OK, here I am responding to my own post where I wrote that I had failed to produce the image of a cut-out sphere in Maple.  Now I have figured out how.  Here it is:

restart;
with(plots):  with(plottools):
clip := transform((x,y,z) -> `if`(x > H2 and z > H1, [H2,y,z], [x,y,z])):
R := 1; H1 := 1/3; H2 := 1/2;
display(clip(sphere(R, grid=[200,200])));


display(clip(sphere(R, grid=[200,200])),
    color=gold, style=surface, lightmodel=light4, axes=none, orientation=[60,75]);



This assumes that H2 is nonnegative.  H1, however, can be negative:

R := 1; H1 := -1/2; H2 := 0;
display(clip(sphere(R, grid=[200,200])));

Perhaps the method may be modified to allow for negative H2 but I haven't given much thought to it.


Your question gives the impression that you regard passing the exam as a goal.  That's a distorted view.  Bear in mind that:

• Passing the exam is not a goal.
• Your goal should be to learn the material.
• Passing an exam only certifies that you have learned the material.

Get your priorities straight.  Learn the material.  Then passing the exam will follow automatically.

Here is how to study:

for t in [course_topics] do
    if not (Do I understand topic t?) then
        study topic t until I understand it;
    end if
end do;

When you exit from that for-loop, you will be ready to pass the exam.

In short: Don't place the focus on passing the exam.  Place the focus on learning the material.

Carl, thanks for the details.  I wish that Maple offered more control on the placement of legends.  Your first example, shown below, would look better if the legend were placed inside the fourth quadrant where there is a lot of room.

I can imagine a syntax such as

legendstyle = [vertical, location = -5:-10]

which will position the legend at a distance equal to 5% of figure's width measured from the right edge, and a distance of 10% of figure's height measured from the  bottom.

To place the legend at the upper right corner,  we will do

legendstyle = [vertical, location = -0:+0]

@Kitonum  Thanks for the explanation.

@Kitonum How do you get your legend to look like that?   I like that.  Mine looks different:

@tomleslie I agree with your comments.  A had assumed that all _Zi's are positive (although I failed to state that explicitly), but as you have pointed out, that would produce only a subset of all possible solutions.

@tomleslie Why don't you like isolve()'s solution?  It looks good to me.

I don't know whether isolve()'s result is deterministic or it varies from one run to another.  When I tried, I obtained:

a;
                              _Z1
b;
                              _Z2
c;
                              _Z3
d;
                              _Z4
e;
                              _Z5
f;
                    2 + _Z3 + 2 _Z4 + 3 _Z6
g;
          2 _Z1 + 3 _Z2 + 2 _Z3 + _Z4 + 3 _Z5 + 4 _Z7
h;
   66640 - 5 _Z1 - 10 _Z2 - 25 _Z3 - 35 _Z4 - 25 _Z5 - 40 _Z6

      - 5 _Z7 - 10 _Z8
i;
                              _Z8

Thus, a, b, c, d, e, f and i are arbitrary, and f, g, h are given as above, all in terms of eight parameters _Zi, as you have noted.

Fortunately the only negative terms appear in h.  Therefore to get a solution among the positive integers, we take _Zi, i=1..8 as arbitrary integers subject to the constraint that

@Athar Shahabinejad This discussion gives the impression that you are just shooting in the dark, hoping that you will hit a target by accident.  That's not a very productive way of doing science.

You say that ph(t)+pc(t)+pa(t)+pgd(t)+prd(t)+prj(t)+pf(t)=1  for all t. That is not consistent with your system of differential equations, as Preben has demonstrated.  This shows that there is an error in the logic that has lead you to those equations.   Instead of asking "Should I change parameters?", your question should be "What is wrong with my logic?".

See if you can review the derivation of the equations, and find out what it is that leads you to the inconsistency.  Only after you have fixed that issue it makes sense to worry about evaluating the integral that you had asked in the beginning.

There is something called the Routh-Hurwitz stability criterion which may be relevant to your quesiton.  After you have produced the correct set of equations, I will see if the Routh-Hurwitz criterion provides useful information about it.

Just yesterday you asked for the solution of a very closely related problem, to which Carl Love gave a complete solution.  Can't you modify his answer to solve your current problem?  The purpose of these homework assignments is to exercise your brain. What's the point in asking others to do the thinking for you?

@javaneh0 Your copy/paste method is not a good way of communicating.  As I suggested in an eralier reply, upload your worksheet. 

In the fragments that you have shown, you have:

pf(t) = ...
int(1-pf(t), t = 0 .. infinity);

That's definitely incorrect, so it's not surprising that you are not getting an answer.  If you upload your worksheet, people will be able to point out where things are wrong, and how to fix it.

@Markiyan Hirnyk A more challenging problem is to produce a picture of the cut-out sphere, like the gray 3D picuture shown, in Maple.  I tried, and then had to give up.

I conjecture that the error is due to missing multiplication signs in your worksheet, however It is impossible to be sure based what you have posted.

Consider uploading your worksheet.  Use the large green up-arrow in the reply screen for that.

@tellap I can't tell whether you are asking for help with the math or with Maple.  Do you know how to determine the equation of the shock in terms of a and b?  Once you have that equation, you can ask Maple to plot it for you.  Maple can't do that on its own.

Your reference/textbook should tell you how to determine the shock speed.  Look it up.

@tellap Forget about the cases (i) through (vi) for now.  Take a simple case.  Suppose that the inital data is a when x < 0, and b when x > 0.   There are two cases:

Case (1): a < b    [example: a = -1, b = 2]

Case (2): a > b    [example: a = 3, b = -2]

Can you do the plots for cases (1) and (2)?  Unless you can do these, there is no point in attempting the more complex cases (i) through (vi).

@tellap After you remove the Magenta and Cyan plots, don't forget to remove the comma after the Blue plot.