I have recently begun studying fluid dynamics. Coming from a pure mathematics background, there is much about the derivation of the relevant equations I'm still struggling to grasp (a lot of the physics and chemistry that underpin the logic that helps simplify an expression or necessitates adding other effects into the equations). This is clearly a complex, well-studied area so I didn't and don't expect to understand everything immediately. Nevertheless, I have realized that the majority of my confusion comes when the author begins to introduce tensors and/or variational derivatives. Both of these topics I had heard of, but have almost no actual practice in.
I was wondering if there exist good references on these topics that are relatively short and concise. My goal is not to master or understand everything about tensors and variational derivatives but rather have enough of a rudimentary understanding so as to be able to comprehend these fluid governing equation derivations more precisely.
Any suggestions would be greatly appreciated! Links to "cheap" (or better yet free) references would be ideal!