Should Apostol's calculus be supplemented with Courant/Spivak

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SUMMARY

The discussion centers on the necessity of supplementing Apostol's "Calculus - Volume 1" with Courant's "Introduction to Calculus and Analysis" or Spivak's "Calculus." The consensus among participants is that mastering Apostol's material is sufficient for progressing to Rudin's "Principles of Mathematical Analysis." Participants recommend reviewing previous chapters in Apostol to regain understanding after breaks in study, rather than starting over or relying on supplementary texts.

PREREQUISITES
  • Understanding of Apostol's "Calculus - Volume 1"
  • Familiarity with Rudin's "Principles of Mathematical Analysis"
  • Basic knowledge of calculus concepts
  • Ability to solve calculus exercises independently
NEXT STEPS
  • Review Apostol's previous chapters to reinforce understanding
  • Explore advanced topics in Rudin's "Principles of Mathematical Analysis"
  • Consider studying Spivak's "Calculus" for alternative perspectives
  • Investigate Courant's "Introduction to Calculus and Analysis" for additional insights
USEFUL FOR

Students of mathematics, particularly those studying calculus and preparing for real analysis, as well as educators seeking to understand the interplay between different calculus texts.

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Hello ,
I am currently studying from the book Calculus - Volume 1 by Apostol . I am doing it as a pre cursor to studying Real Analysis by Rudin.

I am currently on the second chapter of the book. I am solving the exercises as best as I can.
My question is , while I am doing this book is it necessary to supplement it with a book such as 'Introduction to calculus and Analysis' by Courant or Spivak's Calculus. I usually don't face any difficulties in understanding the material from Apostol.

What has happened is that there has been a 1 month gap since I studied it last. And I am unable to gain the flow which I initially had with the book. This has happened because sometimes I have to refresh some of the older concepts. Should I restart the book from the beginning to regain the flow or should I use Courant's book to do those parts ?

Is it possible to approach Rudin after doing Apostol's book or one should also attempt Spivak/Courant before doing so?
 
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My opinion is that you should study straight from Spivak's Calculus.
 
Only doing Apostol should be enough. Spivak or Courant is on the same level as Apostol.
If you're stuck you should read previous chapters to refresh your memory.
 
I agree with micromass. If you master and complete Apostol, there is no need to read Spivak or Courant.
 

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