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Harold Edwards: Advanced Calculus: A Differential Forms Approach (https://www.maa.org/press/maa-reviews/advanced-calculus-a-di....)

Tristan Needham: Visual Complex Analysis (https://www.maa.org/press/maa-reviews/visual-complex-analysi...)

Tristan Needham: Visual Differential Geometry and Forms (https://press.princeton.edu/books/paperback/9780691203706/vi...)

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Damn! You beat me to mentioning Harold Edwards' book, as it perfectly fits the description. The first three chapters are intuition and concept building, the next three chapters revisit the topics with more rigor and proofs, and then there are follow-on applications chapters with all sorts of nuggets. It is virtually mistake free and can be opened up and read at any point and still be understood, a stated goal of the author.

Thank you! I really loved Visual Complex Analysis..and started Needham's next book, which just arrived in the mail! :-) Worth it for all the other great books he mentions alone. It's also awesome, very much a sequel to VCA.

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