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Undergraduate Analysis (Undergraduate Texts in Mathematics)
by Serge Lang
ISBN 0387908005 / 9780387908007 / 0-387-90800-5
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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" -AMERICAN MATHEMATICAL SOCIETY [via]