Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

How to convert maple file into the pdf file?For example the attacahed file is maple file.I want to convert this to a pdf file.

conservation_of_wave_eq.mw

Hi, i want to investigate  chaos for the problem , cantilever beam under random narro band excitation, but the code has errors .the code is this:

      restart:with(plots):      h:=1: Omega:=(0..376):alpha1:=617.2:alpha2:=1.02*10^(8): c:=.002:k:=18.4:  step:=0.1:imax:=376:  for i from 0 to imax do;  Omega[i]:=i*step:   f:=evalf(solve({((-a*Omega[i]^(2)+alpha1*a+3/(4)*alpha2*a^(3)+1/(4)*k*Omega[i]^(2)*a^(3)-(3)/(4)*k*Omega[i]^(2)*a^(3))^(2)+(c*Omega[i]*a^())^(2))=h^(2),a>0}));  ff[i]:=((rhs(f[1]))^(2))/(2):  end do:   l1:=[[Omega[n],ff[n]] $n=0..imax]:  p1:=plot(l1, x=0..3,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    jmax:=914: f1:=array(377..914):f2:=array(377..914):f3:=array(377..914):Omega1:=array(377..914):  for j from 377to jmax do;  Omega1[j]:=j*step:   fff:=evalf(solve({((-a*Omega1[j]^(2)+alpha1*a+3/(4)*alpha2*a^(3)+1/(4)*k*Omega1[j]^(2)*a^(3)-(3)/(4)*k*Omega1[j]^(2)*a^(3))^(2)+(c*Omega1[j]*a^())^(2))=h^(2),a>0}));  f1[j]:=((rhs(fff[1,1]))^(2))/(2):f2[j]:=((rhs(fff[2,1]))^(2))/(2):f3[j]:=((rhs(fff[3,1]))^(2))/(2):  end do:   ll1:=[[Omega1[n],f1[n]] $n=377..jmax]:  pp1:=plot(ll1, x=0..10,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    ll2:=[[Omega1[n],f2[n]] $n=377..jmax]:  pp2:=plot(ll2, x=0..10,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):    ll3:=[[Omega1[n],f3[n]] $n=377..jmax]:  pp3:=plot(ll3, x=0..15,y=0..1,  style=point,symbol=solidcircle,symbolsize=4,color=red):       plot({  seq(seq(p1), seq(seq(pp1),seq(seq(pp2),seq(seq(pp3))  },style=point,title=`Pitchfork Diagram`);  Thanks for your help

Does any body have example of maple code for solving optimal control problem in deterministic model using Pontryagin's maximum (or minimum) principle?

Hello everyone,

I am experiencing a strange result. The Theta_double_dot got equated to zero in line 1.7. Please see the red arrow.

(I am using the Physics package)

How can I solve this issue?

Hello.

Please help me. I Have to solve some equations with Adomian Decomposition Method in Maple. But i don't know it.

I just know AGM, HPM and Perturbation Method in Maple.

please send me instructions and codes.

I'm sorry, I can't speak English well. I hope you understand what I mean.

thank you

hello , there , i want ask a Question ,

i have a vector result n hier , and there is a long part with ^1/2 (like unter) , which is not defined before , just from compute ,i want to replace this part with A, and have tried to use subs , but it didnt work . 

And i have tried to define it before compute, and then use subs , aber it also didnt work .

so how can i replace or define this part in the result?

thanks

 

how do i solve a system of PDE's with variable coeffiecients in Maple?

Hi everyone

I have a problem with differentiating an equation. I have the following code:


(sum((x(i)-M)^3, i = 1 .. n))/(n*((sum((x(i)-M)^2, i = 1 .. n))/(n-1))^(3/2));


The values of x(i) is available in Excel and I want to import that. For this case, I copy the column and paste in maple and it seems work fine. But, I want to calculate the differentiate of the summation with respect to x(i) and M and find the answer. I don't know how to write the code appropriately.

In other words, how could I differetiate the following function with respect to x(i) and put the values from excel into it.

(sum((x(i)-M)^3, i = 1 .. n))/(n*((sum((x(i)-M)^2, i = 1 .. n))/(n-1))^(3/2));

 

Thank you so much for your kind attentions  in advance

 

I am new to maple. how do i segregate different term in long PDE in maple

Dear Maple users,

I am solving a system of linear equations Ax=b where A is a matrix (243*241) which contains a rational polynomial of unknown "kappa" along with floating numbers. As suggested in some other posts I am using Linear algebra package with the LinearSolve command and option "solve" to find out unknown vector x. b is a vector having entries zero and 1. The system is such that two equations are redundant but it is difficult to recognise which two are redundant and hence for the time being I am keeping them in the matrix. (For a known value of kappa (say kappa=2) I have checked that two equations are redundant.) For the reference, the matrix and the right-hand vector b is attached as text.

