What makes Jackson's Electrodynamics so difficult?

[Simfish]

Is it the mathematical sophistication? Or the lack of intuition that some grad students might have?

What is the best way to prepare for a course on Jackson's Electrodynamics? Many grad students haven't even taken a formal course in partial differential equations (and don't have much beyond their "mathematical methods in physics" course, so it's quite possible that mathematical sophistication is one of the main barriers to student understanding of it.

 

[yungman]

That is a very very difficult book! I have my eye towards this book all along and working up to it. I finished PDE, am planning to study Complex analysis in the future. According to my friend whose a PhD and is the director of the Lazer weapon project in Lochkeed, he think it is mighty important to study Complex analysis and some general analysis. PDE is a must to even have a better feel of the simpler book like Griffiths.

 

[Pengwuino]

Yah Jackson is TOUGH. It seems like most textbooks are there to guide the reader and kinda give them simple problems and as you go through the problems they get tougher and tougher and you feel like you're learning something. With Jackson, on the other hand, from the very first chapter he seems like he's out to destroy you. I've done at the most, ONE question that didn't require at the most, 2 pages of work. The rest are very long... hell one problem felt like I was doing a thesis.

I think what makes the subject so difficult is that it is probably the first text you run into in your studies where the solutions and work are just unintuitive. You have to just deal with long calculations taking like 5 approximations/conditions into account. You also are really introduced to functions that just don't have any nice properties at all (I consider Legrendre polynomials a "nice" set of functions but Neumann functions are "WTF" territory to me"). If you have any trouble at all in the SLIGHTEST with vector/integral calculus or integration, the book is a disaster waiting to happen.

Though if you survive the book, then you're like "Oh, so THAT'S what a physicist is".

One problem I remember is at some point he talks about how to solve for some angular frequency. The problem was, he defined the frequency as complex. So, big deal right? Well at some point you do an integration and he just mentions "Principal value" of an integral. That's it. BOOM, complex integration in your face. You do integrations in real space for 6 chapters then randomly a complex integration that you have no idea how to do pops up (or at least I didn't) and at first I didn't even realize it was a complex integration and wondered "hmmm but this integral has a singularity...". Everyone else did the integral the stupid way (it was a 1/w type integral) and just said "oh it's the logarithm" and they just wrote down some BS when in fact that's not how you do it. It's a wild ride.

 

[Fredrik]

Is it the mathematical sophistication? Or the lack of intuition that some grad students might have?

What is the best way to prepare for a course on Jackson's Electrodynamics? Many grad students haven't even taken a formal course in partial differential equations (and don't have much beyond their "mathematical methods in physics" course, so it's quite possible that mathematical sophistication is one of the main barriers to student understanding of it.

I don't think you can prepare for it, other than by making sure that you understand the basics, like partial derivatives and Taylor's formula.

Though if you survive the book, then you're like "Oh, so THAT'S what a physicist is".

A very special kind of physicist maybe, the kind that does advanced calculations for problems in engineering. Unfortunately I don't think the stuff in Jackson is even useful for theoretical and mathematical physicists. They're better off studying abstract algebra, topology, differential geometry, functional analysis, etc.

 

[Pengwuino]

A very special kind of physicist maybe, the kind that does advanced calculations for problems in engineering. Unfortunately I don't think the stuff in Jackson is even useful for theoretical and mathematical physicists. They're better off studying abstract algebra, topology, differential geometry, functional analysis, etc.

I think there is something to be said about being able to do Jackson problems though. It just doesn't feel right to say someone knows electrodynamics if they just know "about electrodynamics" and have on idea on how to do a problem. It would be like saying I learned about quantum mechanics without knowing how to actually solve Schrödinger's equation.

 

[Dickfore]

The problems given for homework every week.

 

[Fredrik]

I think there is something to be said about being able to do Jackson problems though. It just doesn't feel right to say someone knows electrodynamics if they just know "about electrodynamics" and have on idea on how to do a problem. It would be like saying I learned about quantum mechanics without knowing how to actually solve Schrödinger's equation.

