Education

Teaching and learning about math, Maple and MapleSim

Using the syntax in Maple we develop the energy with conservation equations here we are applying the commands int, factor, solve among others. We also integrate vector functions through the scalar product and finally we calculate conservative fields applying the rotational to a field of force. Exclusive for engineering students. In spanish.

Work_of_a_Force.mw

Lenin Araujo castillo

Ambassafor of Maple

And the Nobel prize in physics 2017 went for work in General Relativity ! Actually, experimental work involving sophisticated detectors and Numerical Relativity, one of the branches of GR. The prize was awarded to Rainer Weiss (85 years old, 1/2 of the prize), Barry Barish (81 years old, 1/4 of the prize) and Kip Thorne (77 years old, 1/4 of the prize) who have "shaken the world again" with their work on Ligo experiment, which was able to detect ripples in the fabric of spacetime.

General Relativity continues to be at the center of work in theoretical and experimental physics. I take this opportunity to note that, in Maple 2017, among the several improvements in the Physics package regarding General Relativity, there is a new package, Physics:-ThreePlusOne, all dedicated to the symbolic manipulations necessary to formulate problems in Numerical Relativity.

The GR functionality implemented in Physics, Physics:-Tetrads and Physics:-ThreePlusOne is unique in computer algebra systems and reflects the Maplesoft intention, for several years now, to provide the very best possible computer algebra environment for Physics, regarding current research activity as well as related education in advanced mathematical-physics methods.

For what is going on in theoretical physics nowadays and its connection with General Relativity, in very short: the unification of gravity with the other forces, check for instance this map from Aug/2015 (by the way a very nice summary for whoever is interested):

It is also interesting the article behind this map of topics as well as this brilliant and accessible presentation by Nima Arkani-Hamed (Princeton):  Quantum Mechanics and Spacetime in the 21st Century, given in the Perimeter Institute for Theoretical Physics (Waterloo), November 2014. 

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

Group of exercises solved using Maple scientific software, with the necessary considerations of some basic commands: evalf and convert that will show the solutions with the user-defined digits and the angular measurement in sexagesimal degrees. Important use of the law of the triangle through of vector position applied to vectors in vector spaces, vector force and vector moment for engineering students. In spanish.

Exercises_of_vectors_forces_and_moment_with_Maple.mw

Videotutorial:

https://www.youtube.com/watch?v=DxpO0gc5GCA

Lenin Araujo Castillo

Ambassador of Maple

# Riemann hypothesis is false! (simple proof)
 

restart;
assume( s>0, s<1/2, t>0 );
coulditbe(abs(Zeta(s+I*t))=0);

                              true

# Q.E.D.

Unfortunately coulditbe(Zeta(s+I*t)=0) returns FAIL, but our assertion is already demonstrated!

The moral: the assume facility deserves a much more careful implementation.

The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.

Moment_of_a_force_using_vectors_updated.mw

Lenin Araujo Castillo

Ambassador of Maple

With this app you will be able to interpret the curvatures generated by two position vectors, either in the plane or in space. Just enter the position vectors and drag the slider to calculate the curvature at different times and you will of course be able to observe its respective graph. At first I show you how it is developed using the natural syntax of Maple and then optimize our
 app with the use of buttons. App made in Maple for engineering students. In spanish.

Plot_of_Curvature.mw

Videotutorial:

https://www.youtube.com/watch?v=SbXFgr_5JDE

Lenin Araujo Castillo

Ambassador of Maple

With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.

 

Vector_space_with_projections_and_forces_UPDATED_2018.mw

Vector_space_with_projections_and_forces_UPDATED.mw

Movie #01

https://www.youtube.com/watch?v=VAukLwx_FwY

Movie #02

https://www.youtube.com/watch?v=sIxBm_GN_h0

Movie #03

https://www.youtube.com/watch?v=LOZNaPN5TG8

Lenin Araujo Castillo

Ambassador of Maple

I'd like to present the following bugs in the IntTutor command.

1. Initialize

Student[Calculus1]:-IntTutor((1+cos(3*x))^(3/2), x);

then press the All Steps button. The command produces the answer (see Bug1_in_IntTutor.mw)

(4/9)*sqrt(2)*sin((3/2)*x)^3-(4/3)*sqrt(2)*sin((3/2)*x)

which is not correct in view of

plot(diff((4/9)*sqrt(2)*sin((3/2)*x)^3-(4/3)*sqrt(2)*sin((3/2)*x), x)-(1+cos(3*x))^(3/2), x = 0 .. .2);

One may compare it with the Mathematica result Step-by-step2.pdf.

2. Initialize

Student[Calculus1]:-IntTutor(cos(x)^2/(1+tan(x)), x);

In the window press the Next Step button. This crashes (The kernel connection has been lost) my comp in approximately an half of hour (see screen2.docx). One may compare it with the Mathematica result Step-by-step.pdf .

Indeed,  "We wanted the best, but it turned out like always" .

