Courant/John vs. Apostol for In-Depth Studying of Calculus?

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Dear Physics Forum personnel,

I would like to investigate the depth of single-variable calculus by reading either Courant/John's "Calculus and Analysis" or Apostol's "Calculus Vol.1". Of course, I know the best route of action is to go to mu university library, but I just found out that all of them were checked out! I am seeking one that covers both theories and applications of 1-variable calculus in an insightful manner. Studying either of those texts will also aid my research in the computation theory and also my preparation for the Putnam Compeititon.

As for my background, I had read Serge Lang's "A First Course in Calculus", and I am currently studying Artin's "Algebra" and Hoffman/Kunze's "Linear Algebra".

Sincerely,
PK
 

Answers and Replies

  • #2
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Anyone?
 
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I have Apostol and Spivak. Spivak is easier to read, however, the exercises in Spivak are a bit more difficult.

I have never seen Courant. Apostol is a good book, but it is written in a formal manner. I quite enjoy it. It is very clear. Even clearer than Stewart Calculus for me.

You cannot go wrong with Apostol. Not sure if it meets your demand for putnam practice.

I think Apostol Calculus would be a great starting point, because you can get familiar with his writing style and tackle his other books. I am looking forward to completing both volumes of Apostol, in order to read his analysis book and his number theory book.

If you do go for Apostol. Volume 1 and 2 can each be found around the 30-40 dollar price range for a hardcover 1st edition. Avoid the paperback from the eastern continents.
They are printed on cheap quality paper, pages can be missing, and the font makes the learning experience not enjoyable.
 
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  • #4
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^
Thank you for the advice! My research adviser strongly recommend to read the analysis books of Rosenlicht, Apostol, Pugh, Rudin, Folland, and Royden, so I switch my plan from reading the advanced calculus books to real analysis books. I have been reading them, and I actually like Apostol's Mathematical Analysis and Pugh's Real Mathematical Analysis. Also according to Professor Apostol, he said that his Calculus books are not prerequisite to his Mathematical Analysis. I really hope that I do not miss anything from those advanced calculus books of Apostol, Spivak, and Courant by jumping directly to the real analysis.
 
  • #5
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Thank you for the advice! My research adviser strongly recommend to read the analysis books of Rosenlicht, Apostol, Pugh, Rudin, Folland, and Royden, so I switch my plan from reading the advanced calculus books to real analysis books. I have been reading them, and I actually like Apostol's Mathematical Analysis and Pugh's Real Mathematical Analysis. Also according to Professor Apostol, he said that his Calculus books are not prerequisite to his Mathematical Analysis. I really hope that I do not miss anything from those advanced calculus books of Apostol, Spivak, and Courant by jumping directly to the real analysis.
Not really a pre-rec. However, doing more rigorous mathematics is great! Helps you over the long run.
 

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