# Items tagged with maplemaple Tagged Items Feed

### November Live Webinars...

November 04 2014 Maple Maple T.A.
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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.

Creating Questions in Maple T.A. – Part #1

This webinar will demonstrate how to create questions in Maple T.A., Maplesoft’s testing and assessment solution for any course involving mathematics. The presentation will begin with an overview of the basic types of questions available, and then delve into how to create various types of questions in Maple T.A. Incorporating algorithms and feedback directly into questions will also be touched on. Finally, the session will wrap up with an explanation and several examples of how to create better questions using the question designer.

This first webinar in a two part series will cover true/false, multiple choice, numeric, mathematical formula, fill in the blank, sketch, and FBD questions. A second webinar that demonstrates more advanced question types will follow.

Clickable Calculus: Linear Algebra

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

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.

### Incorporating Variable Window size in Maple...

November 03 2014
0 3

I'm brand new to Maple and was assigned a problem to modify a code provided by my professor to incorporate variable window size. However, I don't know where to begin or what I'm doing. I've attached the link to the problem below. Plz help.  NA1_Project_IDW_01.2014_Fall.pdf

### Exponential fit for AIDS data...

October 30 2014
1 1

Hi I am working on the following problem (See below the line) from the text A Introduction to the Mathematics of Biology (Ch 2 pgs.21-23). I am working in Maple 18 and the code for this problem is from Maple 11 I think. If you look at the last line of code, I ran into a snag. Can anyone help????? We are in a study Gourp and alll are stumped.

_______________________________________________________________________________________________________

Problem # 2 - Find a fit for the cumulative US AIDS data as a polynomial function. Alsoo find an exponential fit for the data. (assume the Data I have inputed is correct if you don't have the book).

AIDS := [97, 206, 406, 700, 1289, 1654, 2576, 3392, 4922, 6343, 8359, 9968, 12990, 14397, 16604, 17124, 19585, 19707, 21392, 20846, 23690, 24610, 26228, 22768];
print(output redirected...); # input placeholder
[97, 206, 406, 700, 1289, 1654, 2576, 3392, 4922, 6343, 8359,

9968, 12990, 14397, 16604, 17124, 19585, 19707, 21392, 20846,

23690, 24610, 26228, 22768]

CAC := [seq(sum(AIDS[j]/(1000.0), j = 1 .. i), i = 1 .. 24)];
print(output redirected...); # input placeholder
[0.09700000000, 0.3030000000, 0.7090000000, 1.409000000,

2.698000000, 4.352000000, 6.928000000, 10.32000000,

15.24200000, 21.58500000, 29.94400000, 39.91200000,

52.90200000, 67.29900000, 83.90300000, 101.0270000,

120.6120000, 140.3190000, 161.7110000, 182.5570000,

206.2470000, 230.8570000, 257.0850000, 279.8530000]

Time := [seq(1981+(i-1)*(1/2), i = 1 .. 24)];
ln(CAC)=k*lnt+A
LnCAC := map(ln, CAC);
print(output redirected...); # input placeholder
[-2.333044300, -1.194022473, -0.3438997525, 0.3428802329,

0.9925107578, 1.470635510, 1.935571171, 2.334083760,

2.724054775, 3.071998629, 3.399328971, 3.686677031,

3.968441145, 4.209145378, 4.429661370, 4.615387808,

4.792578782, 4.943918402, 5.085810791, 5.207062453,

5.329074480, 5.441798471, 5.549406770, 5.634264465]
LnTime := map(ln, [seq((i+1)/(2*(1/10)), i = 1 .. 24)]);
print(output redirected...); # input placeholder
[ln(10), ln(15), ln(20), 2 ln(5), ln(30), ln(35), ln(40), ln(45),

ln(50), ln(55), ln(60), ln(65), ln(70), ln(75), ln(80), ln(85),

ln(90), ln(95), 2 ln(10), ln(105), ln(110), ln(115), ln(120),

3 ln(5)]
with(stats);
fit[leastsquare[[x, y], y = k*x+lnA]]([LnTime, LnCAC]);
print(output redirected...); # input placeholder
y = 3.293411005 x - 10.12289000
k := op(1, op(1, rhs(%))); LnA := op(2, rhs(%%)); A := exp(LnA);
print(output redirected...); # input placeholder
Error, invalid input: rhs received exp(LnA), which is not valid for its 1st argument, expr
Error, invalid input: rhs received exp(LnA), which is not valid for its 1st argument, expr
exp(LnA)