I agree to some extent, but most theorists only study a few solutions of the Schrödinger equation (particle in a box, potential well, potential barrier, harmonic oscillator, hydrogen atom, and perhaps a few others), and they're still forced to study Jackson, which is 800+ pages about how to solve boundary value problems in electrodynamics. For a theorist, I think it makes a lot more sense to study a small number of examples and then move on.

 

[Pengwuino]

I agree to some extent, but most theorists only study a few solutions of the Schrödinger equation (particle in a box, potential well, potential barrier, harmonic oscillator, hydrogen atom, and perhaps a few others), and they're still forced to study Jackson, which is 800+ pages about how to solve boundary value problems in electrodynamics. For a theorist, I think it makes a lot more sense to study a small number of examples and then move on.

Definitely. This is definitely a book for people who need to be doing stuff like this at more than their leisure.

 

[|squeezed>]

I think that this book is more like a reference textbook than a course book. It covers a plethora of topics which however are not all covered in depth. For example, if you want to study waveguides and optical fibres or diffraction and scattering then you should follow a different book. Even though these topics are presented there, they are too compact and short for my taste. Jackson relies heavily on math and less on intuition. You could say that this is its advantage - you will find a lot of useful formulas there.

I imagine it would be painful to go through the whole book even within a 2-semester course. But even if you did so, i don't think you would benefit much.

 

[Vanadium 50]

but most theorists only study a few solutions of the Schrödinger equation

That's because the Schrödinger equation has only a few closed-form solutions. That's partly why so much time is spent on perturbation theory.

Jackson is important because it is the only time that the full implications of a U(1) gauge theory - the prototype for all of our theories - are explored. Jackson is difficult because this exploration included problems that don't have trivial symmetries to exploit.

 

[Andy Resnick]

Is it the mathematical sophistication? Or the lack of intuition that some grad students might have?

What is the best way to prepare for a course on Jackson's Electrodynamics? Many grad students haven't even taken a formal course in partial differential equations (and don't have much beyond their "mathematical methods in physics" course, so it's quite possible that mathematical sophistication is one of the main barriers to student understanding of it.

For me personally, it was the math. Lots of new concepts, introduced rapidly. And specifically, it was chapters 2-6 and 12-14; I found chapters 7-10 to be 'easy' (so to speak).

Also, it was the first course that was unapologetically difficult- up until then, my coursework was loosely based on the idea "The *real* concepts are difficult and you will learn them later, so here's an easier simplification". The homework problems were also significantly harder than anything else I had seen until then.

A funny story: our class was taught by Judy Franz, who knows Jackson. One day while we were slogging through some exquisitely complicated integral, Judy paused to comment that Jackson had recently been involved with the magnet design for some accelerator (possibly the SSC, I've forgotten which), and that he needed to go back to his own book as a reference. Jackson, she informed us, was just as flummoxed by his book as we were.

 

[lalbatros]

In the Jackson book you can read, on the same page, very elementary topics, intermediate topics, up to very advanced topics. Jackson always goes deep, even if it cannot be understood at first reading.

Just look in the very beginning of the book: §I.3 . Jackson goes very deep in explaining linear superposition. This material cannot be found in any other book on classical electrodynamics, at any level. But it makes sense, since it points to the limits of applicability of the theory, as well as to its most important feature.

And there is even more striking: in the previous section, §I.2, Jackson discusses the "Inverse Square Laws or the Mass of the Photon". A full understanding of this introductory paragraph almost implies a full knowledge of quantum field theory as well as electrodynamics. Without this knowledge, on can only guess at the meaning of this paragraph, and become either very motivated or very disappointed.

This book is more than a course.
This book is about how a top scientist understand this field.
This book needs more than one reading, it even needs more than simply reading!

I have stored this book on the same shelf as Feynman's books and Landau's books.