Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016


WARNING: This is a pretty silly question. I know it, but I've been on this for hours already...
I have this function rather simple but which depends on a natural number n. When I try a Fourier transform on it, it cannot evaluate the result for any n.

I have to define another function, and evaluate n=2, in order to get an explicit result.

h := piecewise(abs(t) < 2*Pi*n, cos(t), 0)
                    piecewise(abs(t) < 2*Pi*n, cos(t), 0)
---------->         fourier(piecewise(abs(t) < 2*Pi*n, cos(t), 0), t, w)         # doesn't work for any n

h2 := eval(h, n = 2)
                      piecewise(abs(t) < 4*Pi, cos(t), 0)

   F.T.               2 w sin(4 Pi w)
---------->          ------------------                                          # works with fixed n=2
                      (w - 1) (w + 1)

How can I have an explicit result for any natural n ?

Thanks for your time

A catenoid is the minimal surface between two 3D circles which are co-axial and parallel.

Is there a technique for finding the formula for the minimal surface if the circles are "stretched" into ellipses with proportional major and minor axes?

Dear All,

I am trying to calculate a product of a complex function and its complex conjugate, for instance, conjugate(exp(I*phi))*exp(I*phi), and integrate phi from 0 to 2*pi. The product is supposed to be 1 and the integral should be 2*pi. However, with the following code:

phi::real; simplify(conjugate(exp(I*phi))*exp(I*phi))

I obtain the result as shown in the attached figure. It still gives a bar over one phi and does not give 1. Could you please tell me how I can fix this problem? Any of your hellp is appreciated.


Best regards,



Dear All. I am a beginner of using Maple. My calculation gives a complex expression as shonw in Line (23) in the attached figure. I used "simplify" to simplify it. However, the result is not the simplest form. The numerator can be divided by the denominator. Could you please tell me what command I can use to further simplify the expression? Any of your help is highly appreciated!

Best regards,


Please help me with the following worksheet containg a sample ODE. I need to integrate this ode untill at least one of the terms is derivative free


odetemp := -(diff(U(z), z))*c*v+U(z)*(diff(U(z), z))*c-(diff(U(z), z, z))*c^2

-(diff(U(z), z))*c*v+U(z)*(diff(U(z), z))*c-(diff(diff(U(z), z), z))*c^2






In the following program why the first row of Matrix P is costant, while I expect it varies?






MCK := Matrix(1, 1, {(1, 1) = 0.1627682387e-16*mu})

P := Matrix(2, 111):

`&rho;__&infin;` := 1.225:

j := 1:

for `U__&infin;` from 333 to 335 do `M__&infin;` := `U__&infin;`/(331.2); mu := `&rho;__&infin;`*`U__&infin;`*(`M__&infin;`^2-2)/sqrt((`M__&infin;`^2-1)^3); P[1 .. 2, j] := `<,>`(`<,>`(MCK), `<,>`(j)); j := j+1 end do:

P[1, 1 .. j-1]

Vector[row]([0.1627682387e-16*mu, 0.1627682387e-16*mu, 0.1627682387e-16*mu])





e1 := tau-gamma*S__1-beta*S__1*S__3/(S__3*alpha__1+1)-beta*xi*S__1*S__4/(S__4*alpha__1+1)+phi*S__5 = 0;
e2 := beta*S__1*S__3/(S__3*alpha__1+1)+beta*xi*S__1*S__4/(S__4*alpha__1+1)-(gamma+eta__1+eta__2)*S__2;
e3 := eta__1*S__2-(gamma+gamma__1+delta__1+omega)*S__3;
e4 := eta__2*S__2+omega*S__3-(gamma+gamma__2+delta__2)*S__4;
e5 := delta__1*S__3+delta__2*S__4-(gamma+phi)*S__5;
solve({e1, e2, e3, e4, e5}, {S__1, S__2, S__3, S__4, S__5});

This is my code in which I try to solve the system of differential equations where the unknowns are the vectors x(t),y(t).
dsolve({sys, x(0) = Vector([1,1,1]), y(0) = Vector([1,1,1]), eval(diff(x(t),t),t=0) = Vector([0,0,0]), eval(diff(y(t),t),t=0) = Vector([1,1,1])}, type = numeric, output = listprocedure);
The message I get is "Error, (in DEtools/convertsys) invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received {Vector(3, {(1) = YP[1], (2) = YP[2], (3) = YP[3]}, attributes = [coords = cartesian]), Vector(3, {(1) = YP[4]-1, (2) = YP[5]-1, (3) = YP[6]-1}, attributes = [coords = cartesian]), Vector(3, {(1) = YP[1]+1/2-2*((1...."

Any help would be much appreciated!

