Lang S. Undergraduate Analysis

Second edition. — Springer, 1997. — 665 p. — ISBN: 0-387-94841-4.
This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration.
From the reviews: "This material can be gone over quickly by the really well-prepared reader, for it is one of the book’s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it."