Mathematical Analysis and its Inherent Nature

ISBN-13: 9781470428075 / Angielski / Twarda / 2016 / 351 str.

Hossein, Hosseni Giv

Opis

Mathematical 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.

Spis treści

• 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