Preparing for Jackson Electrodynamics

[mordechai9]

I would like to know recommendations for the best way to prepare for Jackson's electrodynamics next Fall. I have taken Griffith's E&M as well as the usual undergraduate math (linear algebra, advanced calculus, complex variables, probability). I realize there have been some similar posts to this in the past, but I would like to try and get some new responses.

I have heard that it would be excellent preparation to study Green's functions. Also, I have heard it would be best to focus on going back and reviewing Griffith's E&M intensively. Alternatively I'm sure one could spend the summer reviewing PDE's and a more general math book like Arfken. So there are a lot of different options, but unfortunately, a fairly limited amount of time (say, 2.5 months). If I were to choose to focus on one subject intensively for the summer (with say 3-4 books on that subject), what subject would people recommend? Book recommendations?

 

[Norman]

I have heard that it would be excellent preparation to study Green's functions.

This will pay off immensely for Jackson in my opinion. One of the big things most students (in my experience) have an issue with when the first get to grad school in physics is the quantity of material thrown at you. Often times this is compounded by having to re-learn (or just learn) the mathematical techniques used in dealing with the new physics you are learning. I think if you had a solid as possible understanding of the mathematics involved it would make your studies easier.

I would also suggest that you pick up Jackson and start doing some of the problems and reading. Going to the lectures prepared and having seen the stuff before makes a vast difference- at least it did when I took my graduate level Electrodynamics.

Don't be too scared or taken aback by everyone who talks about how difficult Jackson is. They all did it, so can you! Good luck!

 

[mordechai9]

Thanks for the comment. It seems that you agree that Green's function are really crucial for the graduate electrodynamics course. As I understand, the Green's functions are a method for solving PDE's. Would it be best to go to a book on PDE's and sort of study the general theory, or do you think I should find a more "applied" book that focuses on Green's functions and just focus on those specifically? What do you think would be more interesting?

Also, you recommend picking up Jackson's over the summer and start looking at and reading some of it and so on. However, I feel like it might be more entertaining and informative to pick up some alternative books on electrodynamics, such as the Landau "classical theory of fields" book. I am just a little bit concerned about getting burnt out on the material and I think it would be more interesting to try and hit the subject from a lot of different books. I figure this will make Jacksons more interesting when I encounter it in the fall. What do you think about this idea?

 

[Norman]

Interesting is a question only you can answer, so I won't touch that.

For the question of getting burnt out, I completely understand and would always suggest having multiple resources when learning something new. I would still use Jackson, however, to guide what you are learning.

Regarding solving PDE's, it depends on how much time you are going to put into studying. I would rank things in the following manner:

1. Electrodynamics
2. Green's Functions
3. General PDEs

I ranked them in that order mainly on my personal experience in my Electrodynamics class which focused on a lot of Green's Function solutions to boundary value problems.

 

[ExactlySolved]

Why not just start reading Jackson? I second the recommendation that Green's functions are the main new mathematical topic, along with delta functions if you have not seen those before.

In the second and third quarters of my Jackson class we did a lot of relativity, four vectors, tensors, etc and it helped that I had tried to learn that stuff beforehand.

 

[mordechai9]

I don't particularly want to focus on Jackson itself this summer just because it would be a little bit redundant, considering I'll be focusing on it so much in the Fall.

It sounds like the Green's functions come up quite a bit from what everyone is saying. I am also planning on trying to test out of an introductory math methods course by reading this book called "advanced engineering mathematics" by o'neil. This book covers all the standard undergrad stuff like first and second order ODE's, Laplace transform, Fourier series and Fourier transform, linear algebra, basic PDE's, and complex variable theory. I will probably try to go through this book in 4-6 weeks (spending 8 hours a day probably) and then move on to a book on Green's functions. More suggestions on which specific books might be good?

Do Green's functions come up a lot in advanced PDE theory or is it more just like a standard solution technique that gets used a lot in mathematical physics?

 

[diazona]

I'm actually inclined to agree with the people recommending that you actually look at Jackson over the summer. I don't know about you, but I (and I think most people) learn things better the second time through. People often underestimate the benefits of familiarity in learning, even in the trivial sense of just having seen things before - so even if you were to read it and not understand it at all, you'd still probably be better prepared for your course this fall than if you hadn't even looked at it. (And anyway, having worked through Griffiths' textbook, you will understand a fair amount of what you read in Jackson)

 

[nbo10]

Start Jackson early. Greens functions and problem solving are the most important items to focus on. It's been a while but it seems like some other math was important also. You might want to browse through Arfken.

Jackson was the toughest and most painful class I ever took.

 

[siyphsc]

Definitely focus on Green's functions.

I can send you some notes that I made if you want.