The only rigorous multi-variable analysis that I have read is from Rudin's PMA and it was only two chapters but I am sure that there are more theorems that calculus 3 course cover that was not in the final two chapters from Rudin's PMA.
I need to review multi-variable calculus again because it has been so long since I encountered anything related directly to it but I think it would be better if I read a whole book dedicated to multi-variable analysis than the two chapters from Rudin's and a calculus 3 book.
So I want to ask for rigorous math book for function of several variables and multi-variable analysis.
