The Fourier series of waveforms with discontinuties experiences an overshoot near the discontinuity known as the "Gibbs phenomenon".  There is quite a bit of literature showing that the overshoot for a rectangle function is ~ 1.089.  What about other functions such as (1-x) or a decaying exponential for x positive?  Is there any reason to expect the overshoot ratio to be identical to the rectangle function?  I do know for a fact that the behavior of the overshoot is different for the triangle function (1-x) than for the rectangle function.  For low harmonics there is an undershoot for the triangle function case, but this is not the case for the rectangle function.  The overshoot occurs for the triangle function after a sufficient number of terms are included in the Fourier series.  The same is true for the decaying exponential.  This is illustrated in my worksheet linked below.

GIBBS_effect.mw

Does anyone know of MAPLE code that computes the theoretical overshoot if there is an infinite number of terms in the series for different waveforms or functions?

So I have the following:

restart;
with(Physics):
Setup(mathematicalnotation=true,coordinatesystems=cartesian);
Define(A[mu](X));

First of all X ist defined in terms of (x,y,z,t). Is is also possible to define it in terms of (t,x,y,z) with t being mu=0.

When I do

alias(X=(t,x,y,z))

this applies only to this one vector and

d_[4] is still the time differentiation, right?

Then I wanted to construct the divergence

d_[`~mu`] A[mu](X);
TensorArray(%,performsumoverrepeatedindices=true);

This should give me sth like d1 A1 + ... + d4 A4, but it stays with d_mu A_mu ?!?

Why?

Is there also a "function" which does the contraction?

So if I have

f[mu,nu]=d_[mu] A[nu](X)

eval(f[mu,nu],nu=mu)

contract(%)

??

evalf(Int(x*(1-2*x^(3/10))^(10./3),x=0..1));  # Crashes Maple

Note that:

int(x*(1-2*x^(3/10))^(10./3),x=0..1);
int(x*(1-2*x^(3/10))^(10/3),x=0..1);
are OK.

(Windows 7, Maple 2017.3, 64 bit)

Hi everyone,

I'm looking for some way to simplify the following procedure:

scm := proc(X, x) global xx;

if 1 <= X and X < 10 then xx := cat(x)

elif 10 <= X and X < 100 then if 1 <= x and x < 10 then xx := cat(0, x) else xx := cat(x) end if

elif 100 <= X and X < 1000 then if 1 <= x and x < 10 then xx := cat(0, 0, x) elif 10 <= x and x < 100 then xx := cat(0, x) else xx := cat(x) end if

elif 1000 <= X and X < 10000 then if 1 <= x and x < 10 then xx := cat(0, 0, 0, x) elif 10 <= x and x < 100 then xx := cat(0, 0, x) elif 100 <= x and x < 1000 then xx := cat(0, x) else xx := cat(x) end if

elif 10000 <= X and X < 100000 then if 1 <= x and x < 10 then xx := cat(0, 0, 0, 0, x) elif 10 <= x and x < 100 then xx := cat(0, 0, 0, x) elif 100 <= x and x < 1000 then xx := cat(0, 0, x) elif 1000 <= x and x < 10000 then xx := cat(0, x) else xx := cat(x) end if

end if

end proc

Any tips? Thank you in advance.

Hi 

I want to solve these equations in MAPLE, but something goes wrong. 

Download 11111111111111.mwWould you mind please check out my code11111111111111.mw

11111111111111.mw

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?

u:=(x,t)->(40/Pi)*sum((1/r)*sin(r*Pi*x/2)*exp(-lambda^2*t),r=1....infinity);     r=1,3,5.... 

this is one dimensional heat equation solution. r values must be odd numbers and we can take the random r variable like 1000 .x=0...2 and t=0...1   but I don't know how can I draw 3d plot. If I write plot3d([u(x,t)],x=0...2,t=0...1); give an error.(bad range arguments)

Dear Maple useres,

I have a polynomial in the form f(s)/g(s) where f and g are polynomial of order 4 with coefficients in symbolic form. I want to convert it in a form of (s-a)*(s-b)*(s-c)*(s-d)/(s-a1)*(s-b1)*(s-c1)*(s-d1)

When i provide the numic value of  symbolic coefficients, Maple find it easy to factor it in the desired form. Otherwise i get a messy solution in the form of root of... expression. Even with assume command, I see no difference in the result. Is there a way to get the above simple form rather than root of expression?

thanks.

