Studying Sturm-Liouville Form: Finding Resources & Problem Sets

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In summary, the speaker has been studying the Higg's field and came across an equation that made them realize they need to better understand Sturm-Liouville. They searched through their calculus textbooks but found they didn't cover it in enough detail. They are looking for a good resource with practice problems to study Sturm-Liouville, as it has been a while since they last studied it. They did some searching online and received a recommendation for Arfken's "Mathematical Methods for Physicists," which they found to be helpful in their studies. They are now using this textbook to work through their dissertation.
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Mordred
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I have been studying the Higg's field and ran across a particular equation that made me realize I need to better understand Sturm-Liuoville. So naturally I went looking through my differential calculus textbooks but was surprised they didn't cover this detail. While the article covers how to get to the Sturm-Liouville form in the following equation.

[tex]-p(\varphi\frac{d^2\overline{\phi}_n}{d\phi^2}-\acute{p}9\varphi\frac{d\overline{\phi}_n}{d\varphi}+q(\varphi)\overline{\phi}_n=\lambda_nw(\varphi)\overline{\phi}_n(\varphi)[/tex]

I would much rather have a solid good resource so I can study Sturm-Liouville. Ideally one that has a good range of problem sets I can practice with. Particularly since its been over 15 years since I completed University.

However like a lot of things if you don't keep in practice one tends to forget lol

I did some google searching on the topic but would like to know if anyone has any recommendations.
 
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Arfken's "Mathematical methods for physicists" has a good chapter on SL theory.
 
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Perfect precisely the details I needed. I glanced through the ebook and liked the textbook so much I ordered a hardcopy thanks a bunch for the recommendation.

edit studying this textbook further it has provided me all the tools to work through the dissertation I am studying. Once again thanks
 
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Related to Studying Sturm-Liouville Form: Finding Resources & Problem Sets

1. What is the Sturm-Liouville form?

The Sturm-Liouville form is a mathematical method used to solve certain types of differential equations. It involves transforming the differential equation into a standard form, known as the Sturm-Liouville equation, which can then be solved using various techniques.

2. Why is studying Sturm-Liouville form important?

Studying Sturm-Liouville form is important because it allows scientists and mathematicians to solve a wide range of problems in physics, engineering, and other fields. It provides a powerful tool for understanding and predicting the behavior of systems described by differential equations.

3. What types of resources are available for studying Sturm-Liouville form?

There are many resources available for studying Sturm-Liouville form, including textbooks, online courses, videos, and tutorials. Additionally, many universities offer courses on the topic, and there are also research papers and articles available for more advanced study.

4. How can I practice solving problems using the Sturm-Liouville form?

One of the best ways to practice solving problems using the Sturm-Liouville form is to work through problem sets. These can be found in textbooks or online, and often include step-by-step solutions to help guide your understanding. Additionally, some online courses may also offer practice problems and quizzes.

5. Can Sturm-Liouville form be applied to real-world problems?

Yes, Sturm-Liouville form has many applications in real-world problems, particularly in physics and engineering. It can be used to model and predict the behavior of systems such as vibrating strings, heat transfer, and fluid flow. It has also been applied in finance and economics to model stock prices and interest rates.

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