Maple 14 Questions and Posts

These are Posts and Questions associated with the product, Maple 14

As part of the class I am teaching in biofluid mechanics, the students are learning about the Buckingham Pi theory for finding dimensionless groups (pi-groups).  The process involves the dimensions of parameters in terms of their basic units of measure: mass, M, length, L, and time, T.  Fore example, fluid density is M/L3 .  A typical step is to represent a product of parameters in terms of these measures raised to exponents.  Here is an example

(M/LT)a(M/L3)b(L2)c

where the exponents a,b,c are to be determined. What command(s) will massage this form to look like

Ma+b  L2c-3b-a T-a  ?

Cheers

I am teaching a course in biofluid mechanics and am looking to help the students get more use out of Maple. Often it is advantageous to scale a differential equation (and initial conditions) using dimensionless variables to reduce the number of free parameters in a problem. For example, the simple linear oscillator differential equation:

Eq(1)         m*d2x(t)/dt2 + k*x(t)=0

where k and m are parameters.  If we define a dimensionless time, s=t/T, and a dimensionless position, X=x/L, where T and L are constants, , Eq(1) becomes

Eq(2)         (mL/T2 ) *d2X(s)/ds2 +  kL*X(s)=0

Then choosing T=sqrt(m/k) we arrive at

Eq(3)         d2X(s)/ds2 +  X(s)=0

which has no parameters.  Can this sequence be done in Maple for a differential equation...i.e. change of variables?

Thanks

I am writing a textbook in biomedical engineering and using Maple 14 for generating figures.  In many of the graphs, my axis labels have subscripts or superscripts.  For example in a 2D plot statement I type   labels=[x,f[0](x)] which gives a subscript 0.   However, both x and f0(x) appear in italics.  How can I have them appear as normal...i.e. without italics? The labelfont command does not seem to have an instruction to remove the italics.  Can you assist me?

Hi!

Here below is the code I got problems:

#################################

Dens := proc(v)
local theta, r;
evalf[8](
    Int(
        Int(
            4*r/(1-0.84*cos(theta)^2)^(1/2)*exp(-r*(6.25-5.245*cos(theta)^2)^(1/2))
        , theta = 0. .. 2*Pi)
    , r = 0. .. v)
) assuming v>=0
end proc;

#
#

FitFinalDens := NonlinearFit(
  b*(1+a*u)/u*Dens(u/(1+a*u))
, depth
, veloc
, [u]
, initialvalues = [a = 1.4, b = 0.13]
, parameternames = [a, b]
, output = [leastsquaresfunction, residuals, parametervector]
, parameterranges=[a=1.1..3.0,b=0.02..0.8]
);

#################################

Then, I obtain two sort of errors:

First error message:

Error, (in Statistics:-NonlinearFit) invalid input: no implementation of NonlinearFit matches the arguments in call, 'NonlinearFit(0.13*(1.+1.4*u)*(int(int(4*r/..........

etc...

 

Second error message:

Error, (in Statistics:-NonlinearFit) complex value encountered

 

So, really I don't known how to correct the code.

I tried a lot  of things such as using  "value" command,  "Re" command, etc.

Do you have a solution?


Sincerely yours.

 

Jacqr

 

 

i wrote a procedure for determine a lambda symmetries and first integrals of ODEs.

Procedure is running but commands is getting error.

Can  anybody help me.

Thanks in advance. procedure.mws

i wrote a procedure to  find some functions but at the end  of the procedure gives unexpected string error. i didn't find any way out.

Best regards. 

Download procedureA.mws

Hello

I wonder if there is a way to see the progress of a specific procedure.  I have checked the forum for some answers and found that some of them propose a progress bar. However the progress bar doesn't seem to fit within a procedure.   

I don't need anything fancy but I need to see the progress of the loop inside of the procedure (over 3,000,000 times).   

Any suggestions?   

Many thanks

 

PS. I am running Maple 2016 too but I would rather see a solution that works on Maple 14 too, if possible.

Hello

I wonder if there is a function to retrieve only the monomials from a multivariable polynomial in x, y and z. Below is one such polynomail.

 

theta[2]*x3*x0-theta[8]*x2*x1*x0-theta[2]*x2*x1-theta[6]*theta[2]*x2*x0^2-theta[4]*theta[2]*x2*x0-theta[2]*theta[7]*theta[10]*x1*x0^3+theta[8]*theta[2]*theta[9]*x1*x0^2-theta[2]*theta[5]*theta[10]*x1*x0^2-theta[2]^2*theta[3]*theta[10]*x0^3+theta[6]*theta[2]^2*theta[9]*x0^3+theta[4]*theta[2]^2*theta[9]*x0^2

and the result

[x3*x0,x2*x1*x0,x2*x0^2,x2*x0,x1*x0^3,x1*x0^2,x0^3,x0^2]

Many thanks

 

Ed

 

 

 

 

 

 

 

 

Hello,

I have a sequence of functions :  solution[i] , i = 1..n

I have a sequence of times:          Time[i], i = 1..n+1

I need help to plot in the same graph:

 plot(  Sol[1] , t = Time[1]..Time[2] )  

 plot(  Sol[2] , t = Time[2]..Time[3] )  

 plot(  Sol[3] , t = Time[3]..Time[4] )  

etc...

plot(  Sol[n] , t = Time[n]..Time[n+1] )  

Thank you

 

 

 

using worksheet mode, is there a way to automatically color any comments after (#) with a different color than the default red?

I have been using Maple for years and did not need to significantly document or comment on my worksheets before because I only needed to share my worksheets with close collegues who have a lot of experience with Maple too. However, now I need to share my code with a general audience that might not be a Maple user. So I need to add enough comments after each line, and I have been manually changing the color of comments after the # to green to give the reader the indication that this is a comment and not part of the code, like this for example:

 

restart;

f:=(x,y)->sin(sqrt(x^2+y^2))/sqrt(x^2+y^2); # Define f as a function of the variables x and y

proc (x, y) options operator, arrow; sin(sqrt(x^2+y^2))/sqrt(x^2+y^2) end proc

(1)

df:=(x,y)->eval(diff(f(a,y),a),a=x); # Define df as the partial derivative of f with respect to x

proc (x, y) options operator, arrow; eval(diff(f(a, y), a), a = x) end proc

(2)

df(1,3); # Evaluate df at x=1, y=3

(1/10)*cos(10^(1/2))-(1/100)*sin(10^(1/2))*10^(1/2)

(3)

 

 

Download Worksheet-coloring-comments.mw



It would be great if Maple can automatically color comments like typical editors do. Is this possible? if not, does anyone have an advice for a nice easy way to add proper documentation to worksheets?

Hello,

 

I'm modeling the simple DC motor system in Maple.
The equations describing the system;

eq1:=J*diff(theta(t),t,t)+b*diff(theta(t),t)=K*i(t):
eq2:=L*diff(i(t),t)+R*i(t)=V(t)-K*diff(theta(t),t):
DCMotor:=[eq1,eq2];

First, I create the system using DiffEquation:

Sys:=DiffEquation(DCMotor,[V(t)],[theta(t)]);

And now I have problem. The input var is V(t) (input voltage) and the output var is theta(t) (position of the rotor).

But I wont to have in output var not position of the rotor but speed of the fotor - diff(theta(t),t)

How to set output var for diff(theta(t),t) (the speed of the motor)?

 

Best

Rariusz

 

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