Mathematical treatement of electrodynamics

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Discussion Overview

The discussion revolves around finding mathematical texts that focus on electrodynamics, special relativity (SR), and general relativity (GR), particularly those that utilize exterior calculus. Participants share their experiences with various books and seek recommendations for comprehensive resources.

Discussion Character

  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant expresses interest in finding a book similar to Arnold's "Mathematical Methods of Classical Mechanics" that applies to electrodynamics, SR, and GR, with a preference for exterior calculus.
  • The same participant mentions leaning towards Thirring's book and inquires about Hehl's book, which appears to be a complete textbook on electromagnetism using exterior calculus.
  • Another participant asks about the availability of solutions to exercises in Bamberg and Sternberg's book, indicating a desire for confirmation of their answers while self-studying.
  • A participant clarifies that they are self-studying Bamberg and Sternberg's book without access to solutions.
  • There is a mention of Hehl's website, where a sample from his Classical Electrodynamics book is available.
  • One participant confirms having gone through both volumes of Bamberg and Sternberg's book, noting limited coverage of electrodynamics and expressing a desire for a deeper treatment akin to Jackson's work but with a focus on exterior calculus.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific recommended text, and multiple viewpoints on the adequacy of existing resources remain. The discussion reflects varying needs and preferences regarding the treatment of electrodynamics in mathematical texts.

Contextual Notes

Participants express uncertainty about the depth of coverage in Bamberg and Sternberg's book and the suitability of Hehl's text for their needs. There are also unresolved questions about the availability of solutions to exercises in the discussed books.

redrzewski
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I'm looking for something like Arnold's "Mathematical Methods of Classical Mechanics" that applies to electrodynamics/SR/GR. I'd prefer it exterior calculus based.

So far, I'm leaning towards Thirring:
https://www.amazon.com/dp/0387406158/?tag=pfamazon01-20

Anyone know anything about this Hehl book? It looks like a complete textbook on EM, but using exterior calc:
https://www.amazon.com/dp/0817642226/?tag=pfamazon01-20

I've gone thru Bamberg/Sternberg's "Course in Mathematics for students of physics", but that doesn't treat much electrodynamics.

Thanks
 
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Sorry for the off topic question but when you went through Bamberg and Sternberg's book was it for a class which gave solutions to the exercises? I want to go through the book but I do not like not knowing if my answers were right. If it was for a class, I was wondering if it had a website that gave some solutions to problems.

Again sorry for the off the topic question, but no one has yet to answer my question on another thread, thanks.
 
No. I'm just self-studying this on my own, so I don't have any of the solutions to Bamberg/Sternberg.
 
redrzewski said:
I've gone thru Bamberg/Sternberg's "Course in Mathematics for students of physics", but that doesn't treat much electrodynamics.

Both volumes?
 
Yes, both volumes. There's a few pages in volume 2 on it, but I was looking for a little deeper treatment. Ideally something ala Jackson but with exterior calculus.
 

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