which I would highly recommend to physics-minded folks, but would not recommend at all to maths-minded folks.
Good teachers explain things so that students can understand - and explain the rakes.
Bad teachers put up walls of academic nonsense-speak - point at it with a laser - and expect you to know what they are teaching already.
Not all Academic Speech is "nonsense speak". For example - many students really learn the material from supplementary material (good academic speak) vs textbook (nonsense speak).
These examples show that you explain things well or poorly - explaining things poorly has a direct effect on humanity in the long run.
Later, when I realized what I was missing out on, I tried to teach myself the missing concepts. I failed, until I found H.M. Schey's "Div, Grad, Curl, and All That: An Informal Text on Vector Calculus." It's a pragmatic, friendly, slim little math book that reads more like lecture notes than a classic textbook, and I can fairly say it's taught me everything I know about those operators (which isn't much).
So if you are like me, and got to calc III, vector math, and/or liner algebra without learning div, grad, curl and partial differential equations... check out the book. it's great: https://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161
Also: can we get three cheers for HYPERPHYSICS?? http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html
I see another book with good recommendations, A Student's Guide to Maxwell's Equations (http://www.amazon.com/Students-Guide-Maxwells-Equations/dp/0...) but I have not read that one.
Div, Grad, Curl helped a bit, but what really made it click for me was an excellent professor some other EE math-class-in-disguise that explained those vector calc operations in terms of divergence (source density) and flux (change in time/space).
As far as understanding the linked paper, I can't follow the proof either. Equations 1-4 I've never seen, 5-8 are Maxwell's Equations which are familiar but we wrote them with different notation, 9-18 are again equations I've never seen. The meat of the proof in 19-21 is built on 14 mystery equations and 4 that I recognize.
As a former EE I guess we didn't prove equations as much as take their existence as given and then figured out what that implied for the real world. ;) Other posters aroberge and wraithm have mentioned also needing QM from physics to follow the proof, which must be where the other equations are from!
Fresh book recommendations delivered straight to your inbox every Thursday.