Invitation to Real Analysis
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-4928-5 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4928-5 (ISBN)
Provides a careful introduction to the real numbers with an emphasis on developing proof-writing skills. The book continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions.
This book is an introduction to real analysis for a one-semester course aimed at students who have completed the calculus sequence and preferably one other course, such as linear algebra. It does not assume any specific knowledge and starts with all that is needed from sets, logic, and induction. Then there is a careful introduction to the real numbers with an emphasis on developing proof-writing skills. It continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions.
A theme in the book is to give more than one proof for interesting facts; this illustrates how different ideas interact and it makes connections among the facts that are being learned. Metric spaces are introduced early in the book, but there are instructions on how to avoid metric spaces for the instructor who wishes to do so. There are questions that check the readers' understanding of the material, with solutions provided at the end. Topics that could be optional or assigned for independent reading include the Cantor function, nowhere differentiable functions, the Gamma function, and the Weierstrass theorem on approximation by continuous functions.
This book is an introduction to real analysis for a one-semester course aimed at students who have completed the calculus sequence and preferably one other course, such as linear algebra. It does not assume any specific knowledge and starts with all that is needed from sets, logic, and induction. Then there is a careful introduction to the real numbers with an emphasis on developing proof-writing skills. It continues with a logical development of the notions of sequences, open and closed sets (including compactness and the Cantor set), continuity, differentiation, integration, and series of numbers and functions.
A theme in the book is to give more than one proof for interesting facts; this illustrates how different ideas interact and it makes connections among the facts that are being learned. Metric spaces are introduced early in the book, but there are instructions on how to avoid metric spaces for the instructor who wishes to do so. There are questions that check the readers' understanding of the material, with solutions provided at the end. Topics that could be optional or assigned for independent reading include the Cantor function, nowhere differentiable functions, the Gamma function, and the Weierstrass theorem on approximation by continuous functions.
Cesar E. Silva, Williams College, Williamstown, MA.
Preliminaries: Sets, functions and induction
The real numbers and the completeness property
Sequences
Topology of the real numbers and metric spaces
Continuous functions
Differentiable functions
Integration
Series
Sequences and series of functions
Solutions to questions
Bibliographical notes
Bibliography
Index.
| Erscheinungsdatum | 19.06.2019 |
|---|---|
| Reihe/Serie | Pure and Applied Undergraduate Texts |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 753 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-4928-5 / 1470449285 |
| ISBN-13 | 978-1-4704-4928-5 / 9781470449285 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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