What are some practical applications of linear algebra in electrical circuits?

[hotcommodity]

I'm working on a project to show linear algebras applications in electrical circuits. I don't have a lot of experience with circuits, and I don't have any experience with differential equations, so I'm not quite sure how slim my options are.

Anyways, I've found out how to use augmented matrices to find loop currents, and now I've hit a wall so to speak. I've googled for ideas online but some are either too intense or not applicable. We're just starting eigenvectors, so I barely know how to work those. But if you can think of anything that I could expand on in my project given my circumstances, I would appreciate hearing them, thanks.

 

[Chris Hillman]

Recommended reading

I'm working on a project to show linear algebras applications in electrical circuits. I don't have a lot of experience with circuits, and I don't have any experience with differential equations, so I'm not quite sure how slim my options are.

You might try Bollobas, Graph Theory: an Introductory Course, one of the finest math textbooks ever written, in fact it sometimes frustrates me that American high school students read Dickens or Hawthorne instead of Bollobas, from whom they'd probably learn much more about the way the world works. This is a graduate textbook but it has no prerequisites other than mathematical maturity.

If you are interested in the connections with homology theory and physics you can try the undergraduate textbook A Course In Mathematics For Students Of Physics by Paul Bamberg and Shlomo Sternberg.

As for the particular place where you got stuck, you can try the superb but unfortunately out of print undergraduate textbook Introduction To Finite Mathematics, by John G. Kemeny, J. Laurie Snell and Gerald L. Thompson. Kemeny was a highly influential university president, programmer (think BASIC), and early in his career was the last collaborator of Albert Einstein.

 

[hotcommodity]

The books in the above post sound like a good summer read, and I appreciate the suggestions, but my project is due in 2 weeks. I understand how to find loop currents using matrices, but I'm having a hard time finding other applications without using differential equations, or higher mathematics...