attachments are not allowed by mapleprimes) here init.txt

Some of the snippets that I use the most are also listed below:

#rearrange curves inside an already created plot, so that certain curves are "on top" of the other ones.
#discussed here:
#http://www.mapleprimes.com/questions/201626-Order-Of-Curves-In-A-Plot
rearrangeCurves:= proc(
     v_items::specfunc(anything, PLOT),
     v_reorder::list([integer,integer]):= []
)
local p, curves, rest;
     (curves,rest):= selectremove(type, v_items, specfunc(anything, CURVES));
     curves:= < op(curves) >:         
     for p in v_reorder do
          curves[p]:= curves[p[[2,1]]]
     end do;
     PLOT(convert(curves,list)[], op(rest))
end proc:


#for numerical differentiation
#based on the idea from:
#http://www.mapleprimes.com/posts/119554-Data-Interpolation
#example use:
#alist:=[seq(i, i=0..10, 0.1)]:
#data:=map(x->evalf(sin(x)), alist):
#plot(alist, data);
#plot([cos(x), 'num_diff(x, LinearAlgebra:-Transpose(Matrix([alist,data])))'], x=1..10, thickness=5, linestyle=[solid, dot], color=[blue, red]);
num_diff:=proc(x, v_data, v_options:=[method=spline, degree=3])
 #v_data is a matrix
 #TODO: let the data be in a more arbitrary format that ArrayInterpolation understands, but keep x as first var
 evalf(D[1](x->CurveFitting:-ArrayInterpolation(v_data, [x],v_options[])[])(x));
end:

#extract nth columns/rows from a matrix
#these only work if have a 2d object... should be updated to also work
#with 1d row/column vectors
#Example use cases
#A := LinearAlgebra:-RandomMatrix(20, 20, outputoptions = [datatype = float[8]]);
#nthColumns(A, 2); #Every other column
#nthRows(A, 10)[.., 1..3]; #Every 10th row, but show only first 3 columns
nthColumns:=proc(v_m, v_n)
  v_m[..,[seq(i, i=1..rtable_size(v_m)[2], v_n)]]
end:
nthRows:=proc(v_m, v_n)
  v_m[[seq(i, i=1..rtable_size(v_m)[1], v_n)],..]
end:


#saves a png plot
savePlot:=proc(v_p, v_fileName, v_w:="800", v_h:="500")
    plotsetup("png", plotoutput=v_fileName, plotoptions=cat("quality=100,portrait,noborder,width=",v_w,",height=",v_h));
    print(plots[display](v_p));
    Threads[Sleep](2):
    fclose(v_fileName):
    plotsetup(default);
end:

Currently calculations: equations, regression analysis, differential equations, etc; to mention a few of them; are developed using traditional methods ie even are proposed and solved by hand and on paper. In teaching our scientists and engineers use the chalkboard as a way to reach students and enable them to solve their calculation. To what extent Maple contributes to research on new mathematical models applied science and engineering ?. Maplesoft appears as a proposal to resolve problems with our traditional proposed intelligent algorithms, development process, embedded components, and not only them but also generates type applications for Apple ipad tablets signature. Based on the computer algebra system Maple Maplesoft gives us the package which works exactly like we were on our work. I will show how mathematics is developed from a purely basic to reach modeling differential equations applied to education and engineering. Also visualizare current techniques for developing applications for mobile devices.

link: https://www.youtube.com/watch?v=FdRUSgfPBoc

ECI_2015.pdf

Atte.

Lenin Araujo Castillo

Physics Pure

Computer Science

We’ve just released a free maintenance release to MapleSim 7. This update includes improvements to MapleSim, the MapleSim Battery Library, and the MapleSim Connector for FMI. For details, see the MapleSim 7.01 update page.

From MapleSim, you can get this update from Help>Check for Updates, or download it from the update page. (If Check for Updates doesn't find anything, please try again tomorrow.)

eithne

Happy New Year! Now that 2014 is behind us, I thought it would be interesting to look back on the year and recap our most popular webinars. I’ve gathered together a list of the top 10 academic webinars from 2014 below. All these webinars are available on-demand, and you can watch the recording by clicking on the webinar titles below.

