Which Calculus Book Gives Best Understanding: Spivak or Apostol?

[bennington]

I am looking for a calculus book that gives the reader deep understanding of how calculus works, not just rote memorization. I have heard that the books by Micahel Spivak and Tom Apostol are good. Which of the books provides the best understanding of calculus: Spivak's or Apostol's? My parents will only let me buy one of the authors, so that's why I have to chose.

 

[axeae]

I haven't actually read either of their calculus books, but spivak covers "multivariable" calculus (and much more) in his calculus on manifolds text, and I believe apostol's text actually has two volumes. I've also heard apostol introduces calculus out of order when compared to most texts (I thought I read that he does integration before differenation? or maybe not). another text you might want to check out is the one by Courant or Courant and John. That one is also split up into several texts as well though.

 

[bennington]

I haven't actually read either of their calculus books, but spivak covers "multivariable" calculus (and much more) in his calculus on manifolds text, and I believe apostol's text actually has two volumes. I've also heard apostol introduces calculus out of order when compared to most texts (I thought I read that he does integration before differenation? or maybe not). another text you might want to check out is the one by Courant or Courant and John. That one is also split up into several texts as well though.

So does Spivak or Apostol have more content? I am learning this through self-learning, so I am looking for the most comprehensive one(s).

 

[Howers]

So does Spivak or Apostol have more content? I am learning this through self-learning, so I am looking for the most comprehensive one(s).

Apostol probably has more content. The other user was referring to a book on manifolds, which is sort of like Spivak's volume 2.

I would choose Spivak over Apostol. Apostol has a very good detailed history on calculus and all, but I don't like how he organizes the book. You can also get an answer book for Spivak. Either book is solid though.

 

[JG89]

I have Calculus by Apostol and Introduction to Calculus and Analysis by Courant and Fritz.

They both treat integration before differentiation, which I don't mind at all. I chose Apostol over Courant as I like his style more. I haven't seen much of Spivak, but for what it's worth, you can't go wrong with Apostol...

 

[^_^physicist]

Spivak is a great choice for a calculus text, especially if you plan on eventually studying Differential Geometry, since it gets you use to his style of writing.

 

[WiFO215]

I haven't seen Spivak but I own Apostol. Reading volume I. It is very thorough. And there is no order set in stone to introduce differentiation and integration. I liked it with integration first. Apostol is also very clear. No BS in his book. Everything comes with a proof and detailed analysis. I strongly recommend Apostol.

EDIT: The best person to judge this in my opinion is Mathwonk.

 

[Howers]

EDIT: The best person to judge this in my opinion is Mathwonk.

He is a geometer, and will certainly pick Spivak

And really, its not a big deal over which book you use. They contain the same information.

 

[qspeechc]

I think "Introduction to Calculus and Analysis" by Courant and Fritz is excellent, together with the price, it's unbeatable.

 

[JG89]

The Courant and Fritz book also has some applications to physics in it and also goes into Fourier series.