For all real a, the partial sums s_n= sum((-1)^k (k^(1/k) -a), k=1..n) are bounded so that their limit points form an interval [-1.+  the MRB constant +a, MRB constant] of length 1-a, where the MRB constant is limit(,N=infinity).

For all complex z, the upper limit point of  s_n= sum((-1)^k (k^(1/k) -z), k=1..n) is the  the MRB constant.

We see that maple knows the basics of this because when we enter sum((-1)^k*(k^(1/k)-z), k = 1 .. n) 

maple gives

. 

marvinrayburns.com

I am sure that with this vector file with embedded components will learn how it works the vector operations. The code is free and can be modified to be improved. Forward engineers.

Vectores_con_Components_Embedded.mw     (in spanish)      

Lenin Araujo Castillo

Using MathContainer and Button for 3D vectors.

Angulos_Directores_con_Componentes.mw

(In spanish)

https://www.youtube.com/watch?v=J25P_qNtQe8

Aujourd’hui, je suis ravis d’annoncer la disponibilité d’une large banque de questions françaises supportant les enseignements du secondaire et de l’enseignement supérieur. Ce contenu didactique est disponible via le MapleTA Cloud, et également grâce au lien de téléchargement ci-dessous.

Lien de téléchargement de la banque de questions françaises

Ces questions sont librement et gratuitement accessibles, et vous pouvez les utiliser directement sur vos propres évaluations et exercices dans MapleTA, ou les éditer et modifier pour les adapter à vos besoins.

Le contenu de cette banque de questions françaises traite de sujets pour les classes et enseignements pré-bac, post-bac pour en majorité les matières scientifiques.

Les matières traitées par niveaux et domaines sont:

Lycées :

• Electricité
• Équations Différentielles
• Gravitation universelle
• Langues
• Maths I
• Maths II
• Physique
• Chimie
• Mécanique

Enseignement supérieur (Post-Bac) :

• Astrobiologie
• Introduction au Calcul pour la Biologie
• Chimie
• Déplacement d'onde
• Electricité & Magnétisme
• Maths pour l’économie
• Maths Post-Bac
• Mécanique Angulaire
• Mécanique des Fluides
• Mécanique linéaire
• Physique Post-Bac
• Electrocinétique
• Matériau
• Mécanique des Fluides
• Thermodynamique

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Several Maple T.A. users have developed comprehensive sets of question content and assignments to support full courses in Maple T.A. These questions are available through the Maple T.A. Cloud, and we have decided to also post the associated course modules on Maple Primes as an alternative way of accessing this content.

Below you will find a link to the Introductory Calculus Maple T.A.. course module developed by Keele University.

This testing content is freely distributed, and can be used in your own Maple T.A. tests either as-is, or with edits.

These questions are designed to accompany the first semester of an introductory honours calculus course. The course is intended primarily for students who need or expect to pursue further studies in mathematics, physics, chemistry, engineering and computer science. With over 250 question, topics include: basic material about functions, polynomials, logs and exponentials, the concept of the derivative, and lots of practise exercises for finding derivatives and integrals, and material about series.

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Several Maple T.A. users have developed comprehensive sets of question content and assignments to support full courses in Maple T.A. These questions are available through the Maple T.A. Cloud, and we have decided to also post the associated course modules on Maple Primes as an alternative way of accessing this content.

Below you will find a link to the Introductory Calculus for Biological Sciences Maple T.A.. course module developed by the University of Guelph.

This testing content is freely distributed, and can be used in your own Maple T.A. tests either as-is, or with edits.

The Introductory Calculus for Biological Sciences course module is designed to cover a single-semester introductory calculus course for biological sciences students at the first-year university level. The questions are designed to span the topics listed below, allowing for practice, homework or testing throughout the semester.

Topics include:

• Introduction to Functions
• Composite and Inverse Functions
• Trigonometric Functions
• Logarithms and Exponents
• Sequences and Finite Series
• Limits and Continuity
• Derivatives
• Curve Sketching
• Differentials
• Linear Approximation
• Taylor Polynomials
• Difference Equations
• Log-Log Graphs
• Anti-Differentiation
• Definite Integrals

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Erik Postma from Maplesoft has recently posted a Maple application going through some of the ways how to produce random numbers in Maple: http://www.maplesoft.com/applications/view.aspx?SID=153662&P=TC-4444

Doing a fair bit of work involving random numbers (i.e. simulations) myself, I was naturally drawn to it. The document is a nice extension of the relevant help pages, making practical use of some of the procs in RandomTools easier and clearer.

