Which one is the real deal for multivariable calculus?

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SUMMARY

The discussion centers on the best resources for learning multivariable calculus, specifically comparing "Advanced Calculus: A Differential Forms Approach" by Harold Edwards, "Advanced Calculus of Several Variables" by C. H. Edwards Jr., and "Functions of Several Variables" by Fleming. Participants highlight the importance of geometric intuition combined with rigor in these texts. Concerns about the potential outdatedness of the materials and the effectiveness of linear algebra introductions in Edwards' book are also raised, suggesting a preference for more intuitive approaches.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with linear algebra principles
  • Knowledge of differential forms
  • Ability to interpret geometric representations in mathematics
NEXT STEPS
  • Research "Advanced Calculus: A Differential Forms Approach" by Harold Edwards for its approach to linear algebra
  • Explore "Functions of Several Variables" by Fleming for geometric intuition in multivariable calculus
  • Investigate reviews and comparisons of multivariable calculus textbooks
  • Study the role of geometric intuition in advanced calculus learning
USEFUL FOR

Students and educators in mathematics, particularly those focusing on multivariable calculus, as well as anyone seeking rigorous yet intuitive resources for advanced calculus studies.

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P.S are any of these book too old,or have bad or outdated notion?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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