Hello, i am doing some schmidt-analysis on a stirling engine, but my question is rather simple. I have the measured presure P at a given time T as a 229x2 matrix, i also have a function, V__total(T), for the total volume of the engine at a given time T. 

I then go on to create a pointplot PV, which is rougly the shape of a potato. I now want to find the area enclosed by this point plot, is there any way? 

I do something like:

> DATA:=ImportMatrix(filepath,skiplines=1); %import data from .txt file, skip header line. 

>P:=DeleteColumn(DATA,1); %Isolate presure column

>T:=DeleteColumn(DATA,2); %Isolate time coliumn

>V:=V__total~(T); %Generate volume vector as a function of time T

>pointplot(<P|V>,connect=true);

Is there any wat to finde the area enclosed by the curve/ 

I have the following two PDEs:

PDE := diff(u(x, t), t) = diff(u(x, t), x, x)+sin(x+t)-cos(x+t);

IBC:= D[1](u)(0,t)=-sin(t),
D[1](u)(1,t)=-sin(1+t),
u(x,0)=cos(x);

pds := pdsolve( PDE, [IBC], numeric, time = t, range = 0 .. 1,
spacestep = 1/32, timestep = 1/32,
errorest=true
)

PDE2 := diff(v(x, t), t) = diff(v(x, t), x, x);
IBC2:= D[1](v)(0,t)=0,
D[1](v)(1,t)=-0.000065*v(1, t)^4,
v(x,0)=1;

pds1 := pdsolve( PDE2, [IBC2], numeric, time = t, range = 0 .. 1,
spacestep = 1/32, timestep = 1/32,
errorest=true
);

Now, what I want to do with these two PDEs is the following:

For each h=timestep=spacestep  = 1/16 , 1/32 , 1/64 , 1/128 , 1/256

Calculate the error norm ||E||_h = sqrt(sum_{j=0}^{1/h} h* |u(j*h,tval)-v(j*h,tval)|^2)

where tval is some chosen point between 0 and 1 (this value is fixed for each spacestep chosen).

And then plot the graph of log ||E||_h vs. log h above.

What I don't know is how to extract each time the spacestep and its PDE's two solutions, does someone have a suggested script to use here?

How do I construct the seuqence 1/16 , 1/32 , 1/64 , 1/128 , 1/256 in maple?

What's the syntax?

I looked at the examples in here:

http://www.maplesoft.com/support/help/maple/view.aspx?path=seq

But didn't find something similar.

I’m using Maple 2015.2 to plot irregular spaced data using the surfplot command. The shape of the plot is as expected, however I’ve been unsuccessful in changing the color of the surface. I would like the surface to be a consistant color instead of the “rainbow” color scheme. I’ve tried both the color and colorscheme options to no avail.  I’m sure I’m making a very basic mistake, however I’m having difficulty finding it.

See attached worksheet

 feildstrength.mw

Best regards,

Ron

[EDIT]: Worksheet didn't attach the first time

In Maple 2015.1 we have

restart;

solve([sin(2*x)/cos(x+3*Pi/2)=1,  x>-4*Pi, x<-5*Pi/2], x, allsolutions, explicit);

solve([sin(2*x)/cos(x+3*Pi/2)=1, x>0, x<2*Pi], x, allsolutions, explicit);

In the first example, the error message is not clear (actually there exists a unique root  x=-11*Pi/3), in the second example, one root  (x=5*Pi/3) is lost.

I am learning to use maple for my notes preparation for the subject Finite Element Analysis. It is interesting to know that how often we blame maple or computer for the silly mistakes we made in our commands and expect the exact answers. I have used a small file and find it easy to analyse my mistakes fatser. If we make a small mistake in a big file, it not only gives us problem finding our mistakes, it leads to more mistakes in other parts as well. A command working in one document need not necessarily work the same way in other document.

I have made my first document and people will come with suggestions to make appropriate modifications in the various sections to improve my knowledge on maple as well as the subject.

