Classical Recommendations for E&M Math Book

[Physics2341313]

Can anyone recommend a good book that deals with the mathematics of E&M? I've read through my calculus books and feel like I understand the material there and can solve the problems. However, when it comes to it's applications in electricity and magnetism I find that I have enormous difficulty applying it correctly. A good example is Gauss' Law. I don't find the mathematics behind it that difficult to understand, and it seems fairly obvious. When it comes to applying it however I find that I almost always apply gauss's law incorrectly or in the wrong scenario. Perhaps this is not understanding the physics correctly. I'm looking for a book that would primarily have examples of the math being applied to solving E&M problems.As an aside, I've taken differential equations, linear algebra, calc 1-3 - basically your typical undergraduate mathematics course outline. Coming from a purely mathematical background with little physics applications so perhaps this is why I'm having difficulty as I'm finding there to be a large bridge to cross between pure mathematics and it's application

 

[axmls]

Do you have a solid grounding in Newtonian mechanics? Sometimes it helps to be exposed to physics thinking first.

Could it be your textbook? Perhaps you could try Purcell or Griffiths. I personally find intro EM textbooks aren't very good at explaining the concepts, because they often dumb it down math-wise. You certainly have the math background I do Griffiths or Purcell.

 

[Physics2341313]

I'm using purcell and I find the notation (CGS units) to be a bit confusing at times in formulas, but trying to struggle through it as I should go ahead and get exposed to different systems of units and I've had an undergraduate course on Newtonian mechanics.

In purcell I don't find most of the problems to be too challenging, but when it comes to applying what I learn from purcell's book in class / tests etc I find there's a disparity as I think purcell is a bit more intensive. I've taken a quick look at griffiths perhaps I'll try his book again.

I switched to purcell after trying to use halliday/resnick.

 

[axmls]

I really enjoy Griffiths's book (I have it two feet away from me). It's very well-written. I don't know about Purcell--it's just something I've heard some people praise.

 

[Physics2341313]

I think A student's guide to maxwell's equations is what I was looking for. Purcell has a great exposition as does griffiths, but I'm lacking at the problem solving and understanding applying the techniques. More or less going from thinking like a mathematician to a physicist, and that looks to be a decent bridge between the two in regards to E&M. But I'll look at griffiths again after I go through the book mentioned, thanks for the suggestion perhaps I gave up griffiths too soon.

 

[vanhees71]

I'm using purcell and I find the notation (CGS units) to be a bit confusing at times in formulas, but trying to struggle through it as I should go ahead and get exposed to different systems of units and I've had an undergraduate course on Newtonian mechanics.

If you can master SI units, you shouldn't have any problem to master CGS units which are much simpler and much closer to the fundamental structure of electromagnetic theory which is a relativistic field theory for 150 years, although this has become clear only for about 107 years (Minkowski 1908). SCNR.

Concerning the math, I think most introductory theory textbooks provide pretty good introductions to vector calculus at a level needed to master the physics material. My favorite in this respect are two pretty old sources:

(a) A. Sommerfeld, Lectures on Theoretical Physics, Vol. II (Hydrodynamics). You can read the part about vector calculus without bothering about continuum mechanics (although the latter is a very interesting topic, and I consider it unfortunate that it has vanished from the standard physics curriculum, but that's another story).

(b) R. Becker, Electromagnetic Field and Interactions. This has a quite detailed first chapter on vector algebra and calculus.