Mathematical Analysis (Volume I)

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 postcalculus 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.

Contents

• Chapter 1. Set Theory
• Chapter 2. Real Numbers. Fields
• Chapter 3. Vector Spaces. Metric Spaces
• Chapter 4. Function Limits and Continuity
• Chapter 5. Differentiation and Antidifferentiation

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