Jackson Math: Challenges and Solutions

[captain]

Is jackson ridiculously hard? and if so how do people manage doing the problems in the book?

 

[TVP45]

I took E&M from a prof who had been a grad student under Jackson. There were a number of problems that no one had ever completely solved, and we would get one of these about every two weeks. We had podunk files (a file cabinet full of work from previous grad students) to use as a start and we would try to move the solutions forward. We seldom finished one of these, but going from, say, 60% to 70% was a major accomplishment and taught us a lot of E&M. The prof felt, rightly I think, that being able to work on a problem with no known answer was good preparation for work. That was decades ago, and it's possible many (most) of those problems have been solved. Jackson remains an outstanding book, but not always easily approachable.

 

[Andy Resnick]

Personally, my initial difficulty with Jackson's book was the mathematical sophistication. For example, we had either just learned or were concurrently learning about spherical harmonics, vector 'things' (grad, curl, etc) in non-euclidean coordinates, so the need to be proficient in vector calculus made doing the homework problems difficult.

On the other hand, once we got past magnetostatics and into electrodyamics, I found the material substantially more intuitive. We did not get into the late chapters (radiation reaction, etc) in my course.

My prof also took E&M under Jackson, and told us a story that he was contracted to design some accelerator magnets- sure enough, he had to consult his own book for some of the details. The rumor was that he had difficulty with his own book, to the delight of his pupils...

 

[seycyrus]

Is jackson ridiculously hard? and if so how do people manage doing the problems in the book?

Find the solutions in Griffiths and Landau/Lifshchitz :)

 

[arunma]

My department, like almost all others, uses that stinking Jackson book for E&M. I took E&M 1 my first semester of grad school (i.e. fall 2007). It was the most grueling, painful, torturous course I've ever taken in my life, all thanks to Jackson. Thankfully our professor graded graciously. Jackson's E&M problem's taught me very little about the subject, mostly because of their mathematical abstraction. I would say I learned a lot more studying for the classical portion of the qualifier. The worst part: I got lazy and decided to skip the second semester so that I could take statistical mechanics. So now I'll have to take the second semester next spring.

For all the torture Jackson put me through, I must say that at least it's a good character-building experience for first year grad students. Jackson did, if nothing else, teach me to get out of my "undergrad mentality," and got me used to the living hell of grad school. I'd probably punch Jackson in the face if I ever saw him on the street (he's still alive!), but he's good for something.

 

[Daverz]

Jackson is pretty miserable without a good instructor who can give you some insight into the subject. Jackson throws tons of detail at you right up front, which is overwhelming if you don't have some kind of guidance through it all. My advice is to buy a bunch of Dover E&M books and check out any good ones you can find in the library.

 

[Ben Niehoff]

I actually thought Jackson's book was kinda fun...but then, I like a good challenge. It's really a math textbook in the guise of an E&M textbook. It should generally not be your first exposure to E&M or vector calculus, and as such, it will not have new physics to teach (you should already know Maxwell's equations and some basic stuff about E&M fields). What it teaches are the mathematical methods for dealing with more complex Poisson problems, by relaxing the symmetries used in more elementary works like Griffiths, hopefully to promote a more general understanding of how electromagnetic phenomena can be calculated.

Some important analytical methods are learned, such as spherical harmonic expansions, Bessel function expansions, eigenfunction expansions, and multipole expansions (using both spherical and Cartesian multipoles). Green's method is demonstrated for solving differential equations with a source term, and is applied to Poisson's equation under several different boundary geometries. The book also gets into (multipole) radiation, various geometries for waveguides, and a demonstration of various laws of optics derived from Maxwell's equations in different media; however, these are covered in the second part of the course, which I haven't taken yet.

For most of the problems in the book, there are (at least) two ways of getting the solution: a long, tedious, but obvious way; and a much shorter, elegant, but non-obvious way. It helps a LOT to think about the problem a bit and try to find the more elegant way to do it. In particular, pay attention to results derived from previous problems, because they will often apply to later problems. Also, many problems actually give you the solution, and ask you to show that it is true; therefore, if you get stuck, you can often simply start with the solution given, and show that it satisfies whatever rules it ought to satisfy, thus working the problem backwards. I suspect this is actually how Jackson intended some of the problems to be solved, though I'm not completely sure.

The one thing that will save you the most time on the homework problems is knowing how to manipulate vector quantities, and do vector calculus, without writing out the components. The only problem with this is that, in my experience, schools don't usually teach this enough in prior vector calculus classes, so it requires some independent learning. Knowing how to manipulate expressions with vector derivatives and integrals, without actually computing those derivatives/integrals, will often get you to the solution in fewer steps. In observing the other students in my class work their problems on chalkboards, this is one of the things they wasted the most time on.

And lastly, many of the problems will seem impossible at first glance, or seem not to provide enough information. The key thing is to start actually trying things to get some insight. Also, the biggest error I made in the class that made it difficult to do problems was forgetting to use Maxwell's equations. It seems they should be obvious enough, but there is a strong tendency to try to rely only on vector identities. If you get stuck on a problem, the first thing to do should be to go back to Maxwell's equations; they often supply the piece of information you thought was missing.