Description
Book SynopsisMathematical analysis is often referred to as
generalized calculus. But it is much more than that. This book has been written in the belief that emphasizing the inherent nature of a mathematical discipline helps students to understand it better. A large variety of exercises and the inclusion of informal interpretations of many results and examples are included.
Trade Review“[T]his is an attractive text, one that certainly merits a look by anybody trying to find a text for a course in undergraduate analysis.” - Mark Hunacek,
MAA ReviewsTable of Contents
- Introduction and Outline of the Book
- Acknowledgments
- Part 1. Rebuilding the Calculus Building
- Chapter 1. The Real Number System Revisited
- Chapter 2. Sequences and Series of Real Numbers
- Chapter 3. Limit and Continuity of Real Functions
- Chapter 4. Derivative and Differentiation
- Chapter 5. The Riemann Integral
- Part 2. Abstraction and Generalization
- Chapter 6. Basic Theory of Metric Spaces
- Chapter 7. Sequences in General Metric Spaces
- Chapter 8. Limit and Continuity of Functions in Metric Spaces
- Chapter 9. Sequences and Series of Functions
- Appendix
- Bibliography
