Dear Physics Forum advisers, Could you recommend books that treat the multivariable calculus from a theoretical aspect (and applications too, if possible)? I have been reading Rudin's PMA and Apostol's Mathematical Analysis, but their treatment of vector calculus is very confusing and not really motivating at all. I unfortunately did not take a Calculus III course, so I am not familiar with the elementary presentation of the calculus of several variables. However, I am very determined to learn it. I know books like Kaplan, Buck, Loomis/Sternberg, Hubbard/Hubbard, Apostol's Calculus, and Zorich, but I personally never had a chance to look through them. All of them were checked out. Is any of them good for learning the multivariable calculus? By the way, I see many names for "calculus of several variables" in the Tags column: multivariate calculus, multivariable calculus, vector calculus, calculus on manifolds, manifolds analysis, etc. Several of the books I mentioned have title called "Advanced Calculus". Are they same description for studying the multivariable calculus?