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Название: Differential forms in mathematical physics
Автор: Westenholz C.
Three things make this book shine: 1. the amount of material in it, 2. the very neat fashion in which it's organized, and 3. the amount of examples found in it. It explains the application of differential geometry to mechanics, electrodynamics, thermodynamics and even has a chapter on general relativity! In short, once you've completed an introductory book, this will definitely be a good choice for a second book.