MaplePrimes Questions

Hi.

I´m making a work sheet where I use the VectorCalculus package to evaluate surface of a plane.

When I try to evaluate a regular tripple integral after loading the VectorCalculus package I get the following error:

Error, (in VectorCalculus:-int) the domain must be an equation with a list of names on the left hand side

If I use the task menu to remove the package it works just fine, however I want it all as executable syntax within my worksheet so I tried "unwith(VectorCalculus)" but the package wont be removed by using this command.

How can I go about solving this issue?

https://i.gyazo.com/0f56ebe62bc54c7db303ab2ae05a601c.png

Hi! 

Tried to solve the PDE below (q and p are time-dependent variabels, q(t),p(t)):

pde := diff(rho(t, q, p), t) = -(diff(rho(t, q, p), q))*p+(diff(rho(t, q, p), p))*(2*q+2);
          

pdsolve(pde, rho(t, q, p));
           

And got the answer: 

rho(t, q, p) = _F1(p^2+2*q^2+4*q, -(1/2)*sqrt(2)*arctan((q+1)*sqrt(2)*(1/sqrt(p^2)))+t)

But I'm not sure how to interpret the result. I understand that  _F1 is an arbitrary function, but then I get confused with the comma? I thought that I'd get a function of q and p, where they depend on t. 

Best regards
Sannis

 

I'd like ot make a 3d graph that is log scaled on at least one of the axis. So far I haven't found a way of doing this that gives a graph that I genuinely like.

The following worksheet shows two ways of making the graph- the first generates the lines on the surface in a very bunched way, the second typesets the tickmarks in a very ugly way.

How can I get a graph with well placed lines and nicely typeset tickmarks?

How do other people make 3d logplots?

 

 

thing := x*log(y)*y^2*sin(1/y)^2;

x*ln(y)*y^2*sin(1/y)^2

 

 

 

``


 

Download logplot3d.mw

 

 

 

Hello all,

I have a question regarding printing to PDF. I am using Maple 2016.1 on Mac OS Sierra. When I choose print and use "Open PDF in Preview", I get to see something like this:

As you can see, the fonts are ugly and not anti-aliased at all (and it makes no difference whether I select that option explicitly in Maple preferences or not).
I've also tried Maple 2015, and it gives the same ugly result.

As a comparison, here is an example of a similar print of the same document that I've made in 2015:

Here, the font looks much better, properly aliased this time.
I also get this result when using Maple 18 on Sierra.

I am wondering: do other people also get this ugly result? In that case, it could indicate an issue with Maple 201X and Mac OS Sierra. Unfortunately, I no longer have Mac OS X El Capitan to compare...

P.s.: If someone wishes to try: just create some text input, choose Print, Open PDF in Preview, and then zoom in on the document.

Many thanks for your reply.

Regards,

Franky

 

$$\textbf{x}' = \begin{bmatrix} -4 & -2 \\ 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix}+\begin{bmatrix} -t \\ -2t-1 \end{bmatrix},\textbf{x}(0)=\begin{bmatrix} 3 \\ -5 \end{bmatrix}$$

As I know firstly, when the matrix is denoted by $A$, we must compute $e^{At}$ by diagonalizing $A$: if $A=PDP^{-1}$ for a diagonal $D$ then $e^{At} = P e^{Dt} P^{-1}$ where $e^{Dt}$ is a diagonal matrix with $(e^{Dt})_{ii} = e^{D_{ii} t}$...
 
How can I write The Maple code? maple.stackexchange)

restart: with(LinearAlgebra):

A := Matrix(2,2,[-4,-2,3,1]);

....

Hello people in mapleprimes,

I have an expression, which apparently can be factored with (beta-1)

e1 := -(beta-1)*L*s*lambda*Omega^3+(beta-1)*L*s*g^k*epsilon*(T*lambda-T+1)*Omega^2+(beta-1)*L*s*(T+lambda-1)*Omega-(beta-1)*L*s*g^k*T*epsilon*lambda;

I want this expresson factored with (beta-1) but keeping other terms the same as

e2:=-L*s*lambda*Omega^3+L*s*g^k*epsilon*(T*lambda-T+1)*Omega^2+L*s*(T+lambda-1)*Omega-L*s*g^k*T*epsilon*lambda;

Is this possible?

I hope you will help me for this.

Thanks in advance.

taro

question_q1_11_28_2016.mw

 

 

How does one retrieve document properties of some target file.

I tried ..

with(DocumentTools):
Retrieve("c:\\Users\laptop22\Documents\Start2Test.mw", "GetDocumentProperty('all')")

however that ended in error

***************edit added****************
From the help pages

Why Apply Document Properties?