Hello!

I am currently working with the A = rosser Matrix. Which is found in Matlab. The task is to find the eigenvectors of this Matrix in Matlab and Maple. I have succeeded in matlab, but I am confused with Maple. What I have done:

1) In Matlab I save the A = roseer so I could import in from Maple

2) I go back to Maple

3) I write with(LinearAlgebra);

3) I use this path "Tools>Assistants>Import Data" and I select the saved Matlab file (Named A.mat) (No specific folder if that is important)

4) I use "Matrix Data Type" as "Anything" and I give the Variable name "A"

5) I now see the Matrix inside Maple. BUT I get dots after each value. Like this --> 99. 3. -147. etc - This might be an issue.

Note: I never get to select file format. Is that because they know it was a matlab file? Or a setting I am missing out on?

6) I write A := A[2] (According to teachers instructions)

7)  Then I write: eigenvects(A);  (Teachers isntructions)

But I am getting no proper values at all. I assume it is something with the import. So I added this 8x8 Matrix by hand. I got a better result with a result. But the result is wrong. I am getting 7 eigenvectors while there should be 8. See the code at: Method-two.mw

I am turning crazy over here. Anyone smart who could help me out please?

Hi,

I use Statistics[Biplot] and the rendering is very bad with those huge arrows.

For the moment I fix this by modifying the definitions of the curves which draw each arrow (after using getdata to recover the Biplot structure)

Does it exist a simpler way to manage the appearance of the arrows ?
(options cb, cw and ch of plottols[arrow] are incorrect in Statistics[Biplot](..., arrow=[...]).

Thanks in advance

My co-author and I recently published the 3^rd edition of our finite element book¹ utilizing routines written with MAPLE. In this latest edition, we include a chapter on the meshless method. The meshless method is a unique numerical method for solving PDEs. The finite element method requires the establishment of a mesh associated with node points. Consideration must be given in establishing a good mesh (and minimizing the bandwidth associated with node numbering). The meshless method does not require a mesh to connect nodes. The following excerpt describes the application of the meshless method for a simple 1-D heat transfer simulation using six nodes.

> restart:
   with(LinearAlgebra):with(plots):

# MESHLESS METHOD SOLUTION USING MULTIQUADRIC RADIAL BASIS
FUNCTIONS (RBF) il:=6:To:=15:TL:=25:L:=1:
>   x:=[0,1/5,2/5,3/5,4/5,1]:
>   S:=1000:n:=1:dx:=1/(il-1):
>   C:=Array(1..il,1..il):phi:=Array(1..il,1..il):d2phi:=Array(1..il,1..il):
b:=Vector(1..il):TM:=Vector(1..il):alpha:=Vector(1..il):
for i from 1 to il do
   for j from 1 to il do
      phi[i,j]:=(1+(x[i]-x[j])^2/(S*dx^2))^(n-3/2):
      d2phi[i,j]:=3*((x[j]-x[i])/20)^2/(4*((x[j]-x[i])^2/40+1)^(5/2) )-1/(40*((x[j]-x[i])^2/40+1)^(3/2)):
   end do:
end do:
>   for i from 2 to il-1 do    
>       for j from 1 to il do
>         C[i,j]:=d2phi[i,j]+phi[i,j];
            b[i]:=-x[i];
>         C[1,j]:=phi[1,j];
           C[il,j]:=phi[il,j];
         end do:
      end do:
      b[1]:=To:b[il]:=TL:
> #ConditionNumber(C);
>   alpha:=LinearSolve(convert(C,Matrix),b):
TM[1]:=To:TM[6]:=TL:
for i from 2 to il-1 do
   for j from 1 to il do
>         TM[i]:=TM[i]+alpha[j]*(1+(x[i]-x[j])^2/(S*dx^2))^(n-3/2);
 >     end do:
>   end do:
     evalf(TM);

