I have some general questions on Sturm-Liouville theory. We are planning to introduce a graduate course on Sturm-Liouville theory and every one has been asked to propose topics which might be suitable for the course. 


I would like to know the following. 


1. Is it worth to have a course exclusively on just Sturm-Liouville theory?
2. If we have a course like that what are the topics that could be introduced in the course?
3. Would it be possible for an exclusive course on sturm-liouville theory without much background in functional analysis.


Any suggestions would be really appreciated. 



A graduate course on Sturm Liouville theory?
A more advanced/comprehensive course can be based on Atkinson's book Discrete and continuous boundary
problems. No functional analysis is required, neither for Hilbert-Courant nor for Atkinson.
(When Courant wrote the first volume of HC, functional analysis did not exist yet:-)


Another book which studies some of these questions in depth (and without any functional analysis)
is Gantmakher-Krein, Oscillation matrices and kernels. (Gantmaher, Gantmacher...)


Is it worth offering such a course?
The answer depends on whether you can find enough students who will enroll. This depends on
your local conditions. Of course this is a beautiful and useful subject and worth learning.


