What is the best book for learning Calculus at a higher depth?

[NeoXx]

Hello,

I am an A-level student in Cambridge finishing the A2.
From doing Mathematics I got very interested in Calculus, and
now I'm looking for a complete course for Calculus in order to
learn it at a much higher depth.

Can anyone suggest a great book on Calculus?


Regards,

NeoXx

 

[micromass]

If you already are familiar with some calculus (like knowing roughly what derivatives are and what continuity is), then you're ready to tackle the big boys:

There's Spivak's "Calculus". This is very challenging but will give you a divine mastery of calculus.
There is Apostol's "Calculus" which is very similar to Spivak. I do somehow get the feeling that Spivak is a bit more theoretical.

 

[NeoXx]

If you already are familiar with some calculus (like knowing roughly what derivatives are and what continuity is), then you're ready to tackle the big boys:

There's Spivak's "Calculus". This is very challenging but will give you a divine mastery of calculus.
There is Apostol's "Calculus" which is very similar to Spivak. I do somehow get the feeling that Spivak is a bit more theoretical.

Thank you for your answer. Yes I am familiar with some calculus.
Will take a look at those books. :)

 

[JPKelly6]

I read about the first 200 pages of Spivak before switching to Apostol. In my opinion the books have very little in common.
Spivak is really an intro analysis book & does not spend enough time on the math that you need to know for physics. However, it is great for learning to do proofs & the details of number theory. He starts from ground zero & builds up numbertheory followed by calculus, so the start is somewhat slow.
Apostol is superb. The two volumes must be the best there is for a science major (with the possible exception of Currant).
Morris Kline's text is great for self study & spends a good amount of time on applications. Reading it is like sitting in a lecture with a friendly wise professor.
If you want to rapidly become proficient & skip the proofs, then Technical Calculus with Analytic Geometry (Dover Books on Mathematics) by Judith L. Gersting is hard to beat.

John Kelly

 

[micromass]

I read about the first 200 pages of Spivak before switching to Apostol. In my opinion the books have very little in common.
Spivak is really an intro analysis book & does not spend enough time on the math that you need to know for physics. However, it is great for learning to do proofs & the details of number theory. He starts from ground zero & builds up numbertheory followed by calculus, so the start is somewhat slow.
Apostol is superb. The two volumes must be the best there is for a science major (with the possible exception of Currant).
Morris Kline's text is great for self study & spends a good amount of time on applications. Reading it is like sitting in a lecture with a friendly wise professor.
If you want to rapidly become proficient & skip the proofs, then Technical Calculus with Analytic Geometry (Dover Books on Mathematics) by Judith L. Gersting is hard to beat.

John Kelly

Just to be clear: Spivak doesn't do number theory. It covers axioms of the real numbers and then builds everything from that. This is very different from number theory.

I do agree that if you just want to do calculus for physics, then all you need to know are computations. Spivak (and even Apostol) will be overkill for this goal. Spivak is however an excellent book for math majors or people interested in the mathematics (such as theoretical or mathematical physicists). The exercises in Apostol are more applied and less theoretical, but it's still quite a theoretical book.

 

[xristy]

I prefer Courant & John's 2 volumes "Introduction to Calculus and Analysis" to Spivak for a treatment balanced between math and physics. Also Hardy's "A Course in Pure Mathematics" follows right from A2 I believe. Shortly after Spivak was published it was used for my calculus I course and the next year Courant and John's second volume was used for calculus 2. I found the latter a whole lot more satisfying as a text.