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I've got Spivak and Courant books on calculus for a good price. Which one would you buy to learn calculus deeply and enjoy learning it? What are the ups and downs for each one?

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I highly recommend Courant's Introduction to Calculus and Analysis. Extremely well written and enjoyable to read. Plus you say you want a deep understanding of the material, and Courant's book can certainly provide you with that. –  A.E Aug 14 '13 at 17:55
    
Thanks,could you compare it to spivak or apostol,please? –  Daniel Faust Montana Aug 14 '13 at 22:26
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Sorry Daniel, I have not read either of their texts. –  A.E Aug 14 '13 at 22:27

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Spivak is great book and you can learn some deep ideas about calculus from it. It also has a separate detailed solution manual which can be very helpful with self learning. Another nice thing about Spivak is that it is a good prelude to some of his more advanced books like Calculus on Manifolds. On the down side Spivak's book is not a comprehensive as a good book on real analysis such as Elementary Analysis by Ross or Principles of Mathematical Analysis by Rudin. These texts lay out the deep theorems and definitions on which calculus is based in much more detail that Spivak. Courant is a great book that I would consider somewhere between Spivak and an analysis book but the exposition is not as modern and can therefore be a little difficult for some. All in all I feel the a basic calculus book like Larson followed by Spivak and the finished off by Ross is a great way to get a very deep understanding of calculus.

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Thanks,could you extand your review of courant's book? –  Daniel Faust Montana Aug 14 '13 at 19:24

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