E&M and beyond books for very mathematically adept

[Lanza52]

I'm looking for a Electricity and Magnetism (and beyond if possible) textbook that suits my capabilities better. I just read "Electric flux is proportional to the amount of electric field lines penetrating some surface" in my current textbook. I find that this is for the mathematical incapable. It tends to avoid any usage of integrals or derivatives.

I took Multivariable Calculus this past semester and did phenomenal. I'm extraordinarily good at understanding concepts and applying mathematics to describe the concept: ie what Calculus is all about. But that's not to say I'm good at math. I'm terrible with abstract math because I tend to approach everything by trying to understand the reality first and then letting the numbers fall into place.

So, back story aside; I'm looking for opinions about a textbook that is for the much more mathematically capable, but not one that says "flux is F dot dr" and leaves it as an abstraction. I guess a book that vividly explains the concept physically and then describes how it works with calculus without holding back in fear of offending the integral-challenged.

Any opinions?

Thanks!

 

[transphenomen]

For E&M A Student's Guide to Maxwell's Equations https://www.amazon.com/dp/0521701473/?tag=pfamazon01-20 has both the integral and differential forms of the 4 Maxwell equations as well as explains why there is a dot product used in certain formulas as well as other del operators. It is at a slightly higher level than what most probably learn in Calc III, but it is very accessible to those who have taken it. The only thing it adds to a Calc III class is that it take surface integrals in spherical and cylindrical coordinates. It is a very small at about 130 pages of material, but it is far denser than most books you have probably seen and will take you a bit longer per page than normal, but it should be what you are looking for. And it's cheap too!

 

[Daverz]

The Feynman Lectures vol. 2. He explains the math in a physical fashion.

But there are many good undergraduate E&M texts that will also fit the bill. Search this forum for recommendations.

 

[ParticleGrl]

Purcell is the way to go.

 

[dextercioby]

J.D. Jackson wrote a good book on classical electrodynamics. He uses pretty decent mathematics, not too much wording.

 

[Daverz]

J.D. Jackson wrote a good book on classical electrodynamics. He uses pretty decent mathematics, not too much wording.

Going directly from multivariable calculus to Jackson might be a bit of a stretch for the OP. I suppose it wouldn't hurt to check it out at the library.