Numbers and Functions
Steps into Analysis
Seiten
2000
|
2nd Revised edition
Cambridge University Press (Verlag)
978-0-521-78836-6 (ISBN)
Cambridge University Press (Verlag)
978-0-521-78836-6 (ISBN)
- Titel erscheint in neuer Auflage
- Artikel merken
Zu diesem Artikel existiert eine Nachauflage
In this second edition of Numbers and Functions, the reader is invited to tackle each of the key concepts of mathematical analysis in turn, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis.
The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this second edition of Numbers and Functions, Dr Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.
The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this second edition of Numbers and Functions, Dr Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.
1. The counting numbers and mathematical induction; 2. Order: arithmetic with inequalities; 3. Sequences: a first bite at infinity; 4. Completeness: what the rational numbers lack; 5. Series: infinite sums; 6. Functions and continuity: neighbourhoods, limits of functions; 7. Continuity and completeness: functions on intervals; 8. Derivatives: tangents; 9. Differentiation and completness: mean value theorems, Taylor's theorem; 10. Integration: the fundamental theorem of calculus; 11. Indices and circle functions; 12. Sequences of functions; Appendices.
| Erscheint lt. Verlag | 28.8.2000 |
|---|---|
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 153 x 227 mm |
| Gewicht | 578 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-521-78836-6 / 0521788366 |
| ISBN-13 | 978-0-521-78836-6 / 9780521788366 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
59,95 €
