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 will be hosting the 2nd annual Maple T.A. User Summit June 15 - 17 in New York City, USA.

Don’t miss this opportunity to learn about new trends in online education while networking and socializing with fellow educators and Maple T.A. users in the city that never sleeps!

Conference highlights include:

• Hear from long term users who have used the Maple T.A. technology to transform their classroom experiences.
• Get comprehensive hands-on Maple T.A. training.
• Learn about new technology developments at Maplesoft and how they can provide exceptional user experiences that have the power to ‘surprise and delight’.
• Network with other educators and Maple T.A. users from around the world.
• Take advantage of the social events organized as part of this summit. Socialize with peers and enjoy the sights and sounds of this amazing city.

We invite users who are using Maple T.A. in an innovative way in their classroom to submit a presentation proposal by March 18, 2015. For details, please visit: https://webstore.maplesoft.com/taconference/MapleTA_Summit_CFP.pdf

For more details, preliminary agenda, and to register, please visit our website: https://webstore.maplesoft.com/taconference/

Jonny
Maplesoft Product Manager, Maple T.A.

      Method for solving underdetermined systems of nonlinear equations. The idea of the method is to find a connected subset of a set of solutions of the system by moving along this subset from one point in different directions. The direction of movement can be changed in each point.

      Very simple example of  single equation with three variables:

                                   (x1 ^ 4 + x2 ^ 4 - 2) ^ 2 + x3 ^ 4 - 1 = 0;

      From the point (0, -1.31607, 0) or (0, 1., 0) or any point if it is a solution, we first move for a variety of solutions along a curve parallel to the axis Ox3, and then from each point of this curve is moving in a direction parallel to x1Ox2 or vice versa. So we get all the solutions.
      This works for any space of any number of the equations when the number of equations is less than the number of variables.
underdetermined_system.mw

A rigid rotating body is a moving mass, so that kinetic energy can have expressed in terms of the angular speed of the object and a new quantity called moment of inertia, which depends on the mass of the body and how it is such distributed mass. Now we'll see with maple.

Momento_de_Inercia.mw

(in spanish)

Atte.

L. Araujo C.

In this section, we will consider several linear dynamical systems in which each mathematical model is a differential equation of second order with constant coefficients with initial conditions specifi ed in a time that we take as t = t0.

All in maple.

Vibraciones.mw

(in spanish)

Atte.

L.AraujoC.

The procedure  Partition  significantly generalizes the standard procedure  combinat[partition]  in several ways. The user specifies the number of parts of the partition, and can also set different limitations on parts partition.

Required parameters:  n - a nonnegative integer, k - a positive integer or a range (k  specifies the number of parts of the partition). The parameter  res  is the optional parameter (by default  res is  1 ). If  res  is a number, all elements of  k-tuples must be greater than or equal  res .  If  res  is a range  a .. b ,   all elements of  k-tuples must be greater than or equal  a  and  less than or equal  b . The optional parameter  S  - set, which includes elements of the partition. By default  S = {$ 0.. n} .

The code of the procedure:

Partition:=proc(n::nonnegint, k::{posint,range}, res::{range, nonnegint} := 1, S::set:={$0..n})  # Generates a list of all partitions of an integer n into k parts

local k_Partition, n1, k1, L;

k_Partition := proc (n, k::posint, res, S)

local m, M, a, b, S1, It, L0;

m:=S[1]; M:=S[-1];

if res::nonnegint then a := max(res,m); b := min(n-(k-1)*a,M)  else a := max(lhs(res),m); b := min(rhs(res),M) fi;

S1:={$a..b} intersect S;

if b < a or b*k < n or a*k > n  then return [ ] fi;

It := proc (L)

local m, j, P, R, i, N;

m := nops(L[1]); j := k-m; N := 0;

for i to nops(L) do

R := n-`+`(op(L[i]));

if R <= b*j and a*j <= R then N := N+1;

P[N] := [seq([op(L[i]), s], s = {$ max(a, R-b*(j-1)) .. min(R, b)} intersect select(t->t>=L[i,-1],S1) )] fi;

od;

[seq(op(P[s]), s = 1 .. N)];

end proc;

if k=1 then [[b]] else (It@@(k-1))(map(t->[t],S1))  fi;

end proc;

if k::posint then return k_Partition(n,k,res,S) else n1:=0;

for k1 from lhs(k) to rhs(k) do

n1:=n1+1; L[n1]:=k_Partition(n,k1,res,S)

od;

L:=convert(L,list);

[seq(op(L[i]), i=1..n1)] fi;

end proc:

Examples of use:

Partition(15, 3);

Partition(15, 3..5, 1..5);  # The number of parts from 3 to 5, and each summand from 1 to 5

Partition(15, 5, {seq(2*n-1, n=1..8)});  # 5 summands and all are odd numbers 

A more interesting example.
There are  k banknotes in possible denominations of 5, 10, 20, 50, 100 dollars. At what number of banknotes  k  the number of variants of exchange  $140  will be maximum?

n:=0:

for k from 3 to 28 do

n:=n+1: V[n]:=[k, nops(Partition(140, k, {5,10,20,50,100}))];

od:

V:=convert(V, list);

max(seq(V[i,2], i=1..nops(V)));

select(t->t[2]=8, V);

Here are these variants:

Partition(140, 10, {5,10,20,50,100});

Partition(140, 13, {5,10,20,50,100});

 Partition.mws

The equations of motion for a rigid body can be obtained from the principles governing the motion of a particle system. Now we will solve with Maple.

