Regarding the book, "Vector Calculus" by Peter Baxandall is a well-known textbook that covers the basics of vector calculus, including vectors, curves, and surfaces, as well as more advanced topics like differential forms and integration.
Originally published in 1986 by Clarendon Press (Oxford University Press), the book is widely used in undergraduate mathematics courses. It is currently available as an affordable reprint through Dover Publications Key Features Rigorous Foundation vector calculus peter baxandall pdf verified
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