I was asked if I would put together a list of top resources to help students who are using Maple for the first time.  An awful lot of students will be cracking Maple open in the next few weeks (the ones who are keeping up with their assignments, at least – for others, it sometimes takes little longer :-), so it seemed like a good idea.

So then I had to decide what to do. I know Top N lists are very popular (Ten Things that Will Shock You about Your Math Software!), and there are tons of Maple training resources available to fill such a list without any difficulties.  But personally, I don’t always like Top N lists. What are the chances that there are exactly N things you need to know, for nice values of N? And how often you are really interested in all N items? I just want to get straight to the points I care about.

I decided I’d try a matrix. So here you go: a mini “choose your own adventure” guide for getting to know Maple.  Pick the row that corresponds to what you want to do, and the column for how you want to do it.  All on a single, page, and ad-free!

And best of luck for the new school year.

 

 

I like words

I like videos

Just let me try it

Product Overview

Inside Maple, from the Help menu, select Take a Tour of Maple then click on the Ten Minute Tour button.

 

(Okay, even though I like words, too, you might also want to watch the video in the next column. The whole “picture is worth a thousand words” does have some truth to it, much as I don’t always like to admit it. J)

Watch Clickable Math

 

Keep in mind that if you prefer to use commands instead of these Clickable Math tools, you can do that too.  Personally, I mix and match.

You’ll figure it out.

Getting Started Info

Read the Maple Quick Start Tutorial Guide, as a PDF, or from the Help system. To access this guide from within Maple, start Maple, click on the Getting Started icon the left, then select the Quick Start Guide (first icon in the second row).

Watch the Maple Quick Start Tutorial Video.

The most important things to remember are

  1. Right click on your math expression to bring up a menu of things you can do, like plotting or integrating or solving your expression
  2. If you have just entered an exponent or the denominator of a fraction, use the right arrow key to get out of it.

How do I? Essentials

Look at the “How do I” section of the Maple Portal (Start Maple, click on the Getting Started icon, click on the Maple Portal icon; or search for “MaplePortal” in the help system).  Also look at the Maple Portal for Students, using the button from the Maple Portal.

Check out the dozens of videos in the Maple Training Video collection.

You can do a lot with the context menus and the various tools you’ll find on the Tools menu. But when in doubt, look at the list of “How do I” tasks from the Maple Portal described in the “words” column and pull out what you need from there.

What now?

The help system is your friend. Not only does it have help pages for every feature and every command, but it includes both the Maple User Manual and the Maple Programming Guide (also available as PDFs).

Check out the collection of videos on the Maplesoft YouTube channel.  (And the help system is your friend, too. We can’t make videos to cover every last thing, and if we did, you wouldn’t have time to watch them all!)

Maple comes with many examples and applications you can look at and modify.  You can browse through the Start page resources, or search for “examples,index” in the help system to see the full list.

 

And yes, the help system is your friend, too.  But don’t worry, no one is going to make you read the manual.

 

 

 

Download New_ReportGeneration_with_ExcelData.mw

Dear Users,

I have received a congratulations from a Mapleprime user for my post (on Finite Element Analysis - Basics) posted two years earlier. I  did not touch that subject for two years for obvious reasons. Now that a motivation has come, I have decided to post my second application using embedded components. This I was working for the past two years and with the support from Maplesoft technical support team and Dr.RobertLopez. I thank them here for this workbook has come out well to my satisfaction and has given me confidence to post it public.

About the workbook

I have tried to improve the performance of a 2-Stroke gasoline engine to match that of a four stroke engine by using exhaust gas recirculation. Orifice concept is new and by changing the orifice diameter and varying the % of EGR, performance was monitored and data stored in Excel workbook. These data can be imported to Maple workbook by you as you want for each performance characteristic. The data are only my experimental and not authentic for any commercial use.

This Maple workbook generates curves from data for various experiments conducted by modifying the field variables namely Orifice diameter, % Exhaust gas Recirculation and Heat Exchanger Cooling. Hence optimum design selection is possible for best performance.

Thanks for commenting, congratulating or critisising!! All for my learning and improving my Maple understanding!! 

In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.

Displacement_and_distance_traveled_with_vectors.mw Updated

Displacement_and_distance_traveled_with_vectors_updated_2020.mw 

Video

https://www.youtube.com/watch?v=jOcKYZ5EEM0

Lenin Araujo C

Ambassador of Maple

Here in this video you can observe the correct insertion of vectors; Making use of the keyboard, ascii code and tool palette of our Maple program. As our worksheet is very large, I made the explanation in two parts; I recommend that you observe this first part of performing any execution on your Maple worksheet. You can contrast your results with the apps also made in this software. In Spanish.

Shortcut_in_Vectors_for_Engineering.mw

Movie # 01

https://www.youtube.com/watch?v=EJtAli54q_A

Movie # 02

https://www.youtube.com/watch?v=m-JUmhkbWI8

Lenin Araujo Castillo

Ambassador of Maple

Hi MaplePrimes,

another_recursive_sequence.mw

another_recursive_sequence.pdf

These two files have the same content.  One is a .pdf and the other is a Maple Worksheet.  I explore integer sequences of the form - 

a(r) = c*a(r-1)+d*a(r-2) with a(1) and a(2) given.

