Is Elementary Analysis Enough for Understanding Calculus Theory?

[Lechuguin]

Hi all, this is my first post. I'm going to take my fist analysis class next semester. I wanted to know if it is better to learn some more theory of calculus I and II stuff with a more advanced book like Spivak or Apostol (I used Thomas' Calculus to learn I and II stuff) or take a quick look at analysis with an introduction book like Ross' Elementary Analysis? Would it fill the calculus theory gap I think i have?

Lechu

 

[muppet]

Hi lechuguin,
I can't comment on the content of "Calculus I and II", as I'm not familiar with the american system. But I would point out that there is a difference between calculus and analysis, and the seemingly obvious conclusion to draw from this is that the analysis text would be better suited to your course. Most calculus texts include a certain degree of analysis (particular the idea of a limit, and so usually of epsilon-delta proofs) as it is essential for the theory of calculus, but analysis is a broader topic than just the idea of limit and continuity of functions. Typically a first analysis course will also contain notions about series and sequences, some theorems about complex variables, etc that might be omitted from a calculus-orientated presentation. The best thing to do would be to try and find some kind of syllabus for the module off the internet, and see how well the book measures up to that.