## 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

### `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

### 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