The Document Properties feature allows you to record data associated with your document, such as the author or date of creation. This data is not displayed in your document but could be read by an external processing tool.

It does say read by external processing tool, but Maple has the command Retrieve so I would think it is also possible within Maple, maybe not with Retrieve since it is specifically looking for labels.  But perhaps there is another way?

Is it possible to complie maplets into external java applications?

If I go to the menu under file and open.  Or similarily CRTL-o opens the file query dialog box. 

Can I do this crtl-o programmatically?

hi...why solve for this equation dos not answer?

thanks

4.mw
 

restart; dsys3 := {diff(w(x), x, x, x, x, x, x)+diff(w(x), x, x, x, x)+diff(w(x), x, x)+(1-2)*w(x) = -90, w(0) = 0, w(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(1) = 0}; dsol5 := dsolve(dsys3, numeric, abserr = .1, output = array([.5]))

array( 1 .. 2, 1 .. 1, [( 1, 1 ) = (array( 1 .. 7, [( 1 ) = (x), ( 2 ) = (w(x)), ( 3 ) = (diff(w(x), x)), ( 4 ) = (diff(diff(w(x), x), x)), ( 5 ) = (diff(diff(diff(w(x), x), x), x)), ( 6 ) = (diff(diff(diff(diff(w(x), x), x), x), x)), ( 7 ) = (diff(diff(diff(diff(diff(w(x), x), x), x), x), x))  ] )), ( 2, 1 ) = (array( 1 .. 1, 1 .. 7, [( 1, 7 ) = (HFloat(-1.3899459757465982e-7)), ( 1, 3 ) = (HFloat(4.5022670883498417e-8)), ( 1, 1 ) = (.5), ( 1, 6 ) = (HFloat(2.2858770405958895)), ( 1, 5 ) = (HFloat(2.6615438731474126e-8)), ( 1, 4 ) = (HFloat(-0.04747952956114616)), ( 1, 2 ) = (HFloat(0.0019672907400671725))  ] ))  ] )

(1)

"restart;w(x):=C1* (sinh(x))+C2* (cosh(x))+C3 *(sin(x))+C4 *(cos(x))+C5 *(sin(x))+C6 *(cos(x))+90"

proc (x) options operator, arrow; C1*sinh(x)+C2*cosh(x)+C3*sin(x)+C4*cos(x)+C5*sin(x)+C6*cos(x)+90 end proc

(2)

A1 := evalf(subs(x = 0, w(x)))

90.+1.*C2+1.*C4+1.*C6

(3)

A2 := evalf(subs(x = 1, w(x)))

1.175201194*C1+1.543080635*C2+.8414709848*C3+.5403023059*C4+.8414709848*C5+.5403023059*C6+90.

(4)

A3 := evalf(subs(x = 0, diff(w(x), x)))

1.*C1+1.*C3+1.*C5

(5)

A4 := evalf(subs(x = 1, diff(w(x), x)))

1.543080635*C1+1.175201194*C2+.5403023059*C3-.8414709848*C4+.5403023059*C5-.8414709848*C6

(6)

A5 := evalf(subs(x = 0, diff(w(x), x, x, x)))

1.*C1-1.*C3-1.*C5

(7)

A6 := evalf(subs(x = 1, diff(w(x), x, x, x)))

1.543080635*C1+1.175201194*C2-.5403023059*C3+.8414709848*C4-.5403023059*C5+.8414709848*C6

(8)

solve({A1, A2, A3, A4, A5, A6}, {C1, C2, C3, C4, C5, C6})

``

solve*{A5, A6, C1, C2, C3, C4, C5, C6, 1.*C2+1.*C4+1.*C6, 1.*C2*upsilon^2-1.*C4*kappa^2-1.*C6*varsigma^2, C1*sinh(upsilon)+C2*cosh(upsilon)+C3*sin(kappa)+C4*cos(kappa)+C5*sin(varsigma)+C6*cos(varsigma), C1*upsilon^2*sinh(upsilon)+C2*upsilon^2*cosh(upsilon)-1.*C3*kappa^2*sin(kappa)-1.*C4*kappa^2*cos(kappa)-1.*C5*varsigma^2*sin(varsigma)-1.*C6*varsigma^2*cos(varsigma)}

(9)

``

``

``


 

Download 4.mw

 

hi every body...

general solution of six order differential equation for example following equation

diff(w(x), x, x, x, x, x, x)+A*(diff(w(x), x, x, x, x))+B*(diff(w(x), x, x))+(-chi*omega^2+C)*w(x) = 0

is 

w := C1*sinh(upsilon*x)+C2*cosh(upsilon*x)+C3*sin(kappa*x)+C4*cos(kappa*x)+C5*sin(varsigma*x)+C6*cos(varsigma*x)

??