There are two issues

1) Maple takes very long time (12 hours and so) to get x=b\A;

2) The result is a long expression i.e.  x[i] is a rational polynomial in kappa; a very long rational polynomial which I am importing as a text. I am not sure if maple exports all terms in the polynomial as for the different value of kappa I see Ax-b >0. 

How can I overcome this problem? Any help will be greatly appreciated. 

I have final project to make a media for learning mathematic using maple. But I'm so confused to make a net of cuboid, anybody can help me? please :D

Dear all

I have an operator given below in the image. I want expand this operator upto order 5, when there are three independent variables x, y, t(i=1,2,3). The expansion can also be obtained manually, but that is always prone mistake, is the expansion posible using any routine of Differential Geometry package?

Hi everybody

In the attached file, when I run the code an error appears while calculating "omegaL1" parameter. The dimensions of the matrices are correct but the source of error is unknown to me. Can anyone help me?

Thanks in advance

R2_Link_2D.mw 

This must have a simple answer but I have been unable to figure it out after many attempts. 

I am trying to create a Clifford algebra, and then use the results in the multiplication table "MT". The multiplication table elements are correct as displayed, but I don't know how to access the results in the table (i.e. the products of the basis elements).  For example, trying to access the table results as matrix elements like MT[2,3] doesn't work, presumably because it is not a matrix. In other words, I need a matrix that contains the same information as the multiplication table.

DGsetup([x, y, z], M);
I12 := Matrix([[-1, 0, 0], [0, -1, 0], [0, 0, -1]]);
AD3b := AlgebraLibraryData("Clifford(3)", Cl3Q, quadraticform = I12);
DGsetup(AD3b, '[e0, e1, e2, e3, e12, e13, e23, e123]', '[omega]');
MT := MultiplicationTable(Cl3Q, "AlgebraTable");

 

i want to solve the system of equation ( 1 )  , (2)  ,  (3)   under the assumation that x , y have the CDF in (4)  ,  (5)
 

diff(L(lambda[1], lambda[2], alpha), lambda[1]) = n/lambda[1]+sum(x[i], i = 1 .. n)-(sum(2*x[i]*exp(lambda[1])/(exp(x__i*`λ__1`)-1+alpha), i = 1 .. n))

diff(L(lambda[1], lambda[2], alpha), lambda[1]) = n/lambda[1]+sum(x[i], i = 1 .. n)-(sum(2*x[i]*exp(lambda[1])/(exp(x__i*`λ__1`)-1+alpha), i = 1 .. n))

(1)

diff(L(lambda[1], lambda[2], alpha), lambda[2]) = m/lambda[2]+sum(y[j], j = 1 .. m)-(sum(2*y[j]*exp(lambda[2])/(exp(y__j*`λ__2`)-1+alpha), j = 1 .. m))

diff(L(lambda[1], lambda[2], alpha), lambda[2]) = m/lambda[2]+sum(y[j], j = 1 .. m)-(sum(2*y[j]*exp(lambda[2])/(exp(y__j*`λ__2`)-1+alpha), j = 1 .. m))

(2)

diff(L(lambda[1], lambda[2], alpha), alpha) = (n+m)/alpha-(sum(2/(exp(x[i]*`λ__1`)-1+alpha), i = 1 .. n))-(sum(2/(exp(y[j]*`λ__2`)-1+alpha), j = 1 .. m))

diff(L(lambda[1], lambda[2], alpha), alpha) = (n+m)/alpha-(sum(2/(exp(x[i]*`λ__1`)-1+alpha), i = 1 .. n))-(sum(2/(exp(y[j]*`λ__2`)-1+alpha), j = 1 .. m))

(3)

G(x, lambda[1], alpha) = 1-alpha/(exp(lambda[1]*x)-1+alpha)

G(x, lambda[1], alpha) = 1-alpha/(exp(lambda[1]*x)-1+alpha)

(4)

G(y, lambda[2], alpha) = 1-alpha/(exp(lambda[2]*x)-1+alpha)

G(y, lambda[2], alpha) = 1-alpha/(exp(lambda[2]*x)-1+alpha)

(5)

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