Dear all;

Please Have some one an idea to transform or convert 2nd order ODE to system of First ODE ( of course using maple).

Thanks

Hi,

I wrote the following code which is properly run

restart:

# parametrs

MUR:=(1-phi)^2.5:
RhoUR:=(1-phi+phi*rho[p]/rho[f]):
RhoCPR:=(1-phi+phi*rhocp[p]/rhocp[f]):
BetaUR:=(phi*rho[p]*beta[p]+(1-phi)*rho[f]*beta[f])/(RhoUR*rho[f])/beta[f]:

dqu3:=diff(h(x),x$1)-RhoUR*BetaUR*T(x);
dqu2:=5*diff(T(x),x$2)+k[f]/k[nf]*Pr*RhoCPR*f(x)*diff(T(x),x$1);
dqu1:=5/(MUR)*diff(f(x),x$3)
+ 2*(diff(h(x),x$1)*x-h(x))
+RhoUR*(3*f(x)*diff(f(x),x$2)-diff(f(x),x$1)^2);
rho[f]:=998.2: cp[f]:=4182: k[f]:=0.597:   beta[f]:= 2.066/10000:
rho[p]:=3380: cp[p]:=773: k[p]:=36:   beta[p]:= 8.4/1000000:

k[nf]:=((k[p]+2*k[f])-2*phi*(k[f]-k[p]))/((k[p]+2*k[f])+phi*(k[f]-k[p])):
rhocp[nf]:=rho[p]*cp[p]*phi+rho[f]*cp[f]*(1-phi):
rhocp[p]:=rho[p]*cp[p]:
rhocp[f]:=rho[f]*cp[f]:

phi:=0.00:
binfinitive:=6: Pr:=7: lambda:=0:


with(plots):
pppe:=dsolve( {dqu1=0,dqu2=0,dqu3=0,T(0)=1,T(binfinitive)=0,f(0)=0,D(f)(0)=lambda,D(f)(binfinitive)=0,h(binfinitive)=0}, numeric );
-pppe(0);
print(odeplot(pppe,[x,diff(f(x),x)],0..binfinitive,color=black,numpoints=400));
print(odeplot(pppe,[[x,diff(f(x),x)]],0..binfinitive,color=black,numpoints=400));
print(odeplot(pppe,[[x,T(x)]],0..binfinitive,color=black,numpoints=400));

However, in some range of parameters, I must increase the value of binfinitive (for example binfinitive=50). however, my code is doesnt converge for higher values of 10 (at most). Can anyone change this algorithm in a way that it insensitive to the value of binfinitive?

Many thanks for your attention in advance

Amir

Could someone show me how to solve the following equations for real x, y and z.

Thanks

x^2 + 2yz^2 = 0,

y^2  - 3xz = 0, 

1/3*x*y^2 + 2*y*z^3 = 0,

-1/3*y^4 - 6yz^4 = 0.

hi,i want to take differential with respect to another differential using physics package,but using D instead of diff,could anyone help me do that ? for example :

restart; with(Physics):
A1 := -(1/24)*1*rho*((diff(phi[1](x, t), t))^2)*(h^3)-(1/2)*1*rho*((diff(u[ref](x, t), t))^2)*h-(1/2)*rho*((diff(w(x, t), t))^2)*h+(1/24)*1*1*((diff(phi[1](x, t), x))^2)*(h^3)+(1/2)*1*(1*((diff(u[ref](x, t), x)+(1/2)*(diff(w(x, t), x))^2)^2)+K*1*((diff(w(x, t), x)+phi[1](x, t))^2))*h-1*q*w(x, t):

A2:=-diff(diff(A1,diff(u[ref](x,t),x)),x);

here i want to compute A2 using D command,not diff and i do not want use convert command ! i just need to calculate A2 directly using D command. tnx for your help.

Using worksheet mode. It is a strugle to add a new paragraph on its own group so I can document some code.

I open new worksheet, and type a Maple command. say

x:=10; and hit return.

Now the screen looks like

------
|>x:=10;
|                        x:=10
----
|>     curser is here now    (1)

Now I want to make new paragraph, on its own group, before I type new command. (I need it on its own group, to fix another Maple latex export issue) i..e I want it to look like

------
|>x:=10;
|                        x:=10
----
|   this is pargraph I wanted to create
-----
|>     curser is here now    (2)

However, this is not possible using one command.  when in (1) above, if I tell Maple to insert paragraph->Before cursor, it does this:

------
|>x:=10;
|                        x:=10
----
|  it created a paragraph- here, but this is still in the same group as (1) below
|>     curser is here now    (1)

Only way I found to do it is this: create an execution group before the cursor. Then go back to that execution group. Then do insert paragraph->Before cursor, then delete the execution group just created, leaving the paragraph on its own group:

Step 1

------
|>x:=10;
|                        x:=10
----
|> create this as execution group
----
|>

Step 2

------
|>x:=10;
|                        x:=10
----
|   create paragraph here
|>
----
|>

step 3, delete the execution group, leaving the paragraph

------
|>x:=10;
|                        x:=10
----
|   leaving paragraph on its own here
----
|>

there got to be a simpler way? I am using Maple 18 on windows 7. (64 bit)

Maple 18, windows 7.

