## Other Mathematical Software

This is a small collection of useful educational programs that run in
MATLAB.

`fseries`

FSERIES is a function which allows the user to observe the convergence
of Fourier series. It is started with the command fseries at the
MATLAB prompt. This causes the FSERIES Setup window to appear. In
this window the user can enter the function that is to be
approximated. Since it is often the case that the function of
interest is discontinuous, it is possible to give different
definitions on up to four contiguous intervals.
When the function is entered, clicking the Proceed button will cause
MATLAB to compute a large number of Fourier coefficients, and to open
the FSERIES Display window. In this window the function will be
plotted, along with the Fourier approximation of order 0, i.e., the
average value of the function. The order of the approximation can be
changed to anything <= 1000 by changing the number in the edit box,
and hitting the Return or Enter keys.

For many purposes, it is useful to use the MATLAB command ZOOM with
FSERIES. Use HELP ZOOM to get information about ZOOM. The click and
drag option for ZOOM is probably the most useful in this case.

Copywright 1995 - 1998 (c) John C. Polking, Rice University

Last modified: October 14, 1998

Educational users may download and use FSERIES
without charge.

`vstring`

The program VSTRING shows a movie of the displacement of a vibrating
string with fixed end points. Arbitrary initial displacements and
velocities can be used. The motion of the string is shown over one
complete period of its oscillation.
Copywright 1993 - 1998 (c) John C. Polking, Rice University

Last modified: October 14, 1998

Educational users may download and use VSTRING without
charge.

### Sturm- Liouville routines

This is a series of three MATLAB functions that allow the user to
analyze very general regular Sturm-Liouville problems. The equation
is
-(pu')' + qu = lru

and arbitrary functions p, q, and r can be used. Arbitrary boundary
conditions can also be used. The first routine,
SL, computes approximately the eigenvalues and eigenfunctions. The
second routine, SLVIEW, allows the user to visualize the
eigenfunctions. The third, SLSERIES, allows the user to visualize the
expansion of an arbitrary function in the eigenfunctions.
The way to use of each of the three functions can be discovered by
using the MATLAB help command.

Copywright 1993 - 1998 (c) John C. Polking, Rice University

Last modified: October 14, 1998

Educational users may download and use SL, SLVIEW,
and SLSERIES
without charge.

John C. Polking
<polking@rice.edu>
Last modified: Wed Oct 14 17:19:59 Central Daylight Time 1998