Maple 2016 Questions and Posts

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

`~`[int](convert(convert(series(x^x, x), polynom), list), x = 0 .. 1)

Can this sequence (produced above in list form) be displayed as 1, -1/2^2, 1/3^3, -1/4^4, 1/5^5 -1/6^6 etc.

That is with the powers unevaluated.

Please describe the step-by-step application of the rules of differentiation which produce this derivative:

diff(a(x)^b(x), x) =        

a(x)^b(x)*((diff(b(x), x))*ln(a(x))+b(x)*(diff(a(x), x))/a(x));

Below are five subsindets commands.

I believe I understand the actions of B and C, but I fail to understand the actions, individually and taken together, of  E, F and G.

 

B := subsindets(u(i, j)^2*v(i, j)+u(i-1, j), 'specfunc(u)', proc (f) options operator, arrow; subsop(1 = op(1, f)+1, f) end proc);

C := subsindets(u(i, j)^2*v(i, j)+u(i-1, j), 'specfunc(anything, u)', proc (f) options operator, arrow; subsop(1 = op(1, f)+1, f) end proc);

E := subsindets(u(i, j)^2*v(i, j)+u(i-1, j), 'specfunc(symbol, u)', proc (f) options operator, arrow; subsop(1 = op(1, f)+1, f) end proc);

F := subsindets(u(i, j)^2*v(i, j)+u(i-1, j), 'specfunc(`+`, u)', proc (f) options operator, arrow; subsop(1 = op(1, f)+1, f) end proc);

G := subsindets(u(i, j)^2*v(i, j)+u(i-1, j), 'specfunc({`+`, symbol}, u)', proc (f) options operator, arrow; subsop(1 = op(1, f)+1, f) end proc);

Where can I find a thorough explanation of specfunc with examples?

I have learned that the eigenvectors of an solid object's Inertial Tensor are its principal axes and are an orthonormal set, however two of the eigenvectors in the cube in the uploaded worksheet are not orthogonal.

Where is my error?

CubePrincipalAxes.mw

I have defined a function, F, as

F:=(s)->fouriersin(f(r), r, s)

I would now like to plot that function.

plot(F(s), s=0..3)

How can I do that? Calls to plot don't work, as the "s" in the fouriersin definition of the function get replaced by the value I'm trying to plot.

 

 

 

Hi,

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)
   F.T.               
---------->         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,

Toby

 

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,

Toby

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
 

restart

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

(1)

NULL

NULL


 

Download maplerpimes.mw

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


 

``

``

restart

with(LinearAlgebra):

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])

(1)

``


 

Download Sooal.mw

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).
eq1:=diff(y(t),t)=-2*f(y(t),y(t))*B.A(t):
eq2:=diff(x(t),t)=2*(-1*B.Vector([1,1,1])+f(x(t),x(t))*B.y(t)-s(t)*f(y(t),y(t))*B.x(t)):
sys:=eq1,eq2;
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!
 

trig_interp3.mw

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.

Regards

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!

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