electromagnetism - What does it take to understand Maxwell's equations?

Assume I want to learn math and physics enough to reach a level where I understand Maxwell's equations (The terms and reasoning in the equations I.e. why they "work"). What would I have to learn in order to have the tools I need to make sense out of it?

I'm kindof looking for a road map which I can use to get started and know what to focus on. The fields are pretty big so some pruning would be very helpful (if possible)

Answer

Math

1. High school mathematics, including algebra, pre-calculus, and basic solid geometry


2. Single-variable calculus, both differentiation and integration


3. Calculus of functions of several variables, including volume integrals and surface integrals


4. Differential equations


5. Vector algebra, including dot products and cross products



6. Vector calculus, including line integrals, divergence, gradient, curl, and the Laplacian.

I'll second the recommendation for "Div, Grad, Curl", but that's starting at step 6. Silvanus Thompson's Calculus Made Easy is good for step 2. James Nearing's Mathematical Tools for Physicists, especially chapters 1,4,6,8, 10 and 13 should be helpful for steps 3 - 6. The various Schaum's outlines might be sufficient if you need to review the high school stuff in step 1.

Physics

1. Basic mechanics - Newton's laws (technically, you don't need this, but any book you read about electromagnetism will assume you know it)


2. High school electromagnetism - basics of charge, current, electric and magnetic fields, Coulomb's law, Ampere's Law, Lenz' Law, the right-hand rule, and displacement currents.


3. (optional) Special Relativity - Lorentz transformations, the interval, four-vectors (optional because you could choose to learn it concurrently)

That's it - the physics prerequisites are brief. However, it takes quite a bit of time and effort to get used to basic physics if you haven't done so already. In theory you could skip the physics prereqs, but you'd probably have a hard time relating the equations you were learning to the real world.

Volume 1 of The Feynman Lectures on Physics is a good source for the physics prereqs, although you'll probably need to supplement with practice problems from another source.

There is a book called A Student's Guide to Maxwell's Equations that I have heard recommended highly. However, I haven't read it. When you're ready for electromagnetism with Maxwell's equations, I can second recommendations for Purcell and Griffiths.