Calculus in UK/USA and math analysis in wester europe - is this the same?

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SUMMARY

The discussion centers on the comparison of calculus and mathematical analysis curricula between the UK/USA and Western Europe. It confirms that key topics such as L'Hôpital's rule, Taylor's theorem, and the definitions of limits (Cauchy's and Heine's) are included in "Calculus" by Michael Spivak. Additionally, it asserts that these topics are also covered in analysis courses in the US, indicating a significant overlap in content. The user seeks clarity on whether Spivak's book aligns with their math analysis course requirements.

PREREQUISITES
  • Understanding of calculus concepts, specifically limits and series.
  • Familiarity with L'Hôpital's rule and Taylor's theorem.
  • Knowledge of functional maxima and minima.
  • Basic skills in integration techniques, including substitution.
NEXT STEPS
  • Review "Calculus" by Michael Spivak for comprehensive coverage of calculus topics.
  • Study the definitions of limits, focusing on Cauchy's and Heine's definitions.
  • Explore advanced integration techniques, particularly integration by substitution.
  • Investigate the curriculum differences in mathematical analysis courses across the UK and Western Europe.
USEFUL FOR

Students and educators in mathematics, particularly those studying calculus and mathematical analysis, as well as curriculum developers comparing educational standards between regions.

hellbike
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I would like to use book for calculus, but I'm not sure if it cover my "math analysis" course.

And i can't tell that from reading content... So i'll give you some examples of assertions(or definitions), and you tell me, if they are discussed in "Calculus" by Michael Spivak.

Three series theorem
Both, Cauchy's and Heine's definition of limit.
Assertion about two functions(if we got two functions and one is greater (>), and the less one limit is inf, then bigger function limit is also inf)
L'Hôpital's rule
Taylor's theorem
functional maxima and minima
indefinite and definite integral
integration by substitution
 
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dunno aboot western Europe but those topics you mentioned are covered in Analysis course in US as well.
 

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