I am interested in attempting to work through Jackson over the summer and I am wondering what mathematics backround is necessary before doing this. I have ken calc 1-3, DE, complex analysis (for engineers), and a probability and statistics course. Surprisingly, I have never taken a linear algebra course. What mathematics should I beef up on now before studying Jackson in depth? I have taken uphys 1 and 2, Electromagnetics, I am taking thermal/statistical physics and contemporary physics right now, and next semester I plan on taking optics, lasers and microscopy and a solid state physics course.
I used Jackson's book as a reference when I took E&M. It's not THAT mathematically advanced. You'll be fine studying it right now.
I had no problem understanding it at all. I have about the same math classes you have, but with Linear Algebra. I did not have a problem going through the book. It's a standard sophomore level book for physics majors. In fact, that's who I borrowed it from. I took E&M as a junior level EE class.
Note: I only have the 2nd edition (when I heard that the revision used a mix of cgs/SI units, I purposely bought a musty smelling copy of the older edition from alibris.com). Already Ch. 2 starts with boundary value problems, Green's functions, Fourier decomposition, and other subjects from PDEs. I think you should be able to follow this with your background, it's just that one might start to panic with this unfamiliar material if a grade was on the line (and in a graduate course they'd probably go over this material very quickly). I would suggest supplementing with a "math methods for physics" book and some other E&M books, but I wouldn't be afraid to read Jackson first; it's good motivation for learning the math, and you get an idea why Jackson has the reputation it does . One thing to be aware of is that Jackson often covers topics at a very high, generalized level, and this can obscure the basic physics (and does the average physicist really need to know that much about wave guides?) Here's where I give my usual recommendation of Schwartz, Principles of Electrodynamics as a very readable supplementary text. I don't think linear algebra is explicitly used until the later chapters on relativity, though it is somewhat implicit in the subject of orthogonal functions.
Any good second year student should be able to handle Jackson. People always complain about the mathematics being too hard, but its just vector calculus and some PDE's.
There's quite a bit of applied math stuff in Jackson, and I'm not sure that's the best place to start learning it. Lots of PDE subjects, Green's functions and the like, series methods, orthogonal polynomials, special functions, and probably a lot more further on (we only scratched Jackson in our senior-undergrad course, when I was a sophmore.) Beyond math-department courses (linear algebra, Partial DE's...) much of the stuff is usually introduced in physics courses at various levels because it doesn't show up anywhere else. Some places teach "Mathematical methods of physics" which covers a lot of these things at once.
You could study from Jackson and get a bit out of it this summer, but no way you'll "work through it" in three months, there's far too much for that. (Also, the problems tend to be somewhat on the difficult side.) I can suggest a more helpful approach, though: get Griffiths' book, which has much more in it than a one semester course could cover (MIT excepted). Many advanced methods are introduced in there - chapter 3 for instance teaches you how to use PDE's to solve Laplace's eq., in the process explaining everything from Fourier series to spherical harmonics. The last section also introduces multipole expansions. These things will be invaluable for doing EM at Jackson-level! I think Jackson assumes as much as prerequisites. And you probably haven't done too much EM dynamics in undergrad EM; go to Griffiths for this, everything from SR and radiating systems to gauge freedom is done with extreme clarity. And there's another major point here - Griffiths (as usual with undergrad texts) properly emphasizes what is critically important and essential to the physics, which is usually impossible to pick out from a much-more comprehensive graduate text. Unless the most important thing to you right now, is learning fifteen different ways to use multipole expansions. I think at your level, you can do much more if you study out of Griffiths, perhaps using Jackson as a supplement for interesting methods. Or why don't you talk to your EM professor and see what they recommend?
i'd recommend griffiths, personally, to start with. that one isn't necessarily a push-over, and then jackson (apparently) just gets harder.
I'll repeat what my e&m prof told me. basically, jackson is not teaching to people who are learning electrodynamics. jackson is teaching to people who know electrodynamics, but who are _mastering_ electrodynamics. In that sense, the recommendation for me was to work through griffiths and master that before starting jackson. Now, from my own (quite limited) perspective, Jackson does not use any particularly advanced mathematical techniques. However, and this is a big however, there is a great depth of knowledge of the mathematics assumed that requires mastery, and not just understanding, of the tools and techniques learned in undergrad vector calc, linear algebra, PDEs and fourier, etc.