Self teaching Multivariable calculus

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Self-teaching multivariable calculus can be effectively supported by resources like Stewart's "Multivariable Calculus," Spivak's "Calculus," and Courant's volumes, which offer varying levels of rigor and pedagogical styles. Students are encouraged to seek guidance from their math teachers for additional resources and to focus on mastering the AP Calculus BC material before advancing. Recommendations also include exploring differential equations and linear algebra to build a solid mathematical foundation. Engaging with these texts may require a balance between thoroughness and enjoyment, allowing for selective reading based on personal interest and comprehension. Ultimately, a combination of these resources can enhance understanding and prepare students for higher-level mathematics.
  • #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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