:santagrin: This book was suggested by Bradley Lucier

Book excerpts:

This text covers the basic topics of undergraduate real analysis including metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. The text also contains background material on set theory, the real numbers (including consequences of the completeness axiom), and Euclidean and vector spaces, taken from the author's Basic Concepts of Mathematics.

This text is designed to be used as early as possible in the undergraduate curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

Intended Audience:

This text is appropriate for any undergraduate course in real analysis or mathematical analysis, or for a preparatory class for beginning graduate students who will later advance to courses in measure theory and functional analysis. Lecturers can use the author's Basic Concepts of Mathematics, which contains expanded versions of Chapters 1 and 2 and Sections 1 through 10 of Chapter 3 of the present text, as supplementary background material for this text.

Reviews:

theassayer.org

:) "Zakon's 'Mathematical Analysis I' will show you how easy somethings can be by presenting the material in a nice, kind and very clear way with examples and everything you could expect to get a solid background on the subject. "