Which one is the real deal for multivariable calculus?

AI Thread Summary
The discussion focuses on selecting a suitable multivariable calculus textbook, with specific interest in books that provide a rigorous yet geometric approach. Key titles mentioned include "Advanced Calculus: A Differential Forms Approach" by Harold Edwards and "Advanced Calculus of Several Variables" by C. H. Edwards Jr., both of which are praised for their depth. Additionally, "Functions of Several Variables" by Fleming is considered, with questions raised about its comparative quality. Concerns about the potential outdatedness of these texts and the introduction of linear algebra in Edwards' book are noted, particularly regarding its notation. The discussion seeks recommendations for books that balance intuition, rigor, and geometric insight, highlighting the need for contemporary resources that maintain relevance in teaching multivariable calculus effectively.
theoristo
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I'm trying to learn multivariable calculus,and I've heard that one of these is fabulous(the authors have the same name):Advanced Calculus: A Differential Forms Approach by Harold Edwards https://www.amazon.com/dp/0817637079/?tag=pfamazon01-20 or Advanced Calculus of Several Variables by C. H. Edwards Jr.?There 's also Functions of Several Variables By Fleming https://www.amazon.com/dp/0387902066/?tag=pfamazon01-20, is it any better?I like books with a geometric flavor but still rigourous and with a lot of depth,any suggestion would be helpful,thanks.
P.S are any of these book too old,or have bad or outdated notion?
 
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I've read a bit of Advanced Calculus: A Differential Forms Approach ,it seems to introduce linear algebra with some tedious stuff especially the notation,does that make Fleming's book better?please,is there someone who used these books ,or knows something better(intuitive,rigourous and with ''geometric intuition'')?
 
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