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High School Students Tackle Real-World Mathematical...

by: pchin 1421 Maple
April 05 2018
3  3

Last week, my colleague Erik Postma and I had the pleasure of spending a few hours with a group of bright and motivated high school students at the Math for Real: High School Math Solves Real Problems workshop held at the Fields Institute for Research in Mathematical Sciences in Toronto, and sponsored by the Fields Institute and NSERC PromoScience. The purpose of this three-day workshop was to train students for the International Mathematical Modeling Challenge, also known as IM2C.

The IM2C is hosted by York University and run by the IM2C-Canada committee, consisting of parents and high school teachers, as well as faculty and students in York’s Department of Mathematics and Statistics. In this competition, students working in small teams have five days to solve a mathematical modelling problem in diverse application areas. To support the “Real World” aspect of the contest, students are expected not just to showcase their mathematical creativity and problem-solving skills, but they are also asked to clearly communicate their analyses and conclusions through a written report and visualizations.

The contest allows students to use appropriate software tools to help them with their tasks. Of course I am biased but I can’t help thinking that Maple is the perfect tool for students wanting to do a combination of prototyping, modelling, visualization and document-preparation. The IM2C organizers also thought that the students could benefit from our software, so Erik gave an hour-long introduction to Maple. I was impressed by the students’ enthusiastic remarks and sometimes challenging questions, though admittedly they were partly motivated by the chance to receive as prizes our highly coveted limited-quantity “Math Matters” t-shirts.

The workshop also introduced the students to other software products, taught modelling and writing skills, and had them work on fun practice problems. Over the lunch break, I was struck by the sense of camaraderie at this event, which probably should not have surprised me, as unlike many other competitions involving mathematics, this one is a true team-based activity. Both Erik and I are eager to see what the students will be doing with Maple. Responding to the students’ enthusiasm and interest, Maplesoft has agreed to offer complimentary Maple licenses to all students participating in IM2C. 

As a Corporate Affiliate of the Fields Institute, Maplesoft is pleased to provide training and support to students and researchers that come to Fields for its many events. Developers like myself are encouraged to participate in the institute’s events when possible, and I’ve had the opportunity to attend a number of workshops in the past few years. I encourage you to look at their wide range of activities and to consider visiting the culturally diverse city of Toronto!

factor of a polynomial ...

Asked by: gaurav_rs 65
polynomial factor
April 05 2018
0  8


 

> 

restart;
> 

Digits:=50;
> 

A11:= 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> 

 

> 

factor(A11);

Warning,  computation interrupted

  
> 

 

50

 (1)
> 

 

> 

 

> 

``


 

Download factor_puz.mw

Dear Maple users,

I am struck with a polynomial. Is there a way to factor it ?

work sheet is attached.

 

regards,

 

solve the equation......

Asked by: mehran rajabi 120
solve
April 05 2018
0  8

Hi every body: 