### wrong taylor expansion result...

October 30 2014
0 3

taylor(1/(1+z^2), z = 1, 4)

The result is

1/2-(1/2)*z-1+(1/4)*(z-1)^2+O((z-1)^4)

but in fact the result is

1/2-(1/2)*(z-1)+(1/4)*(z-1)^2+O((z-1)^4)

my Maple is Maple 16,How to solve this problem?

### How to define the derivative of a function as a fu...

October 29 2014
0 3

Take a look at below. I was expecting maple to give me "g'(1)"! :)

### Solving system of ODEs whose variables come in 2 p...

October 28 2014
0 1

Let N be an integer.

For each pair of integers (n,m) where 1<= n,m <= N, we have a variable f_{n,m}(t).

Then for these we have a system of ODEs

d/dt f_{n,m}(t) = \sum_{n', m'} f_m'n' * f_m''n'' * (m'n'' - m''n')

where m''=m-m', n''=n=n', and the sum is simply over for all pairs (n',m').

I simply do not know how to put these set of equations into Maple in a nice way.

I will really appreciate any help!

### Dos and don'ts of Maple programming w.r.t. the phy...

October 27 2014
2 5

EDIT 2: Ok, here is what I am trying to do with Maple.

I have the following expression:

with

and

(j times)

Now the above expression should be zero. I get a set of equations in orders of lambda. The H matrices are known. I only need to find the S matrices.

Anyways, the HOffDiag is the sum above and the GetAdvCommutator0 is this nested commutator. And I need this sum evaluated up to order n (n is a given input-number) in lambda. The rest is really not that performance hungry.

EDIT: Ok, it realy seems that this sum of commutators is something that takes Maple forever. I have written a new MWE. Is it possible to speed things up? Maybe using assumptions or so?

 > restart;with(Physics):with(LinearAlgebra): Setup(mathematicalnotation=true):Setup(noncommutativeprefix={M,H,S});
 (1)
 > GetAdvCommutator0:=proc(power::integer,order::integer,M)     if power <= 0 then return M fi:     if power = 1 then         return mtaylor(Commutator(M,add(lambda^l*S[l],l=1..order)),lambda, order+1) fi:          return mtaylor(Commutator(GetAdvCommutator0(power-1,order,M),add(lambda^l*S[l],l=1..order)),lambda,order+1): end proc:
 > HOffDiag(3); # still fast
 (2)
 > HOffDiag(6); # takes a very long time, I didn't even try entering higher numbers
 >

Hi,

I know this question is really unspecific. However, since I am still new to Maple, and since you don't program with Maple as you would do with c++, I would appreciate some advise. I have written a program in Maple and I don't know if it works correctly. All I know is, it is pretty slow :(.

So if anyone of you could just have a short look at my attached worksheet and could tell me, if I at some point used an obvious "don't", I would greatly appreciate it.

