Exploring Calculus: Spivaks' & Apostols' Books & Experiences

[torquerotates]

Hi this question is for all you math people out there. But as you will find shortly, its very specific. I'm interested in learning calculus deeply. I learned nothing in the watered down calculus that is so readily offered because of the disenchantment with "Ivory tower education". But anyways. I'm still in the process of descideing between two supposibly excellent books that treats calculus in a rigorous manner. Spivaks' Calculus and Apostals' Calculus. Did anyone have positive experiences with any of these two? What was frustrating about going through these books? Did you gain anything that you wouldn't have if you just went to traditional route to real analysis?

On a side note: I noticed that all of Spivak's problems are out there in the form of a solutions manual. Can the same be said of Apostol?

 

[john16O]

defiantly go with apostal, It is really dense but if you can learn calculus from that textbook than you can learn it from any other. It is also used at caltech and here is the website that has questions and solutions to the things that were taught in class. I would suggest that if you do go with apostal then try doing these assignments. lol and i cannot find the link but when i do i will post it on here for you

 

[PowerIso]

I took calculus from Apostal. It was a kick in the nuts for my first college math course. Apostal is unique because it starts out with integration and is very proof driven. I think it gives you a nice perspective of what Calculus can be. It was a perspective I wouldn't have until I took advance calculus a few years later. I noticed that taking calculus with theory gave me a leg up on everyone else who did not.

If you can work through Apostal and understand a good deal that he is saying, you will know more about calculus than most people. Even now as I look through the book again, I find new bits and pieces of information that make things become more clear.

I can't speak to much for Spivak, I never read it, but I hear it's good and more theoretical than Apostal (hard to imagine.)