One particular issue I recently ran into, however, is not covered. I needed a random generator for a particular custom pdf (not one of the already recognized pdfs) that happens to be 3-dimensional. And I needed to do this >twice<, with the second generation using the result of the first one as a parameter. the problem is not unlike the last example in the help page for Statistics:-Sample.

Here is what I did:

The pdf looks graphically like this (and note that in this plot it is not normalized):

plot3d(Triangle63:-Trianglef(CrystalAngle,DeflectionAngle),\
       CrystalAngle=-0.8..0.2,DeflectionAngle=-0.6..0.6,projection=0.7);

The first set of random numbers is generated by setting CrystalAngle to a fixed number (-0.1 in this case), normalizing the pdf to the integral over DeflectionAngle and then generating the random numbers. Note that evaluation of the integral is relatively time-consuming (seconds).

trianglepdf:=(CrystalAngle,DeflectionAngle) ->\
             Triangle63:-Trianglef(CrystalAngle,DeflectionAngle)/\
             'evalf(Int(Triangle63:-Trianglef(CrystalAngle,Da),Da=-0.6..0.6,method = _d01akc))':
triangle0pdf:=(t) -> trianglepdf(-0.1,t):
Cr1:=Distribution(PDF=triangle0pdf);
Y:=RandomVariable(Cr1);

samples:=Sample(Y,[1..600],method=[envelope,range=-0.6..0.6]);

Histogram(samples,view=[-0.6..0.6,default],labels=["Deflection Angle  (µrad)","Counts/bin"]);

This looks as it should; and the random number generation is reasonably fast once the initial setup has been done (i.e. the time used scales only relatively weakly with the count of random numbers generated.

The issue now is the second stage, where for each new random number, the number generated above is a new input parameter for CrystalAngle. So I can no longer define the pdf once since the pdf is different for each number generated.

The pedestrian way to do this is like the following:

samples2:=Vector(1..numelems(samples),datatype=float):
CrystalOffset:=0.3;

for ii from 1 to numelems(samples) do
  triangleiipdf:=(t) -> (trianglepdf(samples[ii]-~CrystalOffset,t)); # subtract (VR peak -> 0)
  Crii:=Distribution(PDF=triangleiipdf);
  samples2[ii]:=evalf(Sample(RandomVariable(Crii),1,method=[envelope,range=-0.6..0.6])[1]+CrystalOffset);
end do:

This works, but only sort-of. First, it is very slow, since the whole sertup happens for each number generated (Sample()). Secondly, it tends to hang at a certain number of steps through the loop. The value of ii where it hangs is arbitrary and changes with the other parameters and CrystalOffset. It is however consistent for identical runs.

The last example in help for Statistics:-Sample would indicate that one needs to setup the pdf as a function of t as well as the parameter, call Distribution() only once and then assign the value to the parameter and call Sample() to get the random number(s) drawn from the pdf with the parameter being set to the wanted value. While this works in the example which uses a built-in pdf, I find that I cannot make it work with my pdf. Either the parameter gets ignored (i.e. stuck at the first value) or the thing runs just as slowly as my procedure above.

Ultimately I programmed my own random generator for an arbitrary pdf which, while not as efficient as Maple's built-in generator, does produce the expected set of random numbers for the 2nd path in a reasonable time. It is a simple-minded envelope-rejection method, that works fo reasonably well-behaved pdfs:

Rarbit:=proc(pdf,xmin,xmax,pdfmax)
local dx:=xmax-xmin;
local x1,x2;
x1:=RandomTools[MersenneTwister]:-GenerateFloat64()*dx+xmin; # pick location on x axis
x2:=RandomTools[MersenneTwister]:-GenerateFloat64()*pdfmax; # y axis, probability of returning x1

while (x2>evalf(pdf(x1))) do # if above pdf, reject
  x1:=RandomTools[MersenneTwister]:-GenerateFloat64()*dx+xmin; # new x-axis value
  x2:=RandomTools[MersenneTwister]:-GenerateFloat64()*pdfmax; # check value
end do; # eventually we'll succeed and return one.

x1;
end proc;

Using this routine I get my second and final set of randome:

for ii from 1 to numelems(samples) do
  newpdf:=(DefAng) -> Triangle63:-Trianglef(samples[ii]-CrystalOffset,DefAng);
  samples2[ii]:=Random:-Rarbit(newpdf,-0.6,0.6,28);
  DocumentTools:-SetProperty(ProgressBar,'value',ii,refresh);
end do:
                      CrystalOffset := 0.3
Histogram(samples2+~samples,view=[-0.6..0.6,default]);

 I would be interested in Erik's comment on this.

