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I've owned the revised first edition of Frankel's The Geometry of Physics: an Introduction at least since I was a graduate student. The texts I suggest in this answer are largely based on my personal library. Part I: Manifolds, Tensors, and Exterior Forms Contains 6 chapters which construct the canvas on which the later part of the text plays out. I'll ...


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Feeling bad for you with no answers. It might (or might not!) be opposite to the direction you need, but you take a look at the Kreysig book in this area. He was a mathematician but with a very strong sympathy for engineers and physicists. And in any case, it is very strong pedagogically (progression of ideas based on student learning not math efficiency, ...


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