Mathematical Analysis and Its Inherent Nature
Seiten
2016
American Mathematical Society (Verlag)
978-1-4704-2807-5 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2807-5 (ISBN)
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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.
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. With this in mind, and focusing on the essence of analysis, the text is divided into two parts based on the way they are related to calculus: completion and abstraction. The first part describes those aspects of analysis which complete a corresponding area of calculus theoretically, while the second part concentrates on the way analysis generalizes some aspects of calculus to a more general framework. Presenting the contents in this way has an important advantage: students first learn the most important aspects of analysis on the classical space R and then fill in the gaps of their calculus-based knowledge. Then they proceed to a step-by-step development of an abstract theory, namely, the theory of metric spaces which explores such crucial notions as limit, continuity, and convergence in a wider context.
The readers are assumed to have passed courses in one- and several-variable calculus and an elementary course on the foundations of mathematics. A large variety of exercises and the inclusion of informal interpretations of many results and examples will greatly facilitate the reader's study of the subject.
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. With this in mind, and focusing on the essence of analysis, the text is divided into two parts based on the way they are related to calculus: completion and abstraction. The first part describes those aspects of analysis which complete a corresponding area of calculus theoretically, while the second part concentrates on the way analysis generalizes some aspects of calculus to a more general framework. Presenting the contents in this way has an important advantage: students first learn the most important aspects of analysis on the classical space R and then fill in the gaps of their calculus-based knowledge. Then they proceed to a step-by-step development of an abstract theory, namely, the theory of metric spaces which explores such crucial notions as limit, continuity, and convergence in a wider context.
The readers are assumed to have passed courses in one- and several-variable calculus and an elementary course on the foundations of mathematics. A large variety of exercises and the inclusion of informal interpretations of many results and examples will greatly facilitate the reader's study of the subject.
Hossein, Hossein GivUniversity of Sistan and Baluchestan, Zahedan, Iran.
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
| Erscheinungsdatum | 04.10.2016 |
|---|---|
| Reihe/Serie | Pure and Applied Undergraduate Texts |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Gewicht | 815 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-2807-5 / 1470428075 |
| ISBN-13 | 978-1-4704-2807-5 / 9781470428075 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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