Dinamica_plana_de_cuerpos_rigidos.mw

(in spanish)

Atte.

Lenin Araujo Castillo

Corrección ejercico 4

Download ejercicio4.mw

A heart shape in 3d:

The code of the animation:

A := plots[animate](plot3d, [[16*sin(t)^3*cos(s), 16*sin(t)^3*sin(s), 13*cos(t)-5*cos(2*t)-2*cos(3*t)-cos(4*t)], t = 0 .. u, s = 0 .. 2*Pi, color = red, style = surface, axes = none], u = 0 .. Pi, frames = 100):

B := plots[animate](plot3d, [[16*sin(t)^3*cos(s), 16*sin(t)^3*sin(s), 13*cos(t)-5*cos(2*t)-2*cos(3*t)-cos(4*t)], t = u .. Pi, s = 0 .. 2*Pi, color = "LightBlue", style = surface, axes = none], u = 0 .. Pi, frames = 100):

plots[display](A, B);

Edited. The direction of painting changed.

The precise definition is that the distance between any two points of the rigid body remains constant. Although any body is deformed to move, if the deformation is small movement can be approximated by modeling it as a rigid body. Now let's see how Maple is part of the solution.

Cinematica_plana_de_cuerpos_rigidos.mw

(in spanish)

Atte.

Lenin Araujo C.

Hooke's joint and type of Hooke's joint.  


https://vk.com/doc242471809_363263648
https://vk.com/doc242471809_363264824

Type_of_Hooke.mw

    Intersection of surfaces:

x3-.25*(sin(4*x1)+sin(3*x2+x3)+sin(2*x2))=0;  (1)

(x1-xx1)^4+(x2-xx2)^4+(x3-xx3)^4-1=0;          (2)   

   Surface (1) and a set of surfaces (2). Point (xx1, xx2, xx3) belongs to (1). Moving along the surface (1), we compute its intersection with the surface (2).
   The program is very simple and its algorithm can be used for many other combinations of equations.

intersection_of_surfaces.mw  

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.

The well-known  combinat[composition]  command computes and returns a list containing all distinct ordered  k-tuples of positive integers whose elements sum equals  n . These are known as the compositions of  n .  For some applications, additional constraints are required for the elements of these k-tuples, for example, that they are within a certain range.

The  Composition  procedure solves this problem. Required parameters:  n - a nonnegative integer, k - a positive integer. The parameter  res  is the optional parameter (by default  res is  0 ). If  res  is a number, all elements of  k-tuples must be greater than or equal  res .  If  res  is a range  a .. b ,   all elements of  k-tuples must be greater than or equal  a  and  less than or equal  b .  Composition(n,k,1)  is equivalent to  combinat[composition](n,k) .

The code of the procedure:

Composition := proc (n::nonnegint, k::posint, res::{range, nonnegint} := 0)

local a, b, It, L0; 

if res::nonnegint then a := res; b := n-(k-1)*a  else a := lhs(res); b := rhs(res) fi;

if b < a or b*k < n then return `No solutions` fi; 

It := proc (L)

local m, j, P, R, i, N;

m := nops(L[1]); j := k-m; N := 0;

for i to nops(L) do

R := n-`+`(op(L[i]));

if R <= b*j and a*j <= R then N := N+1;

P[N] := [seq([op(L[i]), s], s = max(a, R-b*(j-1)) .. min(R, b))] fi;

od;

[seq(op(P[s]), s = 1 .. N)];

end proc;

L0 := [[]];

(It@@k)(L0); 

end proc:

Three simple examples:

Composition(10,3); ``;   # All terms greater than or equal 0

Composition(10,3, 2);   # All terms greater than or equal 2

Composition(10,3, 2..4);   # All terms greater than or equal 2 and less than or equal to 4 

A more complex example. The problem - to find all the numbers in the range  1 .. 99999999  whose digits sum is equal to 21 .

Each number is represented by a list of digits from left to right, replacing missing digits at the left with zeros.

M:=Composition(21,8, 0..9):  

nops(M);  # The number of solutions

[seq(M[1+100000*i], i=0..9)]; # 10 solutions from the list M starting the first one

seq(add(%[i,k]*10^(8-k), k=1..8),i=1..nops(%));  # Conversion into numbers

Composition.mws

Greetings to all.

I am writing to alert MaplePrimes users to a Maple package that makes an remarkable contribution to combinatorics and really ought to be part of your discrete math / symbolic combinatorics class if you teach one. The combstruct package was developed at INRIA in Paris, France, by the algorithmics research team of P. Flajolet during the mid 1990s. This software package features a parser for grammars involving combinatorial operators such as sequence, set or multiset and it can derive functional equations from the grammar as well as exponential and ordinary generating functions for labeled and unlabeled enumeration. Coefficients of these generating functions can be computed. All of it easy to use and very powerful. If you are doing research on some type of combinatorial structure definitely check with combstruct first.

My purpose in this message is to advise you of the existence of this package and encourage you to use it in your teaching and research. With this in mind I present five applications of the combstruct package. These are very basic efforts that admit improvement that can perhaps serve as an incentive to deploy combstruct nonetheless. Here they are:

• A parity bias for trees
• Number of nodes with even offspring
• Trees with odd degree sequence
• Ordered rooted trees with all nodes having at least two child nodes
• Average depth of a leaf in an ordered binary tree

I hope you enjoy reading these and perhaps you might want to feature combstruct as well, which presented the first complete implementation in a computer algebra system of the symbolic method, sometimes called the folklore theorem of combinatorial enumeration, when it initially appeared.

Best regards,

Marko Riedel.