                     

> TE:=To*cos(xx)+(TL+L-To*cos(L))/sin(L)*sin(xx)-xx:
> TE:=subs(TE):
> TE:=plot(TE,xx=0..1,color=blue,legend="Exact",thickness=3):
> MEM:=[seq([subs(x[i]),subs(TM[i])],i=1..6)]:
> T:=plots[pointplot](MEM,style=line,color=red,legend="MEM", thickness=3): 
  MEM:=plots[pointplot](MEM,color=red,legend="MEM",symbol=box, symbolsize=15):

>  plots[display](TE,MEM,T,axes=BOXED,title="Solution - MEM");

              

Just over a year ago, someone asked me if Maple could help them pick names for their family gift exchange, because they were fed up with trying to find a solution by hand that met all their requirements. I knew it could be done, of course, and I spent some time (and at least one family dinner conversation) talking about how to do it. There wasn’t enough time to help my friend last year, but I dusted off my ideas, and my somewhat rusty Maple programming skills, and put something together for this year.

The problem, as stated to me, was “Assign everyone in the group the name of someone else in the group (the person they will buy a present for), with the restriction that no one can be assigned their partner.”

I decided to generalize a bit so that you can specify more than one person in the “do not pick” list for each individual, and the restrictions do not have to be reciprocal. That way, you can use it with rules like “parents cannot pick their children”, or “Elizabeth got Martin two years running, so she can’t pick him again this year”.

Ultimately I went with a “guess and check” approach. For each person, pick a name from the pool of suitable candidates (excluding themselves, anyone on their “do not pick” list, and anyone who has been picked already). Keep assigning names until either everyone has a name, or you end up in a situation where you can’t give someone a name. This can happen, for instance, if Todd is the last name, and the only unmatched name is Catherine, and Todd cannot pick Catherine. If that happens, I tossed all the names back into the virtual hat, gave it a good shake (i.e. randomize()) and tried again. Not as elegant as I would have liked, but it seemed like an effective approach.

It does feel like there ought to be a “nicer” solution. Maybe using graph theory? I know that my code will get into trouble if the restrictions are such that no solution exists.  If anyone has any ideas on other/better ways to solve this problem I’d be happy to hear them (now that I’ve had the fun of solving it myself first!).  

The application can be found on the application center: Gift Exchange Helper. The name picker algorithm is in the start-up code.

Happy gift giving!

Hello,

I used the interface(typesetting = extended) command to change the notation used for time derivative of o variable.

But it doesn't seem to be working well when the variable is in the supercript form (check the last line).

How can I solve this issue?

Mapleprimesquestion.mw

x/2 seems completely wrong as a CDF. In other cases Maple correctly writes the CDF as a piecewise-constant function clipped to 0..1:

with(Statistics):

dd := Distribution(ProbabilityFunction = 1/2, Support = 1 .. 2);

PDF(dd, x); # OK
                   (1/2)*Dirac(x-1)+(1/2)*Dirac(x-2)

CDF(dd, x);
                                (1/2)*x

Also CDF seems to have issues with DiscreteValueMap specified using a list, a table or piecewise():

dd := Distribution(ProbabilityFunction = 1/2, DiscreteValueMap = (n -> [1, 2][n]), Support = 1 .. 2);

PDF(dd, x); # OK
                    (1/2)*Dirac(x-1)+(1/2)*Dirac(x-2)

CDF(dd, x); # indeterminate
  int((1/2)*Dirac(0)*Dirac(_t-1)+(1/2)*Dirac(0)*Dirac(_t-2), _t = -infinity .. x)