Mac Dude

Several Maple T.A. users have developed comprehensive sets of question content and assignments to support full courses in Maple T.A. These questions are available through the Maple T.A. Cloud, and we have decided to also post the associated course modules on Maple Primes as an alternative way of accessing this content.

Below you will find a link to the Introductory Mathematical Economics Maple T.A.. course module developed by the University of Guelph.

This testing content is freely distributed, and can be used in your own Maple T.A. tests either as-is, or with edits.

The Introductory Mathematical Economics course module is designed to cover a single-semester course in mathematical economics for economics and commerce students at the second-year university level. The questions are designed to span the topics listed below, allowing for practice, homework or testing throughout the semester.

Topics include:

• Rules of Differentiation
• First Order Differential Equations
• Higher Order Derivatives
• Optimization in One Variable
• Second Order Conditions for Optimization
• Systems of Linear Equations
• Optimization with Direct Restrictions on Variables
• Over Determined and Under Determined Systems
• Matrix Representation of Systems
• Gauss Jordan
• Matrix Operations
• Types of Matrices
• Determinants and Inverses
• Partial Differentiation
• Second Order Partial Derivatives
• Multivariate Optimization
• Second Order Conditions for Multivariate Optimization
• Multivariate Optimization with Direct Restrictions of Variables
• Constrained Optimization and the Lagrangean Method
• Second Order Conditions for Constrained Optimization

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Several Maple T.A. users have developed comprehensive sets of question content and assignments to support full courses in Maple T.A. These questions are available through the Maple T.A. Cloud, and we have decided to also post the associated course modules on Maple Primes as an alternative way of accessing this content.

Below you will find a link to the Introductory Electricity & Magnetism Maple T.A.. course module developed by the University of Guelph.

This testing content is freely distributed, and can be used in your own Maple T.A. tests either as-is, or with edits.

The Introductory Electricity & Magnetism course module is designed to cover a single-semester course in electricity and magnetism for physical sciences students at the first-year university level. The questions are designed to span the topics listed below, allowing for practice, homework or testing throughout the semester. Using the Maple engine that is part of Maple TA, a custom grading engine has been developed to provide even more flexible grading of scalar and vector responses. This partial grading engine can be configured to, among other things, assign part marks for missing units, transposed or missing vector components or missing algebraic terms.

Topics include:

• Cross Products
• Coulomb’s Law
• Electric Fields
• Point Charge Distributions
• Continuous Charge Distributions (Integration)
• Electric Potential
• Electric Potential Energy
• Electromotive Force
• Resistance
• Capacitance
• Kirchhoff’s Laws
• Magnetic Fields
• Magnetic Fields Due to Current Carrying Wires
• Forces on Wires in Magnetic Fields
• Forces on Charges in Electric and/or Magnetic Fields
• EM Waves
• Two Source Interference
• Double Slit Interference
• Single Slit Diffraction
• Diffraction Gratings

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Did Maplesoft make a statistics about questions on MaplePrimes?

There must be some commands frequently meet problems.

I listed 10 commands or packages need to be enhanced much more.

1.fsolve.

eg, roots of transcendental equation on complex plane & system of nonlinear equations.

2.int.

Both numerical integration & symbolic integration need further developed.

3.Eigenvalues&LinearSolve.

large scale computing, everyone needs it.

4.dsolve&pdsolve.

dsolve needs to be enhanced for solve more equations in parallel.

As mathematica 10 contains the FEM package, I think Maple needs to do something, develop a new package needs more time than make the existing pdsolve command better.

5.Threads package.

parallel programing is the future. BTW, why don't make the task model much easier to use, like the mathematica, just a command?

6.plot&plot3d

there is much space to go further about the two commands.

7.Optimization package or Statistics package.

In fact, both packages need to be further enhanced, especially for Optimization package.

Although some modern algorithms about optimization&statistics is much easier to see on the internet, the

Maplesoft should not stop, but go further, add them in Maple.

Above is just my opinion.

Thanks for your attention.

Several Maple T.A. users have developed comprehensive sets of question content and assignments to support full courses in Maple T.A. These questions are available through the Maple T.A. Cloud, and we have decided to also post the associated course modules on Maple Primes as an alternative way of accessing this content.

Below you will find a link to the Statistics Maple T.A.. course module developed by the University of Guelph.

This testing content is freely distributed, and can be used in your own Maple T.A. tests either as-is, or with edits.

