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It's quite a stretch to go from the yellow Vector Calculus book straight to Landau and Lifshitz. There should be an intermediate book, something with continuum integrals would do nicely.
Still... It's Landau and Lifshitz, truly a classic!
Historically significant vector analysis text   (2 Comments)
This isn't from Gibbs himself, there's another book for that, though this book is better because it formalised everything, and is pretty darn close to firsthand anyway.
Furthermore it's really not useful, it's a nice historic text, but the modern way of laying out the exercises in a modern textbook is much easier to comprehend.
Simpler book   
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