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Single and multivariable calculus and analysis

Differential Equations

Partial Differential equations

but I would like it if someone could tell me if there is anything else. Thank you!

- Thread starter fuzzy127
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- #1

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Single and multivariable calculus and analysis

Differential Equations

Partial Differential equations

but I would like it if someone could tell me if there is anything else. Thank you!

- #2

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I would also like to know...

- #3

dx

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- #4

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Thanks and regards,

Mitesh

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On a more serious note, your question doesn't have a specific answer. Certainly, most of the essential structure of Minkowski space and the behaviour of systems within Minkowski space can be put on a rigorous footing with just an understanding of the existence and uniqueness theorems of ODEs. The more powerful PDE techniques, particularly those involving Sobolev spaces and the sub- and super-solution methods become crucially important when looking at something like existence of solutions to the constraint equations of general relativity, but aren't immediately applicable to special relativity. General relativity also would require, of course, a good knowledge of differential geometry (at least to graduate level) if you were interested in looking at non-trivial mathematical results; again, this isn't really an issue in special relativity.

That's not to say that special relativity is trivial: if you're interested in studying something along the lines of the semiclassical stability of Minkowski space, a PhD in mathematics and a tenured position would probably be sufficient. (cf. Christodoulou's book on semiclassical stability.) :-)

- #6

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Thanks for your reply, however, as of now, I am actively involved in chemistry, and wish to study SR (and GR too), by self learning. My uni doesn't provide any courses in any of the subjects sited above, and hence, I would be dependent largely on internet. As it may be, thanks again for the reply.

Regards,

Mitesh

- #7

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an old thread:

https://www.physicsforums.com/showthread.php?t=144202

https://www.physicsforums.com/showthread.php?t=144202

- #8

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Thanks!

One word - Overwhelming!

Regards,

Mitesh

One word - Overwhelming!

Regards,

Mitesh

- #9

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Well, I was responding to the OP, but okay.

Thanks for your reply, however, as of now, I am actively involved in chemistry, and wish to study SR (and GR too), by self learning. My uni doesn't provide any courses in any of the subjects sited above, and hence, I would be dependent largely on internet. As it may be, thanks again for the reply.

Regards,

Mitesh

- #10

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However, if you're starting out, you should definitely consider looking at Spacetime Physics (https://www.amazon.com/dp/0716723271/?tag=pfamazon01-20&tag=pfamazon01-20) and 'Introduction to Special Relativity' by Robert Resnick (https://www.amazon.com/dp/0471717258/?tag=pfamazon01-20&tag=pfamazon01-20).

After reading special relativity at the level of these books, you can refer to books on general relativity (some of which will also introduce special relativity from a more mathematically rigorous standpoint) such as the books by Jim Hartle and Tai Pei Cheng. Books are more a matter of personal taste, but the reason I mentioned books in my response was to give you some idea of the content and presentation style. Books on GR for instance, will generally not dwell much on the basic consequences of SR but will assume that readers are already familiar with them.

PS--When you start out, the level of mathematics is really limited to a little bit of differential and integral calculus, trigonometry and geometry. After that, as OP have pointed out, you will need PDEs and differential geometry.

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- #12

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I wouldn't worry about classes in DEs because Einstein's equations are nonlinear, the DEs classes usually show you how to solve linear equations, and when they're not they're still not as hard as what you see in GR. The only two solutions you'll see in a textbook on GR are the vacuum solution and the wave equation, where you don't really need to know alot about solving DEs to get how they're solved.

One other thing on the physics side, you should study Newtonian gravity because you can get it back out in the appropriate limits, and if you know it well you might appreciate better when the theories act the same way and when they are different.

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