How can I solve this equation with maple? assuming x>0

eq:=-44.51913564*sinh(sqrt(x))*x^5*sin(sqrt(x))*cos(0.6232678986e-1*x)+5.872275982*x^(11/2)*cosh(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)+5.872295982*x^(11/2)*sinh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)-0.1e-5*x^6*sinh(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)+11465.08352*x^6*cosh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)-0.10000e-4*x^(11/2)*sin(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)+.1246535797*cosh(sqrt(x))*x^4*cos(sqrt(x))*cos(0.6232678986e-1*x)+158.9969129*x^(9/2)*sinh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)-94.84329962*cosh(sqrt(x))*x^5*cos(sqrt(x))*sin(0.6232678986e-1*x)-0.2e-2*x^7*sinh(sqrt(x))*sin(sqrt(x))*sin(0.6232678986e-1*x)+0.4000e-2*x^(13/2)*cosh(sqrt(x))*sin(0.6232678986e-1*x)*sinh(sqrt(x))+0.10000e-4*x^(11/2)*cosh(sqrt(x))*sinh(sqrt(x))*cos(0.6232678986e-1*x)-158.9969129*cosh(sqrt(x))*x^(9/2)*sin(sqrt(x))*cos(0.6232678986e-1*x)+38209.64552*sinh(sqrt(x))*x^6*sin(sqrt(x))*sin(0.6232678986e-1*x)-3761.932636*x^(13/2)*cosh(sqrt(x))*sin(sqrt(x))*sin(0.6232678986e-1*x)-3761.924636*x^(13/2)*sinh(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)-0.4000e-2*x^(13/2)*sin(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)-2.*10^(-7)*x^(13/2)*cosh(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)-11465.08352*x^6*cos(0.6232678986e-1*x)+.1246535797*x^4*cos(0.6232678986e-1*x)-94.84329962*x^5*sin(0.6232678986e-1*x)+0.1e-5*x^6*cosh(sqrt(x))^2*cos(0.6232678986e-1*x)-0.1e-5*x^6*cos(sqrt(x))^2*cos(0.6232678986e-1*x)+0.3e-5*cosh(sqrt(x))^2*x^6*sin(0.6232678986e-1*x)-0.2e-2*x^7*cos(sqrt(x))^2*sin(0.6232678986e-1*x)+0.2e-2*x^7*cosh(sqrt(x))^2*sin(0.6232678986e-1*x)+2.*10^(-7)*x^(13/2)*sinh(sqrt(x))*cosh(sqrt(x))*cos(0.6232678986e-1*x)+2.*10^(-7)*x^(13/2)*cos(sqrt(x))*sin(sqrt(x))*cos(0.6232678986e-1*x)-2.*10^(-7)*x^(13/2)*sinh(sqrt(x))*cos(sqrt(x))*cos(0.6232678986e-1*x)+1.159305284*10^5*cosh(sqrt(x))*x^(11/2)*sin(sqrt(x))*sin(0.6232678986e-1*x)-1.159305284*10^5*x^(11/2)*sinh(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)-8.359616334*10^6*x^7*cosh(sqrt(x))*cos(sqrt(x))*sin(0.6232678986e-1*x)+8.359616334*10^6*x^7*sin(0.6232678986e-1*x) = 0

tnx ... 

batch file and directory...

Asked by: taro 505
terminal
April 05 2018
1  2

Hello people in mapleprimes,
I have two files: a batchfile named test.command, and a mpl file,
both in <<my home directory>>.

And, the codes written there are, for the test.command,

/Library/Frameworks/Maple.framework/Versions/2017/bin/maple test.mpl > output.txt

And, for the mpl file,

1+1;
diff(x^2,x);
int(x^3,x);

The test.command was made executable with chmod u+x  test.command, in advance.

From my home directory, I can run the test.command, and obtain output.txt with the result of the calculation of 
the mpl file. The above things have no problem. 

My question is a following.

When I moved the two files, the batch file and the mpl file, to /Users/myname/Desktop/maple_test, 
I cannot get maple to exhaust the appropriate output.txt but an error message, saying it could not read the mpl file.
What should be done to the contents of two files?

I hope you will teach me about this.

Thanks in advance.

taro

 

 

 

How to plot phase portrait?...

Asked by: Yee Voon 20
ode detools differential-equations
April 05 2018
0  2

Phase_potrait.mw
Hello, anybody knows how to plot phase potrait for disease free equilibrium?

> 

restart
> 

interface(imaginaryunit = I)

I

 (1)
> 

with(DEtools), with(linalg)
> 

k := .5; tau := .95; mu := 0.1e-1; pi := 116.1; `&vartheta;` := 0.8e-2; phi := 0.25e-2; `&epsilon;` := 0.2e-2; rho := 0.5e-1; beta := 0.115e-1; chi := 0.598e-2; q := .5; eta := .2; delta := .1; alpha := 0.57e-1; p := .2; Upsilon := 1.2
> 

lambda := k*tau*(C(t)*Upsilon+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))
> 

sys := {diff(C(t), t) = rho*lambda*S(t)+rho*`&epsilon;`*lambda*V(t)+(1-q)*eta*I(t)-(mu+beta+chi)*C(t), diff(I(t), t) = (1-rho)*lambda*S(t)+(1-rho)*`&epsilon;`*lambda*V(t)+chi*C(t)-(mu+alpha+eta)*I(t), diff(R(t), t) = beta*C(t)+q*eta*I(t)-(mu+delta)*R(t), diff(S(t), t) = (1-p)*pi+phi*V(t)+delta*R(t)-(mu+lambda+`&vartheta;`)*S(t), diff(V(t), t) = p*pi+`&vartheta;`*S(t)-(lambda*`&epsilon;`+mu+phi)*V(t)}

