Zakon E. Mathematical Analysis I

West Lafayette: The Triillia Group, 2017. — 365 p. (corrected edition)This text is an outgrowth of lectures given at the University of Windsor, Canada. One of our main objectives is updating the undergraduate analysis as a rigorous post calculus course. While such excellent books as Dieudonne’s "Foundations of Modern Analysis" are addressed mainly to graduate students, we try to simplify the modern Bourbaki approach to make it accessible to sufficiently advanced undergraduates. On the other hand, we endeavor not to lose contact with classical texts, still widely in use. Thus, unlike Dieudonne, we retain the classical notion of a derivative as a number (or vector), not a linear transformation.About the Author.
Set Theory.
Real Numbers. Fields.
Vector Spaces. Metric Spaces.
Function Limits and Continuity.
Differentiation and Antidifferentiation.