Which books to go from calculus to analysis?

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SUMMARY

The discussion centers on transitioning from calculus to advanced calculus and analysis, highlighting the challenges faced by learners. The user initially struggled with Apostol's "Calculus" due to its complexity and opted for a high school calculus book for foundational understanding. Recommendations include reading Schaum's Outline of Advanced Calculus and then progressing to Apostol's volumes, with an emphasis on mastering single-variable calculus before tackling multi-variable calculus and analysis. The consensus is that while Schaum's provides a quick overview, it should not replace comprehensive texts like Apostol.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with Apostol's "Calculus" Volumes 1 and 2
  • Knowledge of Schaum's Outline of Advanced Calculus
  • Ability to grasp mathematical proofs and theorems
NEXT STEPS
  • Read Apostol's "Calculus" Volume 1 for a thorough understanding of single-variable calculus
  • Study Apostol's "Calculus" Volume 2 for multi-variable calculus concepts
  • Explore Schaum's Outline of Advanced Calculus for supplementary material
  • Investigate foundational analysis texts to prepare for advanced topics
USEFUL FOR

Students transitioning from calculus to advanced calculus and analysis, educators seeking structured study plans, and anyone looking to deepen their understanding of mathematical proofs and concepts.

Jimmy84
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I just finished doing pre calculus and I was eager to get started with calculus so I started to read apostol however the book happens to be somewhat dificult for me. It begins proving the exaustation method of Archimedes, and with other subjects, I preferred to start with my brother's high school calculus book which is way easier. I wonder which books should I get for advanced calculus and analysis. Is apostol v2 advanced calculus? I also have mcgraw hill schaums outline of advanced calculus which is 442 pages. I d like to read as less books as possible, In order to have more time to study more advanced math.

Im considering to read as fast as I can the high school calculus book, then to try schaums outline of advanced calculus and then apostol s analysis. but it 'd make me feel bad not to read apostol v1 and v2 a lot.

Any advices about which study plan to follow?
 
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v2 of apostol is multivariable calculus its an extension of the first volume same style, so I am not sure what difference our looking for.
You can't do it all in a month, itl take some time to finish calculus both single and multi. Id recommend after that to then read apostol in you free time etc. in addition with a book on analysis. this i'll probably take more time as analysis is much more difficult to begin with
 
You could probably get the basics of calculus down from a quick reading of the high school book, but once you know more or less what's going on take the time to read Apostol. If you want to understand advanced material, make sure you've got the basics down. Schaum's Outlines aren't bad, but they're certainly no substitute for a more thorough treatment.
 

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