{diff(C(t), t) = 0.2375e-1*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.4750e-4*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+.10*I(t)-0.2748e-1*C(t), diff(I(t), t) = .45125*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.90250e-3*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.598e-2*C(t)-.267*I(t), diff(R(t), t) = 0.115e-1*C(t)+.10*I(t)-.11*R(t), diff(S(t), t) = 92.88+0.25e-2*V(t)+.1*R(t)-(0.18e-1+.475*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t)))*S(t), diff(V(t), t) = 23.22+0.8e-2*S(t)-(0.950e-3*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))+0.125e-1)*V(t)}

 (2)
> 

DEplot(sys, [S(t), V(t), C(t), I(t), R(t)], t = 0 .. 50, S = 0 .. 2, V = 0 .. 2, C = 0 .. 2, I = 0 .. 2, R = 0 .. 2, [[S(0) = 0, V(0) = 0, C(0) = 0, I(0) = 0, R(0) = 0]], stepsize = .1, linecolour = blue, thickness = 1, arrows = slim)

Error, (in DEtools/DEplot/WhichPlot) More than two dependent variables - please indicate the desired scene.

  
> 

``


 

Download Phase_potrait.mw
 

> 

restart
> 

interface(imaginaryunit = I)

I

 (1)
> 

with(DEtools), with(linalg)
> 

k := .5; tau := .95; mu := 0.1e-1; pi := 116.1; `&vartheta;` := 0.8e-2; phi := 0.25e-2; `&epsilon;` := 0.2e-2; rho := 0.5e-1; beta := 0.115e-1; chi := 0.598e-2; q := .5; eta := .2; delta := .1; alpha := 0.57e-1; p := .2; Upsilon := 1.2
> 

lambda := k*tau*(C(t)*Upsilon+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))
> 

sys := {diff(C(t), t) = rho*lambda*S(t)+rho*`&epsilon;`*lambda*V(t)+(1-q)*eta*I(t)-(mu+beta+chi)*C(t), diff(I(t), t) = (1-rho)*lambda*S(t)+(1-rho)*`&epsilon;`*lambda*V(t)+chi*C(t)-(mu+alpha+eta)*I(t), diff(R(t), t) = beta*C(t)+q*eta*I(t)-(mu+delta)*R(t), diff(S(t), t) = (1-p)*pi+phi*V(t)+delta*R(t)-(mu+lambda+`&vartheta;`)*S(t), diff(V(t), t) = p*pi+`&vartheta;`*S(t)-(lambda*`&epsilon;`+mu+phi)*V(t)}

{diff(C(t), t) = 0.2375e-1*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.4750e-4*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+.10*I(t)-0.2748e-1*C(t), diff(I(t), t) = .45125*(1.2*C(t)+I(t))*S(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.90250e-3*(1.2*C(t)+I(t))*V(t)/(S(t)+V(t)+C(t)+I(t)+R(t))+0.598e-2*C(t)-.267*I(t), diff(R(t), t) = 0.115e-1*C(t)+.10*I(t)-.11*R(t), diff(S(t), t) = 92.88+0.25e-2*V(t)+.1*R(t)-(0.18e-1+.475*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t)))*S(t), diff(V(t), t) = 23.22+0.8e-2*S(t)-(0.950e-3*(1.2*C(t)+I(t))/(S(t)+V(t)+C(t)+I(t)+R(t))+0.125e-1)*V(t)}

 (2)
> 

DEplot(sys, [S(t), V(t), C(t), I(t), R(t)], t = 0 .. 50, S = 0 .. 2, V = 0 .. 2, C = 0 .. 2, I = 0 .. 2, R = 0 .. 2, [[S(0) = 0, V(0) = 0, C(0) = 0, I(0) = 0, R(0) = 0]], stepsize = .1, linecolour = blue, thickness = 1, arrows = slim)

Error, (in DEtools/DEplot/WhichPlot) More than two dependent variables - please indicate the desired scene.

  
> 

``


 

Download Phase_potrait.mw

 

 

General mathematics discussion forum...

