What textbook covers in-depth derivations of physics formulas?

[gkiverm]

For one of my physics classes (oscillations, waves, quantum mechanics) we use Young and Freedman University Physics 13th edition. However, the lectures given by the professor are usually more difficult/ on a higher level than the textbook.

For example, right now we're learning about electromagnetic waves, Maxwell's equations, optics, etc. Most of the time the textbook just presents the formulas (Snell's Law, ratio of incident and reflected electric field, etc.) and says they can be derived from Maxwell's equations. I was wondering if anyone knew a textbook that went into more detail with the derivations of these formulas, seeing as our exams reflect that difficulty.

 

[Avatrin]

For electromagnetism, try Melvin Schwartz's Principles of Electrodynamics. He derives all of Maxwell's equations using only Coulomb's law and Lorentz invariance, and then he ventures into optics and waves (but, its focus is electrodynamics).

The downside is that this book has few exercises. However, it is the only book I know of that truly shows how electricity and magnetism are the same force.

 

[jasonRF]

I like Schwartz's book, but it is at a higher level than required, I think. Many sophomore level "physics of waves" type of books include what you are looking for, and are often used in 3rd semester physics courses. gkiverm, I recommend looking at the library at your university and looking for such books. My favorite is "electromagnetic vibrations, waves, and radiation" by Bekefi and Barrett. Another (prettier but not nearly as good) is "the physics of vibrations and waves" by Pain. Many others exist too - perhaps elementary optics books like the one by Hecht would be useful as well.

 

[atyy]

Does anyone not at MIT use Bekefi and Barrett? It's very good but I remember thinking it's made with a typewriter!

I like Dugdale's Essentials of Electromagnetism.

Online there's Fitzpatrick's Classical Electromagnetism. Snell's law is treated in this section:
http://farside.ph.utexas.edu/teaching/em/lectures/node104.html.

 

[jasonRF]

Yes. I did not go to MIT (was rejected for both undergrad and grad!) and for 3rd semester physics we primarily used Bekefi and Barrett. It was the honors track, though.

Yes, it is made with a typewriter. It is one of the few books typeset that way that I can still enjoy. It is a great book but I could understand if the typeset made it a non-starter for many folks.

In any case, for the OP I think a trip to the library is the answer, as opposed to buying a book without seeing it first. So the more suggestions the better.

jason

 

[WannabeNewton]

https://www.amazon.com/dp/1107014026/?tag=pfamazon01-20

As for Schwartz's text, it's a great book but the author tries to be more mathematically sophisticated yet uses horribly antiquated definitions for things like tensors so I don't really see the point.

 

[SredniVashtar]

I like Dugdale's Essentials of Electromagnetism.

My vote to Dugdale. Short, essential, to the point.
Starts with Maxwell' equations and derives all essential results in electromagnetism.

And as far as books on waves go, it is my (bloated) opinion that "nomen omen" applies. To me Pain is a pain and King is the king. :-)
But the one I treasure the most is Crawford's "Waves" from the Berkeley Physics Course (a book I would not suggest to a beginner, though, since it requires a certain amount of destructuring to work out the general principles - a book similar in contents and extent is perhaps "The Physics of Waves" by Georgi which can be legally downloaded from the author's website at Harvard's or from http://web.mit.edu/~alexrod7/www/mites/georgi.pdf).

The 'problem' with introductory waves books is that they are mainly focused on mechanical phenomena. Hence an introductory book on optics could be a better idea. Hecht is a fine suggestion.

 

[jasonRF]

I looked at Georgi - I agree it is waaaay better than Pain. Yes, Pain is not a great book, but it was the only other one I was really familiar with that seemed at the appropriate level.

jason

 

[SredniVashtar]

Yes, Georgi is like Crawford in a suit. :-)

I forgot to add that another outstanding book on waves - still focused on mechanical phenomena like the others - is French's "Vibrations and Waves" from the MIT Introductory Physics course. It's very short but it really is a small jewel, perhaps too much oriented on the vibrations part to be useful to the OP (on the other hand the latest Norton edition is quite inexpensive, but beware: it looks like a bad xerox copy).
I really love French as a teacher, with his digressions in the history of physics (I bought all four his books in that series and I am very happy with them).

 

[jasonRF]

I swung by the library at work yesterday afternoon and looked at French - it looks fine, and does have a construction of Snell's law. I've always been curious about his books, and think they would have been good to learn from.