Cheers

NOh

A Maple worksheet

Setup Maple

 > restart;with(Physics):with(LinearAlgebra):Setup(mathematicalnotation=true):Setup(noncommutativeprefix={MA,MB,H,S});
 (1.1)

Input parameter

 > H0:=Matrix([[ 0 , 0 , 0 , 0 ],             [ 0 , 0 , 0 , 0 ],             [ 0 , 0 , U , 0 ],             [ 0 , 0 , 0 , U ]]);
 (2.1)
 > H1:=Matrix([[ 0 , 0 , 0 , 0 ],             [ 0 , 0 , 0 , 0 ],             [ 0 , 0 , 0 , 0 ],             [ 0 , 0 , 0 , 0 ]]);
 (2.2)
 > H2:=Matrix([[  0 , 0 , -t , -t ],             [  0 , 0 ,  t ,  t ],             [ -t , t ,  0 ,  0 ],             [ -t , t ,  0 ,  0 ]]);
 (2.3)
 > orderNumber:= 4 ;
 (2.4)

Define all necessary functions

 > computeHBlockDiag:=proc( n::posint,firstBlockWidth::posint, H0::Matrix, H1::Matrix, H2::Matrix )     local expr, Orders, i, eq, j, eq2, orders,smatrices,rows::posint,evallist,m,l,cols,Hdiag,ff;               expr:=HOffDiag(n);       # !!!!! this one is one of the slowest parts I think                                          Orders:=[\$1..n];                                                   for i from 1 to n do                                                   eq:=add(coeff(expr,lambda,l)*lambda^l,l=0..i)=0;                for j from 1 to i-1 do             eq:=eval(eq,Commutator(H[0],S[j])=Orders[j]);         od;         eq:=subs(Commutator(H[0],S[i])=MX,eq);         eq2:=solve(eq,MX);         Orders[i]:=eq2;     od;          rows,cols:=Dimension(H0);                                         smatrices:=[seq(H0,i=1..n)];     for i from 1 to n do         evallist:=[*=.,H[1]=H1,H[2]=H2];         for j from 1 to i-1 do             evallist:=[op(evallist),S[j]=smatrices[j]];                 od;         smatrices[i]:=eval(Orders[i],evallist);         for m from 1 to firstBlockWidth do             for l from firstBlockWidth+1 to rows do                 smatrices[i][m,l]:=smatrices[i][m,l]*1/(H0[m][m]-H0[l][l]);                 smatrices[i][l,m]:=smatrices[i][l,m]*1/(H0[m][m]-H0[l][l]);             od;         od;     od;     expr:=HOnDiag(n);            # !!!!! and this one of course (almost identical to the one above)                                            Hdiag:=eval(add(coeff(expr,lambda,l)*lambda^l,l=0..n),lambda=1);     evallist:= [op(evallist), H[0]=H0,S[n]=smatrices[n]];     Hdiag:=eval(Hdiag,evallist);          return Hdiag; end proc:
 >

 > computeHBlockDiag(2,2,H0,H1,H2);
 (1)
 > Eigenvalues(%);
 (2)
 >

Testing

#Fast

 > computeHBlockDiag(2,2,H0,H1,H2);
 (4.1)

#Not so fast

 > computeHBlockDiag(4,2,H0,H1,H2);
 (4.2)

 > computeHBlockDiag(6,2,H0,H1,H2);
 >

### Second order differential equation...

October 25 2014
1 3

Hi!

I am new to Maple and have a problem I've been struggling with all day.

I have a pendulum and need to find a equation of motion in the y-direction. Please find my code in the picture below.

I can see that my problem starts at Eqy where the differentiation deletes one of the right-hand-side parts because I don't have any function y(t), and Maple thinks y(t) a constant (?)
Can somebody please tell me what I'm doing wrong?

### curve fitting on maple 14 with mac...

October 24 2014
1 1

I have Maple 14 on a macbook pro. I recently upgraded to the Yosemite operating system.

I am trying to use the CurveFitting facility:

with(CurveFitting):

But I get nothing. This might be associated with Yosemite, or maple 14, or ????? Anyone have a guess?

### Solving a nonlinear differential equation?...

October 23 2014
2 7

Hello!

I'm trying to solve a differential equation of the form y.y"+y'+y= { 1 for 0<x<1 and 0 for else } with conditions: y(0)=0 and y'(0)=1.

