Studying Picking up necessary Classical Mechanics and E&M for GR

[PhotonSSBM]

My professor is mentoring me through learning GR over the next year with the goal of doing research with me in the long term in the field. I need to pick up a few things along the way. The summer is going to be spent mostly picking up the necessary material for jumping into Carroll's book, and actually starting work in the book and whatever else my professor has me do during the last month before next semester. I want to consolidate my efforts and pick up the necessary parts of Classical Mechanics and E&M. Having already completed all my math classes besides statistics and math methods, and having a strong understanding of SR and setting up differential equations for physics problems, where should I focus my attention in both CM and E&M.Right now I'm working through a Boas' section on Tensor Analysis and trying to get used to the Euler-Lagrange equation's setups and applications from Taylor's book. I'm unsure of what to prioritize in E&M however, and my professor has said it may be overkill to get into the nitty, gritty, PDE aspects of E&M. I thought I'd ask your opinions, not because I don't trust his opinions, but because I feel it will help to get others' perspectives which I feel is a healthy way to approach research in general.

TLDR: What are the quintessential pieces of Classical Mechanics and E&M that are necessary to begin to tackle GR?

 

[robphy]

What aspects of GR?

I would suggest at least...
- Euler-Lagrange equations
- planetary orbits
- Maxwell Equations (in terms of E and B in vector and [spatial-]tensor calculus notation, and in terms of the Field Tensor)
- wave equation
- develop a comfort with tensor notation
- tensor/vector calculus using rectangular, cylindrical, and spherical coordinates
- would be nice to derive the Maxwell Equations from the Euler-Lagrange equations
- develop some geometrical intuition along with the tensor notation