Calculus 2 Book: Advice for Portuguese Students

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SUMMARY

The discussion centers on recommended resources for studying Calculus II, specifically for Portuguese students. Key texts mentioned include "Div, Grad, Curl and All That," and popular calculus textbooks by Stewart, Anton, Thomas, and Larson. The forum participants emphasize the importance of consulting multiple authors for a comprehensive understanding, suggesting that pure mathematicians may prefer more analytical texts like those by Spivak, Apostol, or Courant for a second pass through calculus. Additionally, Marsden and Tromba's "Vector Calculus" is noted as a balanced option between rigor and accessibility.

PREREQUISITES
  • Understanding of basic calculus concepts, including single-variable integrals.
  • Familiarity with double and triple integrals.
  • Knowledge of vector calculus fundamentals.
  • Ability to read and interpret mathematical texts in English.
NEXT STEPS
  • Research "Div, Grad, Curl and All That" for insights on vector calculus.
  • Explore free online calculus resources by Strang and Gill.
  • Read reviews of calculus textbooks on Amazon.com to identify the best fit.
  • Study Marsden and Tromba's "Vector Calculus" for a balanced approach to the subject.
USEFUL FOR

Students enrolled in Calculus II, particularly those in Portugal, as well as educators and tutors seeking effective teaching resources for calculus topics.

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Hello I am having calculus 2 at university in my country ( portugal ).
The topics are basically double and triple integrals all the way through stokes.
Do you guys have any advice on a book that could help me study this course?
Thank you very much and I am sorry about my english
 
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There is a book called "Div, Grad, Curl and All That" that has received favorable mention here, but Calculus II is almost always part of any freshman calculus text, unless it has been split up into smaller volumes. So I think the best thing to do is to get as many cheap used versions of the most popular calculus texts ---- Stewart, Anton, Thomas, Larson, etc., as you can. There are also many free versions on the web, e.g. Strang, Gill, and our own Ben Crowell. When I get stuck, I find that reading two or three different authors' explanations of a topic is usually more effective than puzzling over a single text, even if it's the world's best.

Pure mathematicians prefer the more analytical approaches of Spivak, or Apostol, or Courant, but IMO most people would do better approaching those as their second pass through calculus, not their first.

You can find reviews of all of those texts on Amazon.com, or by using the search feature of this forum.
 
Marsden and Tromba have "Vector Calculus" which is not as dumbed down as books like Stewart, but not as rigorous as Spivak Apostol etc., it is somewhere inbetween. In fact, I think books like Stewart are no good for math or physics students. If you want a book that isn't too rigorous, go for Marsden and Tromba.
 

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