@xx50xx Kitonum is setting z=0 to produce the ellipse in the xy-plane which when rotated about the y-axis will generate the ellipsoid. That way he can use the formula for the area of a surface of revolution.

@nm The Crout factorization is a lower triangular L and unit upper triangular U.

@Carl Love Is anyone working on these problems? I am especially interested in the problem of uploading worksheets for display. I am tired of cut-and-pasting entire worksheets with every input group and every output group requiring a separate cut.

@Thomas Richard Thanks! Plain one-argument simplify didn't do much.

@nm The OP means Pi = sum(..., n= 0..infinity).

@Kitonum You could also replace `` with ` ` and thus maintain the intended blank-line appearence.

This must be considered a bug as `` is common in Maple code, especially as a function.

With that combination of keystrokes, nothing special happens for me. I'm on Windows 8, Maple 17.02/64, Standard GUI.

@J4James You can also use dsolve option method= classical[rk4].

@emmantop Okay, we need a specific numeric value for parameter k_1.

Your code has a variable with no specified value: zeros. Is this something that you assigned earlier? Could you show the plot command that you used?

@adel-00 In general, there are three values of N for each K. Finding those N involves solving a cubic equation. Here's a simple procedure to get those three values.

Nk:= unapply([solve(K(N) = Kn, N)], Kn);

@Markiyan Hirnyk I wish I could delete tags. I would delete "query".

I can't execute your code because there are five Vectors that did not get transcribed when you cut-and-pasted the code. Try setting

interface(rtablesize= infinity);

and then try the cut-and-paste again.

Also, try to upload the worksheet as an attached file. This hasn't been working very well lately, but it works sometimes.

Like I said to your earlier version of the question: Do you really want to use RK4? Is your goal to solve the ODE, or is your goal to complete a programming exercise for RK4? You will need to specify a numeric value for k_1 either way.

@Kitonum Yes, ilog10, ilog2, and length are much faster than ceil@log[10] for exact aritnmetic.