@Preben Alsholm 

To convert any procedure to an inert form, you can prepend % to the name. So your

df_dz[s][i,j]:=subs(D=DD,convert(df_dz[s][i,j],D));

could be

df_dz[s][i,j]:= subs(D= %D, convert(df_dz[s][i,j], D));

The benefit of doing it this way is that it can be converted back to active form with the value command.

@ger89

Here I'm only answering your question #4: <0,0,0,0> is a column vector of four zeros. So, in the line in question, Preben solves the homogenous system of linear equations whose coefficient matrix is A10, and he requests that the prefix p be used for the names of any free variables.

For more information on the angle-bracket notation for vectors and matrices, see ?LinearAlgebra,General,MVshortcut

@kevinmaple The arrow notation -> is an abbreviation allowed for procedures (usually one-liners) that contain only an expression, an expression sequence, or an if statement. So

CountUnique:= (L::list)-> nops({L[]}):

is essentially equivalent to

CountUnique:= proc(L::list) return nops({L[]}) end proc:

See ?operators,functional

It's possible to do what you want using the parse statement. However, there's almost always a better way. What's your ultimate goal? to generate a Cartesian product of sets or lists? or some other combinatorial object? These things can be done without using loops nested to arbitrary depth. Nonetheless, in the Answer below, I show how to do what you asked for.

@Preben Alsholm Yes, thanks, that's what I meant. I corrected the Answer.

@GPY You need to minimize the 2-norm, which is equivalent to minimizing its square. Try this:

Minimize(LinearAlgebra:-Norm(minmat, 2)^2);

This should resolve the absolute-value error.

@ger89 The second argument to pdsolve needs to be w(x,t), not w(u,t).

@mzaman Nobody wants to retype your code. Instead of a screen shot, please post plaintext or upload a worksheet. You can upload worksheets and a few other file types by using the green uparrow that is the last item on the second row of the toolbar in the MaplePrimes editor.

@Kitonum 

Note, however, the significance of round-off. You had to change the OP's 0.36 to 0.3603 in order to get equality. I recommend that the OP work in exact rational arithmetic for such problems. That can be done by not using any decimal points in the input.

@lt I still don't see the problem that is the subject of this Question. The plot shown in your worksheet clearly shows that your textplot3d commands are working.

There is no need for you to direct my attention to your other Questions. I read and consider everything posted on MaplePrimes. 

@UndergradMaths 

Right clicking on the output of your equation brings up a context menu. Select "Solve DE."

If you want to type a command, type dsolve(%);.

@lt Would you please post a worksheet where the above command doesn't work? Your syntax looks fine to me.

What do you mean by "a label coordinate"?

Are the circles in the same plane with one inside the other? On first thought, that seems an easier problem than two arbitrary circles. 

@Axel Vogt

I'm just writing this to clarify Axel's advice: If you want to avoid this anomaly, use 1/10 instead of 0.1. The floating-point anomaly that you point out is just a standard example, not an bug.