OR

w := C1*(cosh(upsilon*x)-sinh(upsilon*x))+C2*(cosh(upsilon*x)+sinh(upsilon*x))+C3*(cosh(kappa*x)-sinh(kappa*x))+C4*(cosh(kappa*x)+sinh(kappa*x))+C5*(cosh(varsigma*x)-sinh(varsigma*x))+C6*(cosh(varsigma*x)+sinh(varsigma*x))

or another form? is correct both of them or no??

please see maple attaced file.

please help me

thanks...

3.mw
 

restart; dsys3 := diff(w(x), x, x, x, x, x, x)+A*(diff(w(x), x, x, x, x))+B*(diff(w(x), x, x))+(-chi*omega^2+C)*w(x) = 0

diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x)+A*(diff(diff(diff(diff(w(x), x), x), x), x))+B*(diff(diff(w(x), x), x))+(-chi*omega^2+C)*w(x) = 0

(1)

dsol5 := dsolve(dsys3):

H := subs(36*B*A+108*chi*omega^2-108*C-8*A^3+12*sqrt(-12*A^3*chi*omega^2+81*chi^2*omega^4+54*A*B*chi*omega^2+12*A^3*C-3*A^2*B^2-162*C*chi*omega^2-54*A*B*C+12*B^3+81*C^2) = E, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)-4*A^2-4*A*E^(1/3)-E^(2/3)+12*B = F, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)+4*A^2+4*A*E^(1/3)+E^(2/3)-12*B = G, 4*A^2-2*A*E^(1/3)+E^(2/3)-12*B = S, rhs(dsol5))

 

_C1*exp(-(1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+_C2*exp((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+_C3*exp(-(1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+_C4*exp((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+_C5*exp(-(1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))+_C6*exp((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))

(2)

convert(H, trig)

_C1*(cosh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))-sinh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3)))+_C2*(cosh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3))+sinh((1/6)*3^(1/2)*(E^(1/3)*F)^(1/2)*x/E^(1/3)))+_C3*(cosh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))-sinh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3)))+_C4*(cosh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3))+sinh((1/6)*(-3*E^(1/3)*G)^(1/2)*x/E^(1/3)))+_C5*(cosh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))-sinh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3)))+_C6*(cosh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3))+sinh((1/6)*6^(1/2)*(E^(1/3)*S)^(1/2)*x/E^(1/3)))

(3)

NULL

``


 

Download 3.mw

 

 

i wrote a procedure to  find some functions but at the end  of the procedure gives unexpected string error. i didn't find any way out.

Best regards. 

Download procedureA.mws

How would I programmatically open a maple worksheet?

I thought this would work but it brought up a -1

ssystem("c:\\Users\laptop22\Documents\Start2Test.mw")

 

I am trying to solve the wave equation in polar coordinates.  The initial condition on u is given by f(r,theta) and the initial condition on u_t is zero.  The weight function is w(r).  I am not sure why it will not evaluate this as I know the solution remains finite on the domain (the unit disk).  Here is the code: 
 

Wave Equation in Polar Coordinates

restart; with(plots); addcoords(u_cylindrical, [u, r, theta], [r*cos(theta), r*sin(theta), u])

Example:

rho := 1; 1; c := 1; 1; w := proc (r) options operator, arrow; r end proc

1

 

1

 

proc (r) options operator, arrow; r end proc

(1)

f := proc (r, theta) options operator, arrow; 2.5*(1-r^2)*r*sin(theta) end proc

proc (r, theta) options operator, arrow; 2.5*(1-r^2)*r*sin(theta) end proc

(2)

assume('n', integer); 1; assume('m', integer)

lambda := proc (n, m) options operator, arrow; BesselJZeros(n, m)^2/rho^2 end proc;

proc (n, m) options operator, arrow; BesselJZeros(n, m)^2/rho^2 end proc

(3)

c0 := proc (m) options operator, arrow; (int(int(f(r, theta)*BesselJ(0, sqrt(lambda(0, m))*r)*w(r), theta = -Pi .. Pi), r = 0 .. rho))/(int(int(BesselJ(0, sqrt(lambda(0, m))*r)^2*w(r), theta = -Pi .. Pi), r = 0 .. rho)) end proc; 1; a := proc (n, m) options operator, arrow; (int(int(f(r, theta)*BesselJ(n, sqrt(lambda(n, m))*r)*cos(n*theta)*w(r), theta = -Pi .. Pi), r = 0 .. rho))/(int(int(BesselJ(n, sqrt(lambda(n, m))*r)^2*cos(n*theta)^2*w(r), theta = -Pi .. Pi), r = 0 .. rho)) end proc; 1; b := proc (n, m) options operator, arrow; (int(int(f(r, theta)*BesselJ(n, sqrt(lambda(n, m))*r)*sin(n*theta)*w(r), theta = -Pi .. Pi), r = 0 .. rho))/(int(int(BesselJ(n, sqrt(lambda(n, m))*r)^2*sin(n*theta)^2*w(r), theta = -Pi .. Pi), r = 0 .. rho)) end proc

