You have a set of equation SysEq which are linear in the variables dq.  The coefficient matrix is obtained through
J := LinearAlgebra:-GenerateMatrix(SysEq, dq)[1];

In your case J is an 8x11 matrix.  To display it, do:
evalm(J);

@assma Here is the code to do that calculation.  I assume that your 6.28 is actually meant to be 2π.  Change it to anything else as needed.

Download mw.mw

Download linearfit.mw

An object of the form [u₁, u₂, ..., u_n] is called a list in Maple. If that list is named X, then X[i] is the ith entry of that list. Each of the u_i can itself be a list. If every u_i is a list, then we say X is a list of lists. In that case the notation X[i][j] indicates the jth element of the ith list in X.

The argument J of your proc is expected to be a list of list.

• The first line of the proc creates a list L from the list J as follows. Let's say the ith entry of L is [a,b,c]. Then the ith entry of L is the two-element list
      [a, (b+c*I)/a + 50*(1+I)/abs(J[1][2])]
  where I is Maple's notation for sqrt(-1), and abs() is the absolute value.
  Note: You would want J[1][2] to be nonzero, otherwise you will be dividing by zero.  In the example in the last line of your post is J[1][2] zero.  That's bad.
• The second line of the proc defines a vector R whose ith entry equals the ith entry in L.
• The next line says that:
      T := abs(L[1][3]);
      r := L[1][4];
  But L[1][4]  makes no sense since it attempts to pick the 4th entry of the list L[1] which is a list of two entries; there is no 4th entry.  Check for typos.

The rest of the code should be self-evident.

In addition to the ways pointed out by Robert Lopez, here are four other methods to calculate the dot product without complex conjugation:

1.  LinearAlgebra:-DotProduct(<a,b>, <c,d>, conjugate=false);
2. LinearAlgebra:-DotProduct(<a,b>, <c,d>) assuming real;
3. <a,b>^%T . <c,d>;
4. <a,b>^+ . <c,d>;

My preferred method is #4 since it requires the least amount of typing.

@Earl If all you want is the final graphics that you have shown in your worksheet, then it can be done through a direct evaluation of parameter ranges.  This produces better-looking graphics, without the need for "cheating" with a hi-res grid.

Here are the details: mw2.mw
Edit: removed a couple of lines of unused code from an earlier version

Are you sure that's Maple?  To me it looks like a mupad notebook.

How do I know that?

Rename Bugged.mw to Bugged.mw.zip , unzip it, then examine the contents.

• You don't need Maple to see that { θ(r,z) ≡ 0 and σ(r,z)  ≡ 0 } is the solution of your equations. Perhaps you meant something else?
• Although you label your equations as PDEs, they are not PDEs.  They are ODEs because they involve derivatives with respect to r only.
• As to Maple's error message, you need to change
  pdsolve(PDE1, PDE2, IBC, numeric);
  to
  pdsolve({PDE1, PDE2}, IBC, numeric);
  but that's not really needed if all you have are ODEs.

Your ibc consist of three boundary conditions but no initial condition.  You don't mean that, do you?  In the following I will ignore the first of the three conditions. It turns out at the end that the first conditions is implied by the other two.

The argument of the complexplot is malformed.  Here is the corrected version.

restart;
with(plots):
z := polar(1.05, (1/10)*Pi);
p1 := polarplot(1, color = grey, axis[radial] = [color = "Blue"]):
p2 := complexplot([seq(evalc(z)^n, n = 1..21)],
    style=point, symbol=solidcircle, symbolsize=15, color=red):
display([p1,p2], scaling=constrained);

Here is a rush answer to a rush question I don't expect it to make much sense to you if this is your first contact with Maple.

restart;
G := (y,v) -> [v, g/H*(mu__B + mu__C - sqrt(1 + v^2))];    # v stands for dy/dx
de := diff~([y(x), v(x)], x)[] = G(y(x),v(x))[];
ic := y(0)=0, v(0)=0;
params := g=1, H=1, mu__B=1, mu__C=1;
sys := eval([de,ic], [params]);
dsol := dsolve(sys, numeric, method=rkf45);
plots:-odeplot(dsol, [[x,y(x)],[x,v(x)]], x=0..5);

Here are my thoughts regarding your questions.

• If you live in the US, you may consider taking a remedial math course in your local community college.  These don't cost very much, and I think will be more effective than trying to learn the material on your own.  Having a teacher and classmates whom you can talk to can be very helpful.
• I don't know of a product that you can buy to test your mathematical ability, but most universities administer a Math Placement Test to entering students to determine their level of mathematical preparation, and then recommend a suitable course within the mathematical hierarchy to begin one's education.
• You should give some thought as to your reasons for wanting to take a college algebra course.  If it is for the sake of learning some new material, that's fine.  But if you do that as a stepping stone toward a further goal, you should really talk to someone who knows about such matters and seek expert advice before you invest your time, money, and effort toward that goal.

@das1404 Kitonum has already answered your question for pyramids with triangular and square bases. The worksheet pyramid.mw shows how to construct and plot pyramids having n-gons for their bases and the altitudes of whose lateral faces are given.  See if it is of use to you.

Download mw.mw