The Statistics course module is designed to cover a single-semester course in statistics for science students at the second-year university level. The questions are designed to span the topics listed below, allowing for practice, homework or testing throughout the semester. The questions are mainly of an applied nature and do not delve very deeply into the underlying mathematical theory.

Topics:

• Introduction to Statistics
• Descriptive Statistics
• Basic Probability
• Discrete Random Variables
• Continuous Random Variables
• Sampling Distributions
• Inference for Means
• Inference for Proportions
• Inference for Variances
• Chi-square Tests for Count Data
• One-Way ANOVA
• Simple Linear Regression and Correlation

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Several Maple T.A. users have developed comprehensive sets of question content and assignments to support full courses in Maple T.A. These questions are available through the Maple T.A. Cloud, and we have decided to also post the associated course modules on Maple Primes as an alternative way of accessing this content.

Below you will find a link to the Statistics Maple T.A.. course module developed by the University of Waterloo.

This testing content is freely distributed, and can be used in your own Maple T.A. tests either as-is, or with edits.

The Statistics content is used in introductory statistics courses at the University of Waterloo, and has been used regularly over several years. The over 700 questions are clearly organized by topic, and provide extensive feedback to students.

Topics include:

• Basics
• Confidence Intervals
• Continuous Distribution
• Discrete Multivariate
• Discrete Probability
• Graphical Analysis
• Hypothesis Testing
• Numerical Analysis for Statistics
• Probability
• Sampling Distributions

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

Several Maple T.A. users have developed comprehensive sets of question content and assignments to support full courses in Maple T.A. These questions are available through the Maple T.A. Cloud, and we have decided to also post the associated course modules on Maple Primes as an alternative way of accessing this content.

Below you will find a link to the Calculus 1 Maple T.A.. course module developed by the University of Guelph. This course material also forms part of Teaching Calculus with Maple: A Complete Kit, which provides lectures notes, Maple demonstrations, Maple T.A. assignments, and more for teaching both Calculus 1 and Calculus 2.

This testing content is freely distributed, and can be used in your own Maple T.A. tests either as-is, or with edits.

The Calculus 1 course module is designed to accompany the first semester of an introductory honours calculus course. The course is intended primarily for students who need or expect to pursue further studies in mathematics, physics, chemistry, engineering and computer science.

Topics include:

• trigonometry including the compound angle formulas
• inequalities and absolute values
• limits and continuity using rigorous definitions, the derivative and various applications (extreme, related rates, graph sketching)
• Rolle's Theorem and the Mean Value Theorem for derivatives
• the differential and anti-differentiation
• the definite integral with application to area problems
• the Fundamental Theorem of Calculus
• logarithmic and exponential functions
• the Mean Value Theorem for Integrals

The Calculus 2 course module is designed to accompany the second semester of an introductory honours calculus course.

Topics include:

• inverse trigonometric functions
• hyperbolic functions
• L'Hôpital's Rule
• techniques of integration
• parametric equations
• polar coordinates
• Taylor and MacLaurin series
• functions or two or more variables
• partial derivatives
• multiple integration

Jonny Zivku
Maplesoft Product Manager, Maple T.A.

I would like to pay attention to a series of applications by Samir Khan
http://www.maplesoft.com/applications/view.aspx?SID=153600
http://www.maplesoft.com/applications/view.aspx?SID=153599
http://www.maplesoft.com/applications/view.aspx?SID=153596
http://www.maplesoft.com/applications/view.aspx?SID=153598
My congratulations to the author on his work well done. New capacities of Global Optimization Toolbox are spectacular. For example, in the first application  an optimization
problem in 101 variables under 5050 nonlinear  constraints
(other than 202 bounds) is solved.
I think it requires a very powerful comp and much time.
I tried that  problem for n=20 with the good old DirectSearch
on my comp (4 GB RAM, Pentium Dual-Core CPU E5700@3GHz) by

soln2 := DirectSearch:-GlobalSearch(rc, {cons1, cons2, rc >= 0,
seq(`and`(vars[i] >= -70, vars[i] <= 70), i = 1 .. 2*n), rc <= 70},
variables = vars, method = quadratic, number = 140, solutions = 1,
evaluationlimit = 20000)

and obtained not so bad rc=69.9609360106765 (whereas www.packomania.com gives rc=58.4005674790451137175957) in about one hour.

Packing_by_DS.mw
For n=50 the memory of my comp cannot allocate calculations or the obtained result by the Search command is far away from the one in packomania.

You guys might find this article interesting.

It presents a linear algebra problem, then writes a program to solve it in Maple, Mathematica, and Maxima to see which one is better. What do you think?