GEM Blog 28: Deriving How to Derive Field Equations (1/5)

[sweetser]

For anything this central, I like to took at it from multiple view points. You suggest the math theorem road, a fine suggestion. Our minds get the 3D illustration.

Here is the limitation with that approach: all this stuff is dynamic in a way that lost by 3D geometry. Time is toying with space in so many ways. That at least is at the heart of my own research: the math of transience.

[zahari20]

It seems to me that this path to the Maxwell equations is short, but too theoretical to be appreciated by an ordinary student. It is good to learn about this method after you have seen the intrinsic connection of the ME with the major vector field theorems - The Stokes' theorem, and the Gauss-Ostrogradski theorem. They explain the unity of geometry and physics and are supported by easy to understand 3d illustrations and geometrical intuition..