proc (m) options operator, arrow; (int(int(f(r, theta)*BesselJ(0, sqrt(lambda(0, m))*r)*w(r), theta = -Pi .. Pi), r = 0 .. rho))/(int(int(BesselJ(0, sqrt(lambda(0, m))*r)^2*w(r), theta = -Pi .. Pi), r = 0 .. rho)) end proc

 

proc (n, m) options operator, arrow; (int(int(f(r, theta)*BesselJ(n, sqrt(lambda(n, m))*r)*cos(n*theta)*w(r), theta = -Pi .. Pi), r = 0 .. rho))/(int(int(BesselJ(n, sqrt(lambda(n, m))*r)^2*cos(n*theta)^2*w(r), theta = -Pi .. Pi), r = 0 .. rho)) end proc

 

proc (n, m) options operator, arrow; (int(int(f(r, theta)*BesselJ(n, sqrt(lambda(n, m))*r)*sin(n*theta)*w(r), theta = -Pi .. Pi), r = 0 .. rho))/(int(int(BesselJ(n, sqrt(lambda(n, m))*r)^2*sin(n*theta)^2*w(r), theta = -Pi .. Pi), r = 0 .. rho)) end proc

(4)

u := proc (n, m, r, theta, t) options operator, arrow; sum(BesselJ(0, sqrt(lambda(0, j))*r)*c0(j)*cos(sqrt(lambda(0, j))*c*t), j = 1 .. m)+sum(sum(BesselJ(i, sqrt(lambda(i, j))*r)*(a(i, j)*cos(i*theta)+b(i, j)*sin(i*theta))*cos(sqrt(lambda(i, j))*c*t), j = 1 .. m), i = 1 .. n) end proc

proc (n, m, r, theta, t) options operator, arrow; sum(BesselJ(0, sqrt(lambda(0, j))*r)*c0(j)*cos(sqrt(lambda(0, j))*c*t), j = 1 .. m)+sum(sum(BesselJ(i, sqrt(lambda(i, j))*r)*(a(i, j)*cos(i*theta)+b(i, j)*sin(i*theta))*cos(sqrt(lambda(i, j))*c*t), j = 1 .. m), i = 1 .. n) end proc

(5)

soln := evalf(u(3, 3, r, theta, t));

(Float(infinity)+Float(infinity)*I)*BesselJ(1., 3.831705970*r)*sin(theta)*cos(3.831705970*t)+(Float(infinity)+Float(infinity)*I)*BesselJ(1., 7.015586670*r)*sin(theta)*cos(7.015586670*t)+(Float(infinity)+Float(infinity)*I)*BesselJ(1., 10.17346814*r)*sin(theta)*cos(10.17346814*t)-0.3676566232e-9*BesselJ(2., 5.135622302*r)*sin(2.*theta)*cos(5.135622302*t)-0.1879633956e-10*BesselJ(2., 8.417244140*r)*sin(2.*theta)*cos(8.417244140*t)-0.5146823927e-10*BesselJ(2., 11.61984117*r)*sin(2.*theta)*cos(11.61984117*t)+(Float(infinity)+Float(infinity)*I)*BesselJ(3., 6.380161896*r)*sin(3.*theta)*cos(6.380161896*t)+(Float(infinity)+Float(infinity)*I)*BesselJ(3., 9.761023130*r)*sin(3.*theta)*cos(9.761023130*t)+(Float(infinity)+Float(infinity)*I)*BesselJ(3., 13.01520072*r)*sin(3.*theta)*cos(13.01520072*t)

(6)

plot3d(soln, r = 0 .. 1, theta = 0 .. 2*Pi, coords = u_cylindrical, axes = boxed)

NULL

NULL


 

Download Section_6.3.mw

Any assistance would be greatly appreciated. 

Hallo

I'm trying to plot several periods of this 2π-periodic function f (x) = 3x, x ∈]-π; π] with the following code which I got from an older post.

However, when using uneven multipla of PI as x it just gives me a verticle line. Can anyone shed some light to this or perhaps give a better solution?

Thanks in advance

Best regards

Thomas

 

 

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