There a lot of textbooks on multivariable calculus, but most of them are really far away from being rigorous. Is there a rigorous, solid and comprehensive textbook on the subject?
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The reason why is that multivariate calculus is kinda the baby name for the subject. The name of the subject for those interested in rigor is analysis (in your case, likely real analysis). – Rushabh Mehta Oct 09 '21 at 16:19
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Can't go wrong with Rudin's Principles of Mathematical Analysis. Should cover everything, and I think it even has an introduction to forms
Kesav Krishnan
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