Subject: Maxima for numerical methods (v. Scilab)?
From: Robert Dodier
Date: Sat, 29 Apr 2006 08:36:25 -0600
On 4/29/06, Alasdair McAndrew <amca01 at gmail.com> wrote:
> 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.
The advantage that I see for using Maxima for a class like that
would be to construct explicit formulas like they show
in the textbook. For example: construct a Taylor series,
Chebyshev polynomial, rational interpolation function, etc
and plot it together with the function of interest.
Set up equations to find evaluation points for Gaussian
quadrature and solve them. Construct an explicit expression
for the condition number of a matrix and see how it changes
as the matrix becomes more nearly singular.
There is quite a bit of numerical stuff in Maxima but coverage
is uneven and it's not well organized. But that's not a big deal
because the students will presumably be writing their own programs.
Of course back in the good old days we did this stuff
with only a pencil and paper, and naturally that's still the
best way to do it. Now all we need is some Luddite to
bemoan the corrupting influence of the pencil ....
Ha ha, only serious. 8^)
best,
Robert Dodier