-----------------------------------------------

See What’s New in Maple 18 for Educators

In this webinar, an expert from Maplesoft will explore new features in Maple 18, including improved tools for developing quizzes, enhanced tools for visualizations, updated user interface, and more.

Introduction to Teaching Calculus with Maple: A Complete Kit

During this webinar you will learn how to boost student engagement with highly interactive lectures, reinforce concepts with built-in “what-if” explorations, consolidate learning with carefully-constructed homework questions, and more.

Maplesoft Solutions for Math Education

In this webinar, you will learn how Maple, The Möbius Project, and Maplesoft’s testing and assessment solutions are redefining mathematics education.

Teaching Concepts with Maple

This webinar will demonstrate the Teaching Concepts with Maple section of our website, including why it exists and how to use it to help students learn concepts more quickly and with greater insight and understanding.

Revised Calculus Study Guide - A Clickable-Calculus Manual

This webinar will provide an overview of the Revised Calculus Study Guide, the most complete guide to how Maple can be used in teaching and learning calculus without first having to learn any commands.

Clickable Engineering Math: Interactive Engineering Problem Solving

In this webinar, general engineering problem-solving methods are presented using clickable techniques in the application areas of mechanics, circuits, control, and more.

Hollywood Math 2

In this second installment of the Hollywood Math webinar series, we will present some more examples of mathematics being used in Hollywood films and popular hit TV series.

Robotics Design in Maple and MapleSim

In this webinar, learn how to quickly create multi-link robots by simply defining DH parameters in MapleSim. After a model is created, learn to extract the kinematic and dynamic equations symbolically in Maple.

Introduction to Maple T.A. 10

This webinar will demonstrate the key features of Maple T.A. from both the instructor and student viewpoint, including new features in Maple T.A. 10.

The Möbius Project: Bringing STEM Courses Online

View this presentation to better understand the challenges that exist today when moving a STEM course online and to find out how the Maplesoft Teaching Solutions Group can help you realize your online course vision.

-----------------------------------------------

Are there any topics you’d like to see us present in 2015? Make sure to leave us a comment with your ideas!

Kim

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on an upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Creating Questions in Maple T.A. – Part #2

This presentation is part of a series of webinars on creating questions in Maple T.A., Maplesoft’s testing and assessment system designed especially for courses involving mathematics. This webinar, which expands on the material offered in Part 1, focuses on using the Question Designer to create many standard types of questions. It will also introduce more advanced question types, such as sketch, free body diagrams, and mathematical formula.

The third and final webinar will wrap up the series with a demonstration of math apps and Maple-graded questions.

To join us for the live presentation, please click here to register.

Clickable Calculus Series – Part #1: Differential Calculus 

In this webinar, Dr. Lopez will apply the techniques of “Clickable Calculus” to standard calculations in Differential Calculus. 

Clickable Calculus™, the idea of powerful mathematics delivered using very visual, interactive point-and-click methods, offers educators a new generation of teaching and learning techniques. Clickable Calculus introduces a better way of engaging students so that they fully understand the materials they are being taught. It responds to the most common complaint of faculty who integrate software into the classroom – time is spent teaching the tool, not the concepts.

To join us for the live presentation, please click here to register.

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on an upcoming webinars we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Creating Questions in Maple T.A. – Part #2

This presentation is part of a series of webinars on creating questions in Maple T.A., Maplesoft’s testing and assessment system designed especially for courses involving mathematics. This webinar, which expands on the material offered in Part 1, focuses on using the Question Designer to create many standard types of questions. It will also introduce more advanced question types, such as sketch, free body diagrams, and mathematical formula.

The third and final webinar will wrap up the series with a demonstration of math apps and Maple-graded questions.

To join us for the live presentation, please click here to register.

Clickable Calculus Series – Part #1: Differential Calculus 

In this webinar, Dr. Lopez will apply the techniques of “Clickable Calculus” to standard calculations in Differential Calculus. 

Clickable Calculus™, the idea of powerful mathematics delivered using very visual, interactive point-and-click methods, offers educators a new generation of teaching and learning techniques. Clickable Calculus introduces a better way of engaging students so that they fully understand the materials they are being taught. It responds to the most common complaint of faculty who integrate software into the classroom – time is spent teaching the tool, not the concepts.

To join us for the live presentation, please click here to register.