Learning track for quaternions?

Question

I've been out of the math loop for the last decade (although I'm a programmer, I've not done anything with calculus or above for this long) and I'd like to learn about quaternions (particularly interested so as to study Maxwells equations in their original form).

Can someone recommend a track of material that would properly prepare me for the topic of quaternions from a calculus review (probably have to go through some basic courses as a refresher) and on into this?

The most helpful might be a Khan Academy'esque video course, yet I've not really found anything quite appropriate yet.

Answer 1

If you want to strengthen your background online, here is a way.

First go to http://www.saylor.org/saylor-foundation-status/#Mathematics and see what courses you need to refresh your calculus skills, and then look at their Multivariable Calculus You will also need a good deal of linear algebra, that is also available at Saylor. After that (or right away, depending on your readiness!) it makes sense to go through their Introduction to Electromagnetism.

There are not too many relevant courses on https://www.coursera.org yet, but you should keep an eye. In particular, Coding the Matrix: Linear Algebra through Computer Science Applications might be useful.

When you feel stronger, you may want to find a more advanced course at http://ocw.mit.edu/courses/ For instance, their Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra that may be very suitable for your needs.

Secondly, go to Google Try me!, find an item that suits your level of expertise, try hard to understand, and then you will be able to ask here more specific questions.

I've found the following things on the first page of the search results:

• Vic Chrisitianto and Florentin Smarandache, A Derivation of Maxwell Equations in Quaternion Space, http://www.ptep-online.com/index_files/2010/PP-21-06.PDF
• GEM Blog 29: Deriving the Maxwell Source Equations Using Quaternions (2/5) http://www.youtube.com/watch?v=wTazqEjwDkE
• M. Acevedo M. et al. Quaternions, Maxwell Equations and Lorentz Transformations, http://redshift.vif.com/JournalFiles/V12NO4PDF/V12N4ACE.pdf

I personally, would even start with this second part, and then look for courses that are necessary to work through the material. This is much faster!

Anyway, thank you for the cool question. I guess, it would be better to ask it on a physicists' forum, though. Also, a few more tags increase the chance of a good answer.

Answer 2

If you would like to know more about how quaternions work, I would like advice you to read the paper Geometric Algebra Primer, written by Jaap Sutter. Therefore the paper will not discuss quaternions from a physics point of view, but you will have a good understanding how quaternions work from a Geometric point of view. Maybe via that way you could study quaternions used in physics. The reason why I recommend this paper is because it gave me a great understanding about how quaternions work (and I am also a programmer).