I wrote this:

f(x):=heaviside(0)-heaviside(1);

Eq := y(x)*(diff(y(x), x, x))+diff(y(x), x)+y(x)-f(x);

ans := dsolve({Eq, y(0) = 0, (D(y))(0) = 1},numeric);

But it gives an error.

I also tried ODE tools>assistants>analyzer

It says: the ODE system does not contain derivatives of the unknown function heaviside.

It's the first time I use Maple and I don't know what to do. Need your help urgently. Thanks in advance.

### optimal control problem...

October 22 2014
0 2

Hi there,

Is there a way in which i can solve the following optimal control problem numerically with Maple?

dH/dt=λ-µ H-(1-u1)β H V+δ I,

dI/dt=(1-u1)β H V-σ I,

‎dV/dt=(1-u2)k I-γ‎V,

dλ1/dt=-1+λ1µ+β‎‎V(1-u1)(λ1-λ2),‎

dλ2/dt=λ1δ+λ2σ-λ3(1-u2)k‎,‎

‎dλ3/dt=β H(λ1-λ2)(1-u1)‎‎+λ3γ.

where

u1=βHV(λ1-λ2)/A1,

u2=-λ3kI/A2,

σ = α + δ,

and

H(0)=1.7*10^8,    I(0)=0,    V(0)=400.

λ=5*10^5,    µ=0.003,     β=4*10^(-10),    α=0.043,    δ= 0.2                  k=6.24,       γ‎=0.65.

A1=900, A2=1000.

Aylin

### apply convert(,exp) to matrix...

October 20 2014
1 1

Hi all,

I am stuck with the following problem:

convert(cos(alpha), exp); works fine for me.

Once I have the trigonometric functions in a matrix, it does not work any more:

In the latter line, A keeps the trigonometric functions. Why is this the case? Is there any way to force maple to keep the complex exponentials instead of trigonometric functions?

I am using LinearAlgebra and VectorCalculus.

Best Regards

Wassja

### Reducing the size of large pdf (due to figures) ex...

October 19 2014
2 6

According to kernelopts(version), I am using Maple 16.02, X86 64 LINUX, Nov 18 2012, Build ID 7888210 , having just updated

Maple 16.

I have a Maple worksheet with some graphs of 10^5 data points. When I export the worksheet to a pdf for inclusion in a LaTeX document (with pdfpages package, this recognizes page breaks), the file is around 100 Mb, much larger than I would like.

It seems that the file is large as a figure in the pdf is not just an image, the pdf seems to contain all of the information necessary to plot each data point individually.

Is there some way to encourage Maple 16 to treat figures as bitmaps (or something similarly much smaller than the original figures) upon exporting a worksheet to a pdf? I'll be happy for any suggestions.

NOTES:

1. This question was originally for Maple 16.00. Updating to 16.02a has not solved the problem.

2. I am suspicious that there is some bug in how Maple 16 exports figures made with "plot" to a pdf file.

When I try various methods of compressing the pdf that I've seen on the web, such as with pdftk 1.44, or ghostscript 8.70 or 9.07,  or pdf2ps followed by ps2pdf ,

error messages are returned. For example using pdftk:

pdftk input.pdf output.pdf

gives

"Done. Input errors, so no output created"

### How to query for the SIZE of a varibale in maple ?...

October 19 2014
0 7

Is there any command in maple that can show us an assigned varibale how much bytes occupied on memory ?

a:=["just a string", 3.14 , 123 , x/y]

d:=array( 1 .. 2, 1 .. 2, [( 1, 1 ) = ("just a string"), ( 1, 2 ) = (3.14), ( 2, 1 ) = (123), ( 2, 2 ) = (x/y)  ] )

c:=a x^2 + b x + c

 >
 (1)
 >

It should be great for benchmarking !

### Updating Maple Integration Database...

October 15 2014
2 6

I have an integral that maple can not solve but I can solve it by hand. How can I add this to maple integration database?

f:=int(r^2*BesselJ(0,a*r)*BesselI(1,b*r),r)