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Currently reading Manifolds, Tensor Analysis, and Applications by Abraham et al. Basically, how do you do geometry and calculus on surfaces or objects that are enough like a surface?
For STEM nerds: this book discusses manifolds in infinite dimensional spaces as well as finite dimensions. I believe there is a fluid dynamics application in the book that requires the infinite dimensional theory. There are far simpler books to learn this material if you just need to speedrun into calculations, but I really want the "full story".