Maple 2016 Questions and Posts

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

Dear all,

Greeting!

I am a new user of Maple. I want to perform a simple (to me, it is very difficult) integration  defined as follows 

range from 0 to omega (frequency). alpha^2F (omega) is constant function with set of values (already calculated) for the corresponding frequency. I have calculated the frequencies ranging from 54 to 900 cm-1. Suppose I have alpha^2F(omega)=0, 0.5,0.6,0.7......0.1 for omega=58, 80, 110, 190,.....800, how can I perform this integration  in Maple? Please help me how can I cope with this problem.

Thanks a lot.

Best Regards,

 

I would like to animate the motion of a bicycle racer on a classic velodrome track i.e. one with varied vertical and horizontal curvatures along its length.

Is there a source which explains the math expressions which model the shape of such a track?

Hi

I have the values of of a function A(x,y,z) in 3d cartesian coordinates as [x[1],y[1],z[1],A(x[1],y[1],z[1])], [x[2],y[2],z[2],A(x[2],y[2],z[2])], [x[i],y[i],z[i],A(x[i],y[i],z[i])],etc...where i vary from 1 to 300 (or higher).

How to plot A(x[i],y[i],z[i]) in 3d.

Thanks

How can I plot functions Vc=(0.5+t)^n

with t=z/h, 

Hi there,

I have difficulties in solving the first partial derivatives dw/db and dw/dvarphi of this equation with its constraint:

w := exp(exp(x*b)*(r-1)/(1+varphi*exp(x*b))) where ln(r) = varphi*(exp(x*b))(r-1)/(1+varphi*exp(x*b))-1

Please help.

Regards,

Sarni Berliana

Hello, 

I am fairly new to using the Maple software, so I apologize if my question is completely idiotic. Apologies, also, because I could not manage to enter my code as code. When I pressed the button it made the whole text as a code. 

I run the following code to seek -if there are any- analytic solutions for the following differential equation.

odeplus := (r^2+L^2)^(5/2)*(diff(f(r), `$`(r, 2)))+((15/4)*r*(r^2+L^2)^(1/2)+3*(r^2+L^2)^(5/2)/r)*(diff(f(r), r))+M^2*f(r)/(r^2+L^2)^(5/2)-((5/2)*((r^2+L^2)^(1/2))(l-1)+(55/64)*r^2/(r^2+L^2)^(3/2)+(r^2+L^2)^(5/2)*(l^2+3*l+3/2)/r^2)*f(r)+(((r^2+L^2)^(1/2))(5+(5/2)*l)+(5/8)*r^2/(r^2+L^2)^(3/2)-(r^2+L^2)^(5/2)*(3/2+l)/r^2)*f(r) = 0

and then I do 

dsolve(odeplus, f(r))

The solutions that Maple returns is given in terms of DESol. Could anyone try and break it down for me? What is this telling me and if I can indeed from the output obtain analytic solutions? Is this some sort of operator acting on something? 

Thank you in advance. 

`~`[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

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