Rouben Rostamian

MaplePrimes Activity


These are answers submitted by Rouben Rostamian

Do you know how to do a phase portrait when the nullclines are straght lines?  The case of curved nullclines is no different.

The variable named soln in your worksheet contains the PDE's solution.  You may examine the numerical values of the variables or plot them.  See the help page on pdsolve/numeric for details.  Here are a few examples:

soln:-plot(phi(y,t), t=1);

soln:-plot(u(y,t), t=1);

soln:-plot(u(y,t), t=0..1, y=1);

soln:-plot3d(u(y,t),t=0..1, y=0..1);

u_at_1 := soln:-value(u(y,t), t=1);
u_at_1(0.3);  # this produces the value of u(0.3, 1)

If x(t) = 2 + t + t^2, then x'(t) = 1 + 2*t.  Certainly that isn't equal to y(t) = 1 + 2t + 0.5t^2.  Did you mean to write something else?

Need to be patient when executing the code below; it takes several minutes to complete. There must be ways to speed it up but I haven't bothered.

restart;
with(plots):
u := Heaviside;
f := t -> u(t) - u(t-2);
g := t -> t*u(t) - (t-4)*u(t-4);
h := unapply(int(f(t-q)*g(q), q=-10..t), t);
frames := seq(display([
    plot(g(s), s=-10..10, color=blue),
    plot(f(t-s), s=-10..10, color=blue),
    plot(h(s), s=-10..t, color=red, thickness=3)
]), t=-7..9, 0.4);
display([frames], insequence=true);

I have not looked at the details of Maple's series method for solving ODEs, so there may be a way to do what you want.  Consult Maple's documentation on that topic.  My preliminary assessment is that the series method expresses the solution as an infinite sum of nonnegative powers of the independent variable.  Your two differential equations have eta and r in the denominators.  Maple determines, therefore, that the solution cannot be expressed in a series with nonnegative powers.

 

The transform() function used in Example 1 is defined in the plottools package.  Load it with

with(plottools);

and all will be right.

Just looking through you code, I see the following symbols which are undefined:

dsnumsort()

C1

V1

C2

V2

What do you mean by these?

for i in [3,-2,5,12] do
    print(i^2);
end do;

It's hard to give concrete advice without seeing what you have on your Maple worksheet.  See if placing your cursor at the end of the line and pressing the F3 key helps.  If it doesn't, then post a sample worksheet in which you have pasted your homework problems.  Use the big green up-arrow to upload a worksheet.

 

There are too many variables involved here to tell.  It depends on how your operating system (not Maple) handles copying/pasting, and how your text editor receives a pasted copy.

My operating system is Linux, and my text editor is vi.  I just copied a block from a Maple worksheet and pasted into vi, and line breaks were preserved.

Sorry for not being able to offer a more useful explanation.

Load the LinearAlgebra package, then have a look at the GenerateMatrix() function.  The help page provides several examples which should interest you.

 Will this do?

sol := y(x) = (sinh(w) + ln(w))*x;

y(x) = (sinh(w)+ln(w))*x

                             (1)

C := coeff(rhs(sol), x) = c;

sinh(w)+ln(w) = c

                                              (2)

subs(C, sol);

y(x) = c*x

                                                                               (3)

As Thomas Richard has pointed out, the images of the equations that you have posted are hard to read.  Well, actually I don't need to read them because I recognize them as the equations of an Euler beam.  If that is so, then the third equation, M(x) = ..., is incorrect.  Fix that first.

The solution of the beam equation generally will involve integrals of the load function q(x).  Your answer does not involve integrals and actually shows q(x) as a plain q.  That answer is correct if q is a constant, that is, the load distribution is uniform.

So here is what you need to do:

  1. Using Maple to solve the equation with a constant q is an overkill.  You should be able to solve it with paper and pencil and hardly any effort, with very elementary calculus.  Try that first in order to understand what is going on. 
  2. Only after you are done with step 1, see if you can solve the problem in Maple.  Here you will need what you learned in step1, so jumping into Maple without having done that step is not productive.
  3. If you have difficulty with finishing your Maple work, post your incomplete Maple worksheet here, and tell us where you need help.

I could show you my solution, but I am afraid that won't help you understand the material.  I want you to learn the subject well, so that the bridge you build won't collapse when I drive over it.

 

 

 

I needed to do something quite similar some time ago.  See: Math 481: Project 1

I ran into the problem that you have encountered, so I took a roundabout route.  I exported the left and the right panels separately as animated gifs.  Then split each gif into individual frames, attached the resulting frames pairwise, then merged the resulting pairs into a new animated gif.  That's what you see in the web page noted above.

Linux provides all the necessary tools for those operations, but their use requires a certain level of familiarity with command-line tools.  If you have access to Linux and need help with those commands, drop me a line.

 

 

What was the plotting command?  It's difficult to be specific without knowing the details.

Did you, perhaps, specify transparency?  EPS is not designed to handle transparency.

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