Preparing For Jackson Electrodynamics

Question

Hypothetical Scenario: You are an undergraduate physics student who has never taken a course on E&M and you are enrolled in a graduate Jackson electrodynamics course. In general you are good at math, differential equations etc., but have not mastered many of the methods especially pertinent for E&M. You have some knowledge of the content of Griffiths book on the subject. You have four days, maybe 50 hours, to prepare for the course. What do you focus on specifically? Also this is not hypothetical.

Answer 1

What do you focus on specifically?

From Everything I Needed to Know in Life I Learned from Jackson Electrodynamics

Undergraduate E&M is about solving the simple problems exactly. Jackson E&M is about learning to approximate reliably. The entire book, with few exceptions, is a mathematical discussion on finding way to solve only 4 equations for different boundary conditions. Most of the time, this requires series expansions and other approximation techniques.

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As one comment implies, there's little chance of preparing for this course in the time frame you mention. While the following from the linked document may exaggerate a bit, it's not by much.

One Jackson problem takes an average of 1.5 weeks to finish. Most of this time is often spent working on the first part of a multipart problem. An approximate breakdown of the timeline of solving a Jackson problem is:

a. Days 1-2: Arguing about what exactly the problem is asking, what assumptions to make, why the problem can’t be done as stated, why Mathematica cannot handle the integral, why Jackson probably didn’t do any of these problems, why the intial 10 pages of algebra failed to deliver the correct answer.

b. Day 3: Rechecking the 10 pages of algebra for a missing minus signs and factors of 2.

c. Day 4: Starting the problem over the exact same way as before since it is not clear where the algebra mistake came from.

d. Day 5: Discussing with the professor and realizing the problem is not as easy/hard as previously thought and that 4 days were wasted doing the problem the wrong way.

e. Day 6: Reworking the problem this new way: 13 pages of Algebra.

f. Day 7: Realizing this new way didn’t work either, and discussing with professor why it was wrong. After getting an extension and “knowing” the correct way to do the problem, swearing it will get done tomorrow.

g. Day 8: After working 15 pages of Algebra, you realize that a minus sign was left out on page 2. Reworking all of it, you are off by a factor of 2 from the expected answer. Going back and reworking, you find the missing factor on page 3 of 16. The first part of a 3 part problem is now done. No other homework or research was none today (or the past 5 days).

h. Day 9: Part b is not as hard, but still takes 6 pages of Algebra.

i. Day 10: Part c takes 2 pages of algebra and a page of words trying to answer a conceptual question that no one cares about at this point.

j. Day 11: Turn in the homework assignment, and reflect on how much was learned and how horrible the problem was. It takes 24 pages total

Answer 2

Focus on mathematics and basic physical concepts. Many problems will seem impossible but can be solved if you have a solid background in calculus and differential equations.

So, specifically:

• If you are familiar with Griffiths, review physical concepts: what are you about to study? what are the most simple behaviors expected from EM systems? how are such systems represented mathematically?.

• From calculus: master differentiation and integration. Practice doing 'hard' integrals. Search for advanced methods for solving integrals. Remember what are vector equations. Practice with vector operators. Review how transformations of coordinates work. For example, what is $\nabla \frac{1}{\sqrt{x^2+y^2+z^2}}$? how would you use spherical coordinates to make it easier?

• Practice solving differential equations. From techniques like guessing a solution. More advanced techniques like trying a power series solution and everything in between. What are some common differential equations found in physics? how are they solved? What are the Bessel functions?

I agree that the problems in Jackson's book are sometimes very hard, but the exposition is clear if you know your basics. Good luck!