Self teaching Multivariable calculus

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SUMMARY

This discussion centers on self-teaching multivariable calculus, particularly for students seeking resources beyond the AP Calculus BC curriculum. Key recommendations include Stewart's "Multivariable Calculus," Spivak's "Calculus" and "Calculus on Manifolds," and Courant's "Calculus Volume 2." Participants emphasize the importance of rigorous texts like Rudin's "Principles of Mathematical Analysis" and Apostol's works for a deeper understanding of calculus concepts. The conversation highlights the necessity of a solid foundation in single-variable calculus before advancing to multivariable topics.

PREREQUISITES
  • Understanding of single-variable calculus concepts
  • Familiarity with mathematical proofs and analysis
  • Basic knowledge of linear algebra
  • Experience with calculus textbooks, particularly those by Stewart, Spivak, and Courant
NEXT STEPS
  • Study Spivak's "Calculus" for foundational concepts
  • Explore Courant's "Calculus Volume 2" for advanced multivariable topics
  • Learn about differential equations through recommended texts
  • Investigate Apostol's "Calculus" for a rigorous approach to integration and differentiation
USEFUL FOR

Students preparing for advanced mathematics, self-learners in multivariable calculus, and educators seeking quality resources for teaching calculus concepts.

  • #31
does courant go in with the same depth?

thanks :smile:
 
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  • #32
I know that Apostol goes much deeper than Stewart, and I really appreciate that; what I was saying is that I don't enjoy proving things that appear to not require any proof.
 
  • #33
courant does not go into things quite as precisely as apostol. courant is deep, but there is a little more taken for granted. i think courant will assume basic facts from trig as needed, whereas apostol will lay out exactly which proeprties of sina nd cos are going to be used.

they are basically the same properties, but apostol has a fanatical commitment to really spelling out every fact and assumption with complete precision and care.

you can get the idea by going to the library and perusing these two boks, and then comparing with a book like stewart or anton, something along those lines.

apostol and courant are answering questions that do not even arise in books like stewart et al.
 
  • #34
I think Courant may be the book I'm looking for! I'm going to try to check it out as soon as I can.
 

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