Rigorous book for multivariable + vector calc?

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SUMMARY

For rigorous study in multivariable and vector calculus, John Hubbard's "Vector Calculus, Linear Algebra, and Differential Forms" is highly recommended. The discussion emphasizes a preference for classical treatments over modern ones, specifically avoiding Spivak and Munkres. While Apostol's second volume is noted for its content, its high cost and the user's prior knowledge of linear algebra make it less appealing. The focus remains on vector calculus within R3, particularly Stokes' theorem.

PREREQUISITES
  • Understanding of linear algebra concepts
  • Familiarity with multivariable calculus fundamentals
  • Basic knowledge of vector calculus in R3
  • Ability to engage with rigorous mathematical texts
NEXT STEPS
  • Research John Hubbard's "Vector Calculus, Linear Algebra, and Differential Forms"
  • Explore classical texts on multivariable calculus
  • Investigate alternative resources for Stokes' theorem in R3
  • Review Apostol's first edition table of contents for relevant topics
USEFUL FOR

Students and educators in mathematics, particularly those focused on rigorous approaches to multivariable and vector calculus, as well as individuals seeking classical resources over modern treatments.

khemix
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whats a good book to learn multivariable and vector calculus in a rigorous fashion, similar to spivak. id prefer the vector calculus to stick to R3 (ie stokes), ill save the n case for analysis.

apostol II looks like a good book, but its very expensive and i generally don't like apostol. any other books that give a linear algebra treatment?

and please don't recommend spivak manifolds or munkres. those are modern treatments. I am looking for classical.

(note: i would consider apostol II if i had the table of contents for 1st edition; i don't want to pay extra money for linear algebra which i already know)
 
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John Hubbard's Vector Calculus, Linear Algebra, and Differential Forms is outstanding. I recommend it highly.
 

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