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- Taylor & Wheeler's Spacetime Physics is similar. They emphasize the importance of frame invariant representations. (I highly recommend the first edition over the second edition, the second edition was a massive downgrade.)
Kip Thorne was also heavily influenced by this geometric approach. Modern Classical Physics by Thorne & Blandford uses a frame invariant, geometric approach throughout, which (imo) makes for much simpler and more intuitive representations. It allows you to separate out the internal physics from the effect of choosing a particular coordinate system.
- You might be interested in Kip Thorne (of Gravitation fame) and Roger Blandford's book Modern Classical Physics, which is designed to cover the elements of non-quantum physics that are generally ignored in the first year PhD curriculum. Part headers: statistical physics; optics; elasticity; fluid dynamics; plasma physics; general relativity
- Caveat: MTW stalled me for the longest time by omitting two points:
- Tensors (as well as exterior and symmetric powers) have very little to do with differential geometry (and a fortiori physics) as such except for motivation—go study multilinear algebra first if the fanciful pictures of egg crates don’t help. Learn the coordinate-free definition of the determinant and rederive Cramer’s rule while you’re at it.
- Nobody can satisfactorily explain what the Riemann tensor is as a whole, though you can learn to work with it and understand some of the direct summands. (“A little monster of (multi)linear algebra”, as Gromov’s refreshingly frank book[1] puts it.) This is one of the rare cases where the worse meaning of von Neumann’s oft-abused quote is in force.
If you like the geometric viewpoint proselytized in the earlier parts of MTW before it gets to GR proper, try also Modern Classical Physics by Thorne and Blandford, which is that in doorstopper form (an early version[2] is available online though not advertised).
- My personal recommendations for an undergraduate course in physics (based in large part off of my own undergrad curriculum):
Foundations:
1. Newtonian Mechanics by A.P. French (https://archive.org/details/NewtonianMechanics/mode/2up). This will give you a good foundation for what is to come.
2. Spacetime Physics by Taylor & Wheeler --- first edition if you can find it! It is much, much better than the second! Special relativity is conceptually strange, but mathematically pretty easy, so you can jump right into it after learning Newtonian mechanics. Have a little fun!
3. Electricity & Magnetism by Purcell. This book is a little unusual in that it derives magnetism from the laws of special relativity. This is the more natural approach than just asserting the laws of magnetism since magnetism is fundamentally a relativistic phenomenon.
4. Waves by Crawford. (https://archive.org/details/Waves_371/mode/2up) A bit hard to find in print, but a really excellent textbook. Waves are a fascinating topic because they come up in every area of physics, so a course focused around them has a huge number of applications.
5. Introduction to Quantum Mechanics by Griffiths. The best introduction to the topic you will find!
6. Thermal Physics by Kittel & Kroemer. I haven't actually found an introductory book on statistical physics that I'm crazy about, but this one isn't too bad.
That should last you some time. But once you're through with those and are looking for more, then here are some advanced topics:
7. Analytical Mechanics by Hand & Finch. This will teach you advanced Newtonian mechanics --- in particular Lagrangian and Hamiltonian dynamics. There is a chapter on chaotic dynamics towards the end, too. Another option here is Classical Mechanics by Goldstein.
8. Introduction to Electrodynamics by Griffiths. More advanced E&M than Purcell. If you want to go further, then there's always Classical Electrodynamics by Jackson.
9. Principles of Quantum Mechanics by Shankar. This spends more time on the mathematical foundations of QM than Griffiths does and goes into the path integral formalism and touches on relativistic QM towards the end of the book.
10. A First Course in General Relativity by Schutz. There are arbitrarily advanced texts on GR, but I'd recommend starting off with something friendly like Schutz.
11. An Introduction to Elementary Particles by Griffiths. Not super advanced mathematically, but it's a good thing to read over to prepare you for more advanced QFT texts. The first chapter is especially good as a history of the development of particle physics.
12. Quantum Field Theory in a Nutshell by Zee.
13. Modern Classical Physics by Thorne & Blandford. This is a tour de force. It's an enormous book but it really touches on everything that is left out by the above books. It covers optics, fluid dynamics, statistical physics, plasma physics, and more. (I'm currently reading through it and have only gotten through 6 chapters, but it's really an incredible textbook.)
14. Statistical Mechanics: Entropy, Order Parameters, and Complexity by Sethna. This is a really fun book, but almost all the material is in the problems.
Finally, and most importantly --- remember that physics is not a spectator sport! You must do problems. A lot of them --- and hard ones, too!
- Modern Classical Physics is a great book - I've recently started working through it (just about to move on to chapter 2). I'd be interested in chatting about it with others/cross-checking solutions. Anyone who's interested, drop me an email (address in my profile).
If you're thinking of getting it but want to check it out, there's a 2012 draft version that the authors have previously taught from here: http://www.pmaweb.caltech.edu/Courses/ph136/yr2012/. It's not the same as the book, of course, but from a skim it seems quite similar.
- For those who would like a print version, this manuscript eventually got published as Modern Classical Physics https://press.princeton.edu/books/hardcover/9780691159027/mo...
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