If I were teaching analysis to a class of undergrad sophomores without much mathematical maturity I would use

1) Real Analysis by Howie, published by Springer

and/or

2) A Radical Approach to Real Analysis by Bressoud, published by the Mathematical Association of America.

If the class was a trifle more mature, either

3) Undergraduate Analysis, by Abbott, pub. by Spinger,

or

4) Real Mathemaical Analysis, by Pugh, pub. Springer.

__Postscript__: The previous poster mentioned Marsden, which reminds me of Marsden's "Elementary Classical Analysis." This is another phenomenal book, roughly at the level of Apostol, but to my mind written in a more limpid style. I don't kniw if it's in print anymore.