Suggestions of books more complex than Spivak and Apostol for Calculus 1?

Question

I've been using Apostol and reusing until got satisfied, I've done the same with Spivak, and I wan't to take another level now.

Answer 1

Perhaps that Jean Dieudonné's Foundations of Modern Analysis would be appropriate.

Answer 2

If you really want another level, why seek a calculus book? Get something on real and/or complex analysis, or functional analysis, for instance:

• Rudin, Real and Complex Analysis
• Stein & Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces and Complex Analysis
• Yeh, Real Analysis: Theory of Measure and Integration

You should clarify the expected level, and the goal: self learning? Follow a course (then lookup the recommended reading)?

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Answer to the comment below

You can't go too far. I asked the goal because I see (mainly) two possible situations:

• You want to improve grades for your current calculus class. Then it's ok to stick with calculus material, but it's also a good idea to read material from 1 or 2 years ahead (not more), to see where what you are currently learning is leading, and to get a better understanding of the "landscape". I would recommend this, especially if you are comfortable with your current courses.
• You want to learn on your own. Then the only limit is your capacity to digest new and difficult stuff. Good books help (IMO, Yeh is great for self learning, Rudin not so much). And you can choose whatever you like, so it can't be wrong to learn advanced stuff in analysis if you like it.

What's the goal? Do you plan to study mathematics at an advanced level, and to prepare now for the next level, or (for instance) to turn to applied maths and engineering? Or something else?