Download FINITE_ELEMENT_ANALYSIS.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

A strange verical line in output of dsolve.Should be a comma in Jacobi SN function and comma's in invert Jacobi SN function.

Possible_Bug.mw

Can anyone help me confirm this?

Hello,

While doing some tests, we encountered an issue with LinearAlgebra[ConditionNumber], possibly caused by another routine in the LinearAlgebra package (MatrixInverse?). I include an example worksheet bug-maple.mw for easy testing.

To reproduce, you should start by creating this matrix:

restart;
with( LinearAlgebra ):
Digits := 50:
n := 4;
M := [ seq( cos( Pi*j/n ), j=0..n ) ];
V := VandermondeMatrix( M );

Now compute the condition number (infinity-norm) of V:

c1 := ConditionNumber(V);
c1 := simplify(%);
evalf(c1); # this gives exactly 40

We can still compute this exactly and get 40.

This is the same result as with linalg[cond]:

c2 := linalg[cond](V);
c2 := simplify(%);
evalf(c2);

Now increase the value of n to 5 and redo the test.
The exact result should be 120, but LinearAlgebra[ConditionNumber] gives the wrong result!
On the other hand, linalg[cond] gives the correct, exact result (after simplification).

n := 5; # this gives a wrong result :-(

We could use Norm(V) * Norm(Inv(v)) since this should be equal to the condition number.
But then it seems there's something bad inside the MatrixInverse routine.
Again, linalg[inverse] gives the correct, exact result.
So compare the two results:

n := 4;
simplify(MatrixInverse(V));
linalg[inverse](V);

Finally, to make matters even worse, ConditionNumber gives completely wrong results when using a float-matrix, while linalg[cond] does not:

n := 3;
V := VandermondeMatrix( evalf(M) );
c1 := ConditionNumber( V );
c2 := linalg[cond]( V );

For n=3, we get c1=10.6 and c2=16.
For n=4, we get c2=5 and c2=40.
For n=5, we get c1=68.07 and c2=119.999.

Is this what it looks like? With it being a really, really ugly bug?

-- Many thanks for your reply,

Franky

Dear friend,

Recently I noticed, that numerical integration returns different values for the same function.

For example the code

restart;
evalf(int((exp(x)*(4420*cos(4)*sin(4)-544*cos(4)^2+148147*exp(-1)-4225*cos(4)-215203)/(71825*exp(1)-71825*exp(-1))-exp(-x)*(4420*cos(4)*sin(4)-544*cos(4)^2+148147*exp(1)-4225*cos(4)-215203)/(71825*exp(1)-71825*exp(-1))+(32/4225)*cos(4*x)^2+(1/71825)*(4225+(2210*x-6630)*sin(4*x))*cos(4*x)+x^2+8434/4225)^2, x = 0 .. 1));

each time returns values

0.0005951015934
0.0005950850548
0.0005950974588
0.0005950960805
0.0005951297843 etc.

Maybe, evalf uses a stochastic algorithm for integration?

Hi!

I have a problem recently with running RootFinding:-Isolate inside a procedure which is run on threads. I have many polynomial systems to treat so I would like to balance computations between cores. Unfortunately, my code always breaks computation kernel with the error:

java.lang.NullPointerException

at com.maplesoft.mathdoc.model.WmiModelLock.acquireLock(Unknown Source)
at com.maplesoft.mathdoc.model.WmiModelLock.writeLock(Unknown Source)
at com.maplesoft.worksheet.connection.WmiOutputUpdateBuffer$UpdateSynchronizer.run(Unknown Source)
at java.lang.Thread.run(Unknown Source)

I wrote a small example below

f:=proc(n)

   local i;

   for i from 1 to n do
    try

      RootFinding:-Isolate([a^2+b^2-1/3c^2,a^2-1/3b^2+c^2-1/3,a^2-1/3b^2-1/3c^2+1],[a,b,c]):

   catch "":
     next:
   end try:
  end do:
end proc:

Threads:-Task:-Start ( null, Task[f,10000], Task[f,10000], Task[f,10000]);

I have no much of experiences with threads in Maple so I would not be surprise if I'm trying to do something completely wrong here. Any hint or advice will be appreciate. 

