MaplePrimes Questions

 

Let  

f := beta/(2*sigma*GAMMA(1/beta))*exp(-(abs(x-mu)/sigma)^beta);

where mu::real, beta > 0, sigma > 0.
How can we obtain the expression of F?

F := int(f, x=-infinity..s)


Reverse problem (a priori simpler):
It's known that 

F := 1/2+signum(x-mu)/(2*GAMMA(1/beta))*(GAMMA(1/beta)-GAMMA(1/beta, abs((x-mu)/sigma)^beta))

How can we check that diff(F, x)=f?
Even with the assumptions on beta, mu and sigma and additional assumptions x>0 or x<0, I can't verify that diff(F, x)=f.

 

Hello, dear members! I try to solve the 1-D Wave Equation with initial and boundary conditions. And I have a problem when I'm trying to find the coeffs of Fourier series, that they depend on initial conditions. This is my code for Maple:
 

restart;
with(PDETools);

# set the PDE, ic(initial conds) and bc (boundary conds)
pde := diff(u(x, t), t, t) = a^2*diff(u(x, t), x, x);
ic := u(x, 0) = 0, D[2](u)(x, 0) = psi(x);
bc := u(0, t) = 0, u(l, t) = 0;
psi := piecewise(0 <= x and x <= l/2, x, l/2 <= x and x <= l, l - x);

# using Fourier method for solving (I require use this methods)
res := pdsolve(pde, HINT = T(t)*X(x));

ode1 := op(1, op(1, op(2, res)));

ode2 := op(2, op(1, op(2, res)));               

ode2 := subs(_c[1] = -lambda, ode2);
              

# solve 2 ODE
# equation rely X(x)
dsolve({ode2, X(0) = 0}, X(x));

sin(sqrt(lambda)*l) = 0;

solve(%, lambda, allsolutions);

lambda := (Pi*n/l)^2;

X := (x, n) -> sin(Pi*n*x/l);


# equation rely T(t)
ode1 := subs(_c[1] = -lambda, ode1);

dsolve({%, T(0) = 0}, T(t));

T := (t, n) -> C1[n]*sin(Pi*n*a*t/l);

# write the general solutions
Un := (x, t, n) -> T(t, n)*X(x, n);

# find the coeffs series
simplify(subs(t = 0, diff(u(x, t), t)) = psi);

((2/l)*l/(Pi*n*a)*int(psi*X(x, n), x = 0 .. l) assuming (x < l))
simplify(%) assuming n::posint;
combine(%);
C1[n] := factor(%)

But I got it:



How to find this C1 coefficient and solve this equation? Maple doesn't work now. This command does not give the result.
I attached mws files, so pdeLR_11.mw is another code for solving, but it is not working so((! 

Maybe I use this command wrong, or step-function is not convenient for maple?

Any helpful advice would be very cool. I am grateful in advance!

https://drive.google.com/file/d/1VznAvxcpF3ME9MMBjfKKifsbrbOb9uSY/view?usp=sharing

https://drive.google.com/file/d/15D7BCRwHliYb2OseH81i81RjQP7NRFgS/view?usp=sharing

 

I know that the "rotate" can rotate image of a function, but we see that the coordinate axes don't change as much. For example:

with(plots):
with(plottools):
p:=plot(sin(x),x=0..2*Pi):
r := rotate(p, Pi/4):display(p, r)

Although someone seems to have asked a similar question a long time ago, it was far from what I needed.

https://www.mapleprimes.com/questions/97812-Flip-Plot-Exchange-X-And-Yaxes

What I want to do is rotate the axes and the image at the same time rather than just flip axes.  The schematic diagram is as follows.

How can the value of uu(.1, .1, .1)  as a number, and what is the error when drawing?

restart;
uu := proc (x, y, t) options operator, arrow; e^(.2*t)*(e^(-x)+e^(-y)) end proc;

evalf(uu(.1, .1, .1));
                              2.  
                             -----
                              0.08
                             e    
plot3d(uu(x, y, .1), x = 1 .. 2, y = 1 .. 2);
Warning, expecting only range variables [x, y] in expression e^.2e-1*(e^(-x)+e^(-y)) to be plotted but found name e

I have a pair of vectors, one containing x values, and the other containing the corresponding y values.

