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I would like some recommendations on multivariable calculus books.

I already have Susan Jane Colley's "Vector Calculus" and I am planning to get Marsden's book as well(mainly because I can get it for free).

I am not completely satisfied with Colley's book for a few reasons, the main one being the lack of rigour in certain points ( previously I worked through most of Spivak's book and that was quite a transition as far as rigour is concerned).

Any further recommendations?

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  • $\begingroup$ Spivak's book isn't even close to comprehensive (e.g., doesn't cover things like Lagrange multipliers) and it's a bit too abstract. $\endgroup$ – MathematicsStudent1122 Feb 24 '18 at 1:50
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I recommend Hubbard&Hubbard since it has some sophistication that might be appreciated after becoming acquainted with Spivak, but also does not adopt the same ultra-rigorous style.

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Analysis on manifolds by James Munkres is probably better than Spivak. Should be rigorous enough.

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