[Math] Mathematical Physics? (Particularly computational)

mp.mathematical-physicssoft-question

I just saw a post like this one, but particularly for statistical mechanics, I thought I'd ask the question in general.

Where does a mathematically trained person go to learn mathematical physics? By that I mean, what books or manuscripts are demanding in the area of mathematical maturity but not particularly demanding in the area of physics knowledge (physics maturity I guess, idk if they use that word in physics?). I myself am particularly interested in computational fluid dynamics and other kinds of computational physics, but I want to keep this general to help as many people as possible. Also, if someone knows a good book for mathematicians to help with one of the biggest difficulties I've found "Physics INTUITION" that'd be helpful.

As usual, one answer per post so votes can be tabulated well.

Best Answer

A classic reference is Courant and Hilbert (volume 1, volume 2).