Some of these sequences are in (the Online Encyclopedia of Integer Sequences) OEIS.org and some are not.  If we restrict c to 1 and assume that a(1)=1 and a(2) = 2 we have the parameter d remaining.  See additional webpage - 

https://sites.google.com/site/recrusivefunction/

Let me know if you like the code.

Regards,

Matt

 

As you can see this app performs the trace of a given path r (t), then locate the position vector in a specific time. It also graphs the velocity vector, acceleration, Tangential and Normal unit vectors, along with the Binormal. Very good app developed entirely in Maple for our engineering students.

Plot_of_Position_Vector_UPDATED.mw

https://youtu.be/OzAwShHHXq8

Lenin Araujo Castillo

Ambassador of Maple

I'm back from presenting work in the "23rd Conference on Applications of Computer Algebra -2017" . It was a very interesting event. This fifth presentation, about "The Appell doubly hypergeometric functions", describes a very recent project I've been working at Maple, i.e. the very first complete computational implementation of the Appell doubly hypergeometric functions. This work appeared in Maple 2017. These functions have a tremendous potential in that, at the same time, they have a myriad of properties, and include as particular cases most of the existing mathematical language, and so they have obvious applications in integration, differential equations, and applied mathematics all around. I think these will be the functions of this XXI century, analogously to what happened with hypergeometric functions in the previous century.

At the end, there is a link to the presentation worksheet, with which one could open the sections and reproduce the presentation examples.
 

The four double-hypergeometric Appell functions,

a complete implementation in a computer algebra system

 

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft

 

Abstract:
The four multi-parameter Appell functions, AppellF1 , AppellF2 , AppellF3  and AppellF4  are doubly hypergeometric functions that include as particular cases the 2F1 hypergeometric  and some cases of the MeijerG  function, and with them most of the known functions of mathematical physics. Appell functions have been popping up with increasing frequency in applications in quantum mechanics, molecular physics, and general relativity. In this talk, a full implementation of these functions in the Maple computer algebra system, including, for the first time, their numerical evaluation over the whole complex plane, is presented, with details about the symbolic and numerical strategies used.

Appell Functions (symbolic)

 

 

The main references:

• 

P. Appel, J.Kamke de Feriet, "Fonctions hypergeometriques et Hyperspheriques", 1926

• 

H. Srivastava, P.W. Karlsson, "Multiple Gaussian Hypergeometric Series", 1985

• 

24 papers in the literature, ranging from 1882 to 2015

 

Definition and Symmetries

   

Polynomial and Singular Cases

   

Single Power Series with Hypergeometric Coefficients

   

Analytic Extension from the Appell Series to the Appell Functions

   

Euler-Type and Contiguity Identities

   

Appell Differential Equations

   

Putting all together

   

Problem: some formulas in the literature are wrong or miss the conditions indicating when are they valid (exchange with the Mathematics director of the DLMF - NIST)

   

Appell Functions (numeric)

 

 

Goals

 

• 

Compute these Appell functions over the whole complex plane

• 

Considering that this is a research problem, implement different methods and flexible optional arguments to allow for:

a) comparison between methods (both performance and correctness),

b) investigation of a single method in different circumstances.

• 

Develop a computational structure that can be reused with other special functions (abstract code and provide the main options), and that could also be translated to C (so: only one numerical implementation, not 100 special function numerical implementations)

Limitation: the Maple original evalf command does not accept optional arguments

 

The cost of numerically evaluating an Appell function

 

• 

If it is a special hypergeometric case, then between 1 to 2 hypergeometric functions

• 

Next simplest case (series/recurrence below) 3 to 4 hypergeometric functions plus adding somewhat large formulas that involve only arithmetic operations up to 20,000 times (frequently less than 100 times)

• 

Next simplest case: the formulas themselves are power series with hypergeometric function coefficients; these cases frequently converge rapidly but may involve the numerical evaluation of up to hundreds of hypergeometric functions to get the value of a single Appell function.

 

Strategy for the numerical evaluation of Appell functions (or other functions ...)

 

 

The numerical evaluation flows orderly according to:

1) check whether it is a singular case

2) check whether it is a special value

3) compute the value using a series derived from a recurrence related to the underlying ODE

4) perform an sum using an infinite sum formula, checking for convergence

5) perform the numerical integration of the ODE underlying the given Appell function

6) perform a sequence of concatenated Taylor series expansions

Examples

   

Series/recurrence

   

Numerical integration of an underlying differential equation (ODEs and dsolve/numeric)

   

Concatenated Taylor series expansions covering the whole complex plane

   

Subproducts

 

Improvements in the numerical evaluation of hypergeometric functions

   

Evalf: an organized structure to implement the numerical evaluation of special functions in general

   

To be done

   


 

Download Appell_Functions.mw   
Download Appell_Functions.pdf

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

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