Hi all

I have this type of generalized Fourier serie: a0+Sum(an*cos(n*Pi*ln(x)/ln(2))+bn*sin(n*Pi*ln(x)/ln(2)), n = 1 .. N)

The coefficients I calculated and the results seems correct. However, the amplitude of Fourier expansion is twice the amplitude of the function.

Find in the attached file my maple code.


Hi, I am very new to Maple and do therefore probably propose a very simple question, so I would kindly ask you to excuse me in advance.

Basically I want so solve a simple and discrete game by comparing expected utility payoffs. There are only three states of the world (0,1,2) and I must determine for what cost-price-ratio what quantitiy is chosen from the same set (0,1,2).

Mathematically it's easy and I solved it, but Maple does not let me present my findings in a way I would like, as presented in my picture (preview from LaTex):

To achieve this I would have to get all w over p and then define it as z (cost-price-ratio). But when I try solving for w/p or respectively z doesn’t work. Additionally, when I try to apply some rearrangements manually (like multiply by 1/p in the first inequality) it doesn't work either, I just receive a '*' in front of round brackets with my equation inside.

So, is there a possibilty to do these simple rearrangement of my inequalities in Maple? And is it possible to aggregate the solutions in the same way as I pictured it for my LaTeX code?

Thank you very much!


I am currently trying to plot the function: sqrt(x^2+y^2-c), where x & y are variables in cartesian coordinates, and c is an arbitrary real constant. I came across a jagged edged plot when I asked maple to plot:

sqrt(x^2+y^2-c)       *** Code below ***


So I entered in the "Re" command to take the real part:


This smoothed the plot out at the ring x^2+y^2=1, but however also added what looks like a solid disc as well. Is there a way I can plot the function correctly without this disc in the middle?


Can someone help with the simplification of the result of this code? I am sure the "qs" in the final result should not appear.

Thanking you in anticipation of your positive responses

P:=sum(a[k]*x^k, k=0..2):
assume(alpha>0,alpha <= 1):
e1:=simplify(eval(P, x=q))=y[n]:
var:=seq(a[i], i=0..2):

Cc:=eval(<var>, solve(eval({M}),{var}) ):
for i from 1 to 3 do
end do:
E:=collect(Cf, [y[n], f[n], f[n+1]], recursive):
#y[n+1]=collect(simplify(simplify(expand(eval(Cf,x=q+h^alpha)),size)), [y[n],f[n],f[n+1]], factor);
y[n+1]=simplify(eval(Cf, x=q+h^alpha)):
collect(%, [y[n], f[n], f[n+1]], recursive);


In the application whose link is below, an error message results when I right click the fsolve command and select explore.

I would like to explore changes to several of the parameters in the equations named "sys", especially the value of Qoutflow. Can this be done and, If so, how can the solved values, Q1, Q2, Q3, and H be graphed as the slider values of individual parameters values are modified?

I am attempting to reproduce the results claimed by for a band pass filter.

I have checked the circuit specification and found no errors.

Am I expecting too much or am I doing something wrong?

## Filter Requirements for Band-Pass, 4th order Butterworth
## Specifications: Optimize for Power, +Vs= 5, -Vs= -5
## Gain: 10 dB
## Passband: -3dB at 2kHz
## Stopband: -40dB at 40kHz
## Component Tolerances: Capacitor = 5%; Resistor = 1%; Inductor = 5%; Op Amp GBW = 20%

with(Syrup); Version;

ckt := "*60 kHz Band Pass Filter  \n\
vin 1   0 \n\
R1A 1   2 165k \n\
R1B 5   7 169k \n\
R2A 2   0 976 \n\
R2B 7   0 1k \n\
R3A 6   0 221 \n\
R3B 11  0 226 \n\
R4A 5   6 12.7k \n\
R4B 10 11 12.7k \n\
R5A 4   3 97.6k \n\
R5B 9   8 100k \n\
R98 3   0 1e9 \n\
R99 8   0 1e9 \n\
C1A 2   4 270pF \n\
C1B 7   9 270pF \n\
C2A 2   3 270pF \n\
C2B 7   8 270pF \n\
* \n\
X1A 6  3 5  NonIdealOpAmp \n\
X1B 11 8 10 NonIdealOpAmp \n\
.include Library:-NonIdealOpAmp \n\

volts, others := Solve(ckt, 'ac', 'returnall');
gain := eval(v[10]/vin, volts);
H := subs({A=80000, f0=15*10^6, Ro=100}, gain);
tf := evalf(H);
sys := TransferFunction(tf);


An error message during opening a Maple file is seen:

I put the file link in below. The Maple file has been saved as Maple 2016.

I will be grateful if you can recover the file. Thanks

First 12 13 14 15 16 17 18 Last Page 14 of 60