MATH 322 - MATLAB GUIs
Sturm-Liouville Eigenfunctions
© GUI developed by
Benjamin Dyhr, Spring 2007.
Description
This MATLAB GUI explores the orthogonality
properties of several families of Sturm-Liouville
eigenfunctions and emphasizes the geometric
significance of the orthogonality relationship
between two (different) eigenfunctions in the same
family.
The GUI allows the user
- To select a particular family of
eigenfunctions;
- To select two eigenfunctions in the chosen
family;
- To plot two of these eigenfunctions as well
as their weighted product;
- To view the dot product of these functions as
a signed area under a curve.
The GUI also numerically evaluates the dot
product of the two chosen eigenfunctions.
Orthogonal families of eigenfunctions are used
to expand functions as orthogonal series. The
latter are an important tool for solving ordinary
and partial differential equations in applied
mathematics.
How to use the GUI
- Choose a family of eigenfunctions by clicking
on one of the buttons in the panel entitled
Types of orthogonal functions. Sines and
cosines are chosen by default when the GUI
initializes.
- Use the sliders in the third panel to select
and plot two modes in the chosen family. Twenty
one modes are available in each family.
- The bottom panel shows the weighted product
of the two selected modes, as well as a numerical
estimate of their weighted dot product.
- Use the slider in the panel entitled
Domain of the Bessel functions to rescale
the independent variable in the Bessel functions
Jn, n = 1, 2, or 3.
Download
Download (right click on each link below)
the following files into a directory. Set the
MATLAB path to that directory and type
Sturm_Liouville at the MATLAB
prompt.
Type help
Sturm_Liouville at the MATLAB prompt if you
need to be reminded of how to use the GUI.