When I export this to Latex

x:=1/y;

The latex comes out as x:=y^-1 instead of using 1/y as it displays. I prefer 1/y and not  y^-1

i.e. instead of generating {y}^{-1} it should use \frac{1}{y}, just as it appears on the screen. Is there a configurration option one can use for this?

I also like to know if one can insert latex markup directly in Maple text paragraphs?

For example, if I add a text paragraph, (Menu->Insert->Paragraph) and would like to type some math in there, I can't just write $\sin(x)$ as this will not render as math when exported to Latex, as it is in a Maple normal group in the Latex file. 

Is there another way to typeset math in text area of a document? I only use worksheet mode. Not interested in using document mode.

thank you

AOA... I want to convert system of equations into matirx form.

F[0] := u[0, n]-u[0, n-1]+u[1, n]-u[1, n-1]+u[2, n]-u[2, n-1]+u[3, n]-u[3, n-1]

F[1] := u[0, n]-u[0, n-1]-u[1, n]+u[1, n-1]+u[2, n]-u[2, n-1]-u[3, n]+u[3, n-1];

F[2] := u[0, n]/P-u[0, n-1]/P-.7071067810*u[1, n]/P+.7071067810*u[1, n-1]/P+.7071067810*u[3, n]/P-.7071067810*u[3, n-1]/P+0.4549512860e-1*exp(-1.*t)-.3431457508*u[2, n]+.3431457508*u[2, n-1]+1.556349186*u[3, n]-1.556349186*u[3, n-1] = 0;

F[3] := u[0, n]/P-u[0, n-1]/P-.7071067810*u[1, n]/P+.7071067810*u[1, n-1]/P+.7071067810*u[3, n]/P-.7071067810*u[3, n-1]/P+0.4549512860e-1*exp(-1.*t)-.3431457508*u[2, n]+.3431457508*u[2, n-1]+1.556349186*u[3, n]-1.556349186*u[3, n-1] = 0;

I want to export the above system of equation in to matrices of as

AU[n]+BU[n-1]-C = O;

where*U[n] = Typesetting[delayDotProduct](Vector(4, {(1) = u[0, n], (2) = u[1, n], (3) = u[2, n], (4) = u[3, n]}), a, true)*n*d*U[n-1] and Typesetting[delayDotProduct](Vector(4, {(1) = u[0, n], (2) = u[1, n], (3) = u[2, n], (4) = u[3, n]}), a, true)*n*d*U[n-1] = (Vector(4, {(1) = u[0, n-1], (2) = u[1, n-1], (3) = u[2, n-1], (4) = u[3, n-1]})), Help me plz;

Help_Constrct.mw

how to transform

Matrix([[1,0,0],[1,0,0],[0,0,0]])

to

Matrix([[0,0,0],[0,0,1],[0,0,1]])

so we have to Write a maple function with -> that takes an integer N and a boolean function

F: {(i,j) l 0<= i,j<= N} -> {true,false} 

and returns a list containing all [i,j] such that F(i,j). A procedure that does this
would be

proc(N,F) local i, j, RV;
RV:=NULL;
for i from 1 to N do for j from 1 to N do
if F(i,j) then RV:=RV,[i,j] ; end if ;
end do ; end do ;
return RV ;
end proc ;

The problem is to do this inline, i.e. you have to write
(i,j)-> ...

please help...

int(sin(x)^cos(x),x= 0 .. Pi)

with Maple? A closed-form answer is also welcome.

Thank you for your help with this question. I found what I was looking for. 

I am trying some data analysis on an Excel worksheet using Maple. I have the following procedure but I don't know how to make it work for a specific subset of cells (this is a psychological studiy, so I want to have all my scores for each subject, located on the rows, and variable, located on a subset of columns). Example: I want to get an array of all the average scores in a rectangle of cells which goes horizontallyfrom A to AB, and vertically from row 1 to 15. Hope you can help me out! Cheers!

MediaRighe := proc (M) local i, j, r, c, S, N; r := LinearAlgebra:-RowDimension(M); c := LinearAlgebra:-ColumnDimension(M); S := Array(1 .. r); for i to r do S[i] := 0; N := 0; for j to c do if M(i, j) <> "-" then S[j] := S[j]+M(i, j); N := N+1 end if end do; S[i] := S[i]/N end do; return S end proc

I also have this for the columns (same thing, basically):

MediaColonne := proc (M) local i, j, r, c, S, N; r := LinearAlgebra:-RowDimension(M); c := LinearAlgebra:-ColumnDimension(M); S := Array(1 .. c); for j to c do S[j] := 0; N := 0; for i to r do if M(i, j) <> "-" then S[j] := S[j]+M(i, j); N := N+1 end if end do; S[j] := S[j]/N end do; return S end proc

Thanks everybody!

I am interested in using both in the same graph. And I am aware that i can drag from one to the other manually, but I am interesseted in doing it in a command. 

So i have 3 vectors a, b and an error. 

I can define ExponentialFit function based on a and b, and the plotting both observations, errors and the fitted function.

Per Kirkegaard

I know how to find a solution that satisfies the constraints, but in my case I need to find a solution which does not satisfy the constraints. Is there anyway that lp_solve can do that for me?

Lets say I have the following in LP format:

max: a;
1 < a;
a < 10;

Then, I can use lp_solve to give me a solution satisfied by the constraints, but is it also possible to find a solution not satisfied by the constraints using lp_solve?

Is there a Mangoldt function in maple? How do you invoke it?