Asked by: tsunamiBTP 292
April 04 2018
0  2

Does MAPLEPrimes or MAPLESoft host a discussion forum on mathematics in general?  I know this site generally supports troubleshooting & code application.  I have had a couple of instances where I have posted a question that gets no responses because the question may fall outside the perview or objectives of troubleshooting & code application.  Perhaps I should pose these questions elsewhere?

How to calculate an array using initial and final ...

Asked by: m_magooda 20
April 04 2018
1  2

Hello, 

I'm still new to maple, so I hope someone could help me out here

In the file attached I'm trying to generate equations depending on an array of values T[0 to m], of these I've the first T[0] and final T[m] values

before I set these 2 values, I got equations in T0 to T6 setting m=6, when i used the 2 values known i got the same equations only with T0 and T6 substituted, how do i solve them to get the rest of the T values, T1 , T2, and so on

 

thank you,


Download Advheat-ex52.mw

How do I create a function for this? ...

Asked by: slevy2 10
procedure vector index
April 04 2018
0  1

Hi everyone,

I'm trying to create a function that utilizes the index of a vector to preform the following:

 

Where x and y are both nx1 vectors.  I've tried using summation to no avail, as you can see below: 

Of course, it works when I do it this way, but it's incredibly inefficient if the vectors have a large number of rows:

 

Any help y'all can give me would be extremely appreciated!  Thank you kindly

Finding the value intersection between two lines i...

Asked by: MapleUser2017 175
geom3d line intersection
April 04 2018
0  2

Hi I am trying to get Maple to find for which value k two parametric lines intersect using geom3d package. Is that possible?

my code is as follows. 

restart; with(geom3d);

#First I define the the point and vector to construct the line l.

point(P, 1, 0, -2);
 
v := [1, 1, 2];
                    
line(l, {P, v});

Equation(l) = [1 + t, t, -2 + 2 t]
 

#Next I try to define the line m. 
line(m, [k*s+4, 2*s, 3*s], s)

but how (if possible to I get the line to take in the second paramter k? 

and if its possible? which syntax do I use in the intersection-command to get Maple to print out the value k? so it still uses the parameter s for the intersection? 

best regards 

Fred

Can I hide input in a Document Block with inline e...

Asked by: peter2108 95
input inline
April 04 2018
1  2

I want to include the result of an evaluation in a document block that is included in a workbook. It is easy to write sin(Pi) and obtatin sin(Pi)=0 in your document block. Howwever in the case below I want to preserve only y=x/3  removing the isolate(...) expression. Does anyone know if this can be done and if so how to do it?
 

> 

x = 3*y

x = 3*y

 (1)
> 

``

Here  is an inline evaluation of a previous formula isolate(x = 3*y, y) = y = (1/3)*xwhere we have an uneeded '=' sign which can be edited out easily. But is it possible to hide the formula that is evaluated leaving only the output inline and to do this only for the current document block?


Thanks for any help.

Download maple_query_document_blocks.mw

programming code for SPIN TOY PENDULUM...

Asked by: Vasanth kumar 0
plot homework
April 04 2018
0  7

please help me out with maple code/script for "SPIN TOY PENDULUM" using its differential equation..

vader pol limit cycle...

Asked by: josephrajck 5
April 04 2018
0  4

please help me out with maple code/script for vander pol limit cycle using its differential equation..

How do i solve hard spring ode in maple 2016....

Asked by: Rambozz 10
ode homework
April 04 2018
1  8

Step by step for laplace...

Asked by: ssn 0
step-by-step laplace-transform
April 04 2018
0  1

Hi!

 

Is it possible to get step by step solution for:

- Laplace

- taylor

- fourie

Thanks for answers!

Animation of train/hiker/tramper on a mountain. C...

Asked by: das1404 135
animation color cone
April 04 2018
1  4

cone_rail_track_Maple.mws

The attached program is of a point moving along a conical path of a cone, then doing a descent back to the start.   For values R=60, r=20, h=10 the animation seems to work reasonably well.  However when r=19 - only a small change - the development plot of the cone is only partially shown?   Also, I have some variables nameP1, nameP2 which I would like to alter the color of.  Howdo I do this?

  Any comments or help most appreciated. 

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