I plot them using: plot(x_vector, y_vector)

If I have another pair of vectors, x2_vector and y2_vector.

How to I plot them on the same graph so that I can compare them?

Recently I have wanted to add some questions/answers to "Favourites" . I added some posts a few years ago. Now I can't figure out how do do it. A good example is this evenings question on setting up a library. How to install a library on Maple? - MaplePrimes

The answer has useful links. And this is a particular topic I tend to have difficulty with.

On a Windows machine, I want to install a library in Maple? 

Could you please help me?

Thank you in advance.

Sincerely yours

Dear Collaboratory, as a former mathcad user I am trying to transfer slowly towards Maple. In the attached file I have a problem in solving the ODE numerical. I would appreciate it if someone would be willing to help me out. I tried to upload my maple file but I am not sure it is attached.

Hi,

I am trying to integrate a function from -infinity to infinity.  When I enter the integrate command into Maple, I just get the command back.  Does anyone know how to properly code the command for an indefinite integral?

I have attached the relevant worksheet.Indefinite_Integral.mw

When converting a list which includes lists to a set, duplicate entries are dropped.

However converting a list with vectors to a set, no duplicate entries are dropped.

Any explanation to that behaviour?

a := {Vector(2, [1, 0]), Vector(2, [2, 0])}

{Vector[column](%id = 36893490347685388884), Vector[column](%id = 36893490347685389004)}

(1)

b := [Vector(2, [1, 0]), Vector(2, [2, 0]), Vector(2, [1, 0])]

[Vector[column](%id = 36893490347747359308), Vector[column](%id = 36893490347747359428), Vector[column](%id = 36893490347747359548)]

(2)

c := convert(b, set)

{Vector[column](%id = 36893490347747359308), Vector[column](%id = 36893490347747359428), Vector[column](%id = 36893490347747359548)}

(3)

d := [[1, 0], [2, 0], [1, 0]]``

[[1, 0], [2, 0], [1, 0]]

(4)

e := convert(d, set)

{[1, 0], [2, 0]}

(5)

``

Download DuplicateEntries.mw

Hi,

Please can you give me a hand with numerical solving and visualising the integral equation with stochastic term B(t), using quadrature method ?

I had a look at the "stochastic" package by Sasha Cyganowski

Look forward to your help.

Thanks,

nada

I need help on maple code for solving both linear and non linear boudary condition for fractional order partial differential equation 

Hi,

I don't understand the number of solutions of my trigonometric equation if i work with solve command ( see maple file)

Ideas ?

TrigoSolve.mw

I cannot solve the equation. The problem is:

we have the integrals (1) and variable (2)
(1) F := (a1, b1) -> int(1/sqrt(1 + (-1)*b1^2*sin(teta)*sin(teta)), teta = 0 .. a1)

(2) Phi(Pi/2, teta) = 2*(F((Pi/2 - teta_l)/2, sqrt(2/(1 - sin(teta_l)))) - F1(Pi/4, sqrt(2/(1 - sin(teta_L)))))/sqrt(sin(teta_l) - 1)

After the solution for variable (2) I received: 

(-InverseJacobiAM(-Pi/4 + teta_l/2, 1/abs(cos(Pi/4 + teta_l/2))) - InverseJacobiAM(Pi/4, 1/abs(cos(Pi/4 + teta_l/2))))^2/(2*(sin(teta_l) - 1))

Next, I have the equation and (by the followed paper) should solve the equation respect to teta_l

M*B*(L/C)^2/G = 1/8*Phi(Pi/2, teta_l)^2

But I received just empty solution. The reference paper 10.1016/j.jmps.2020.104045

Can somebody recommend the way to solve the problem? 

Hey!

Student here, and I'm currently using a few year old laptop (amd a4-9125  2-core, 8gb ram) running latest stable ubuntu, and maple keeps crashing on me seemingly out of nowhere, even on very simple tasks, like copy-pasting equations and calculating integrals. This doesn't happend all the time, but when it does, it just shuts the program. I checked the logs and found Maple got this error message:
: free(): invalid next size (normal)
: Aborted (core dumped)

I checked a bit online, and it might be a memory issue.
Is my computer just too old for this program, or is it something fixable?

5 6 7 8 9 10 11 Last Page 7 of 2066