This free ebook carefully leads the student through the basic topics of undergraduate real analysis. This text is appropriate for any undergraduate mathematics course in real analysis or mathematical analysis, or for a preparatory class for beginning mathematics graduate students who will later advance to courses in measure theory and functional analysis.

## Book Description

Knowledge of this material will also be of benefit to graduate students in economics, signal and image processing, fluid and structural mechanics, etc.

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 Dieudonn´e’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.

## Table of Contents

- Set Theory
- Real Numbers. Fields
- Vector Spaces. Metric Spaces
- Function Limits and Continuity
- Differentiation and Antidifferentiation