Lectures on Real Analysis
Seiten
2012
Cambridge University Press (Verlag)
978-1-107-60852-8 (ISBN)
Cambridge University Press (Verlag)
978-1-107-60852-8 (ISBN)
Arising from a real analysis course given by the author, this textbook is an ideal rigorous undergraduate treatment of the subject. The exposition is concise and to the point, yet all of the standard topics are covered, as well as topics that longer textbooks often omit. Over 200 exercises are included.
This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.
This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.
Finnur Lárusson has lectured in pure mathematics at all levels, from first-year calculus to postgraduate courses, at universities in Australia, Canada and the United States. He is currently Associate Professor in the School of Mathematics at the University of Adelaide.
Preface; To the student; 1. Numbers, sets, and functions; 2. The real numbers; 3. Sequences; 4. Open, closed, and compact sets; 5. Continuity; 6. Differentiation; 7. Integration; 8. Sequences and series of functions; 9. Metric spaces; 10. The contraction principle; Index.
| Erscheint lt. Verlag | 7.6.2012 |
|---|---|
| Reihe/Serie | Australian Mathematical Society Lecture Series |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 227 mm |
| Gewicht | 190 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 1-107-60852-X / 110760852X |
| ISBN-13 | 978-1-107-60852-8 / 9781107608528 |
| Zustand | Neuware |
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