Multivariable Calculus Texts - Spivak Reviewed

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SUMMARY

The discussion centers on recommended texts for multivariable calculus, highlighting Spivak's "Calculus" as a foundational read. Participants suggest Wilfred Kaplan's "Advanced Calculus" and Piskunov's "Volume 2" as excellent starting points. For advanced study, Richard Courant and John Fritz's "Volume 2 Parts 1 and 2" are recommended. Additionally, Spivak's "Calculus on Manifolds" is noted, with a prerequisite understanding of linear algebra concepts such as linear combinations and matrix operations.

PREREQUISITES
  • Linear algebra concepts including linear combinations and matrix operations
  • Understanding of inverse matrices and linear dependence/independence
  • Familiarity with determinants and linear transformations
  • Knowledge of vector spaces and basis for spaces
NEXT STEPS
  • Study Wilfred Kaplan's "Advanced Calculus" for foundational concepts
  • Explore Piskunov's "Volume 2" for additional multivariable calculus insights
  • Read Richard Courant and John Fritz's "Volume 2 Parts 1 and 2" for advanced topics
  • Learn linear algebra fundamentals to prepare for Spivak's "Calculus on Manifolds"
USEFUL FOR

Students and educators in mathematics, particularly those focusing on multivariable calculus and linear algebra, will benefit from this discussion.

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what is a good multi variable calculus text
i have just finished reading spivak's calculus
thanks
 
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I like Wilfred Kaplan Advanced Calculus to start, also Piskunov Volume 2 is pretty decent. For more advanced, you can see Volume 2 Part 1 and Part 2 of Richard Courant and John Fritz.
 
You could move on to calculus on manifolds by spivak, but you would need some linear algebra first (which you should probably learn before multivariable calculus anyways) . Specifically linear combinations, matrix operations and inverse matrices, linear dependence/independence, determinants, linear transformations, spaces and basis for spaces would all be helpful to know.
 

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