What's a good book after Kline's Calculus?

[foolsgold229]

Exactly as the title asks, I'm wondering what would be the best continuation to Kline's Calculus textbook. I honestly have found it to be absolutely excellent so far but where would I move to from there? Going to Spivak seems redundant but going to Apostol Vol. 2 seems like it'd be too much of a rigorous leap from the applied/physics-based Calculus that is Kline. Or is it? I'm not really sure... Please advise.

 

[verty]

What is it that you want to learn from this new book?

 

[micromass]

If you are interested in pure mathematics, then I can assure you that Spivak will not be redundant.

 

[foolsgold229]

Well, I'm interested in learning multivariate calculus but more so in an introduction to analysis. Though it would seem like Spivak would be the answer. Would it be possible to move from Kline to Apostol Vol. 2 though, for example?

 

[micromass]

Well, I'm interested in learning multivariate calculus but more so in an introduction to analysis. Though it would seem like Spivak would be the answer. Would it be possible to move from Kline to Apostol Vol. 2 though, for example?

For some it is possible, for others not. I would say that for most people it is not possible. But you should probably try yourself.

One other thing, if I'm not mistaken then the end volume of Apostol contains an intro to linear algebra. You will definitely need this for Apostol 2.

 

[foolsgold229]

Thank you. I'll certainly consider perhaps going through Apostol Vol. I then. So long as it's not merely a rehash of what I learned from Kline.

 

[micromass]

Thank you. I'll certainly consider perhaps going through Apostol Vol. I then.

Well, that seems redundant. Why not Spivak's Calculus and follow-up with his calculus on manifolds or something?