Main Question or Discussion Point
Generally speaking, what physics and math should one be comfortable with before taking a course on General Relativity? If it helps, the course will be using Shultz's A First Course in General Relativity.
Presumably the course is for physics students, so it would be unreasonable to assume any of them have prior experience with differential geometry. The math will not be particularly difficult, but it might take a little bit of simmering to let it conceptually sink in. There's a lot of index manipulation and algebra in GR as well, so familiarity with tensors is a plus (but not necessary! Likely, it will be the first time working with these concepts for most of the students).I know very little differential geometry. Although the professor says he'll cover all of the required math as needed, I'm still wary. I have no problem with picking up math as I go (and I've done it before for other classes), I just feel this might be particularly difficult. Has anyone tried it before or taken a similar class?
There are so many different approaches that you can't really speak "generally". In your case, you need the physics and maths necessary to understand Schutz. Schutz says in the preface what you should know. OK this is a bit general & vague, but no one here is going to give any more detailed advice (are they?) The best thing is to start reading Schutz and when/if you get stuck post questions here, or (better) ask your kind lecturer. (He must be kind if he's taking the trouble to give you the mathematics as you go along!)Generally speaking, what physics and math should one be comfortable with before taking a course on General Relativity? If it helps, the course will be using Shultz's A First Course in General Relativity.
Unlike most introductory texts, this one does not assume that the student has already studied electromagnetism in its manifestly relativistic formulation, the theory of electromagnetic waves, or fluid dynamics.
The student is assumed already to have studied: special relativity, including the Lorentz transformation and relativistic mechanics; Euclidean vector calculus; ordinary and simple partial differential equations; thermodynamics and hydrostatics; Newtonian gravity (simple stellar structure would be useful but not essential); and enough elementary quantum mechanics to know what a photon is.
Now, I know this may sounds crazy, but, if you've been exposed to more kinds of math, and different ways of dealing with equations, then MAYBE, just maybe, you'll have a LITTLE more intuition about other maths...The math used in QM has nothing to do with the math used in GR