Maxima for numerical methods (v. Scilab)?



It seems I may be teaching an elementary subject in numerical computation
next semester.  The usual sorts of things: error analysis, solution of
equations, interpolation, eigenvalues and eigenvectors, quadrature,
differential equations.  I want to base the subject around free software, so
the students can use it at home.  This pretty much restricts me to Scilab
(or Octave, but I prefer Scilab) and Maxima.  Does anybody know of any
compelling reasons why I should (or shouldn't) choose Maxima over Scilab?
And is there any online documentation about numerical methods with Maxima?

Thanks,
Alasdair