Should Apostol's calculus be supplemented with Courant/Spivak

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Discussion Overview

The discussion revolves around the necessity of supplementing Apostol's "Calculus - Volume 1" with other calculus texts, specifically Courant's "Introduction to Calculus and Analysis" or Spivak's "Calculus." Participants explore the implications of studying Apostol alone versus incorporating additional resources, especially in the context of preparing for Rudin's "Real Analysis."

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant expresses confidence in studying solely from Apostol and questions the need for additional texts like Courant or Spivak.
  • Another participant suggests that studying directly from Spivak's "Calculus" may be beneficial.
  • A different participant argues that mastering Apostol is sufficient and recommends revisiting earlier chapters if difficulties arise.
  • There is a shared sentiment among some participants that completing Apostol negates the need for supplementary texts.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the necessity of supplemental texts, with some advocating for studying only Apostol and others suggesting the value of Spivak or Courant. The discussion remains unresolved as no consensus is reached.

Contextual Notes

Participants mention the challenge of retaining flow in study after a gap, indicating that refreshing older concepts may be necessary. However, there is no agreement on the best approach to address this issue.

capsicum
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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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