I'm trying to solve a system of equations thats expressed as a summation (the original has the summation symbol as opposed to 'sum'):

d_actual := solve(W_actual = sum(W_guess(def-asp_rad_inverse[i], E, asp_rad[i]), i = 1 .. n), def);

When n<5, I get an answer after a few seconds, but when n is higher, the program sits and 'evaluates' forever...I've waited up to 30 min. 

Background:

I have a plate with a number of hemispheres on the surface (# of impacted hemispheres given a force = n). Each has a unique radius and they're listed from largest to smallest in 'asp_rad[]'. I have an equation for the deflection of a single hemisphere as a function of Force and material properties that I have rearranged with respect to Force (W_guess(deflection, E, r)). There's an opposing plate that stays parallel to the original plate while pushing down on the asperities with Force W_actual. The total deflection of the opposing plate is the sum of: 1) the difference between the tallest radius and the impacted radius in question (asp_rad_inverse[]), and 2) the deflection of the impacted radius in question. 

I'm attempting to solve for the total deflection of the opposing plate via solving for the 'def' in the summation above, but when I run it, the program is not able to compute a solution.

Thanks in advance.

Hello!

If I type this into a CAS calculator from Texas, I get the right result for Uc wich is 545.2.

solve(Uc&angle;-90=400&angle;X-150&angle;0+j*174.4,Uc,X)

This is used in AC circuits.

However, in Maple I'm using polar coordinates, so Im using this preamble:

phasor := proc (r, theta) options operator, arrow; r*cos(convert(theta*degrees, radians))+I*r*sin(convert(theta*degrees, radians)) end proc

This basically means that I can write phasor(value,angle in degrees) and get the lenth and angle of a vector on the complex plane.

Basically I want to know how I can make Maple solve this:

evalf(solve({phasor(U__C, -90) = phasor(400, X)-phasor(150, 0)+phasor(174.4, 90)}, {Uc, X})) Where I'm just interested in U_C , X doesn't matter.

I can't figure out how to do this with my current preamble. Does anyone know how to make this work?

I once opened Tools-Tutors-Precalculus-Polynomials. Now every time I click the button of 'execute the entire worksheet', the same Tutor  window will pop up before Maple executes my codes. I wanna know how to prevent the window to pop up? 

Hello!

I'd like to define a function after loading the Units package. But when using the defined function, Maple displays "Units:Standard-" everywhere. Even in labels of plots. I'd like to avoid that. A sample file is attached. Is there a better way of doing it?

Thanks.

Bruno

Test.mw

Hi, I'm new to Maple and I have to produce a recursive procedure with the nomenclature Puis:=proc(X,n::integer) which calculates X^n with:

for n<0   ->   1/(X^(-n))

for n=0  ->   1

for n being an even integer   ->   X^(n/2) * X^(n/2)

for n being an odd integer   ->   X*X^(n-1)

The procedure I produced is:

Puis:=proc(X,n::integer)
option remember;
if n<0 then Puis(X,-n);
elif n=0 then 1;
elif rem(n,2,x)=0 then Puis(X,n);
else X*Puis(X,n-1);
end if;
end proc;

i don't have any eror up to this point, but when I try to evaluate, only Puis(4,0) works

Puis(4,-1);
Error, (in content) too many levels of recursion
Puis(4,0);
                               1
Puis(4,3);
Error, (in content) too many levels of recursion
Puis(4,4);
Error, (in content) too many levels of recursion

I was wondering what was wrong with my procedure, I changed the 1/(X^(-n)) with X^n and X^(n/2)*X^(n/2) for X^n because it is equivalent. I think I should put some sort of initial value to limit the recursion, but with that kind of function i really don't know how. I also tried with the X^(n/2)*X^(n/2) for the even numbers, but it says Puis expects its 2nd argument, n, to be of type integer, but received 1/2.