Numbers and Functions

Steps to Analysis

R. P. Burn (Autor)

Buch | Hardcover

352 Seiten

1992
Cambridge University Press (Verlag)
9780521410861 (ISBN)

Infos

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this book, Dr Burn follows a route that proved successful with A Pathway to Number Theory and Groups: A Path to Geometry. He invites the student reader to tackle each of the key concepts in turn, progressing from experience (using computers for graph drawing where appropriate) 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 by historical insight and complemented by historical discussion. The sequence also takes into account recent research which has shown how intuitive ideas about numbers, limits, functions and infinity may be at odds with the standard definitions. 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. Teachers in sixth forms will find that questions at the beginning of every chapter provide ways of preparing those at school for university mathematics. Lecturers in universities will be challenged to rethink their conventions about the best way to introduce the central ideas of analysis to undergraduates.

Inhalt

Introduction; Part I. Numbers: 1. 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; Part II. Functions: 6. Functions and continuity: neighbourhoods, limits of functions; 7. Continuity and completeness, functions on intervals; 8. Derivatives, tangents; 9. Differentiation and completeness: mean value theorems; 10. Integration: the fundamental theorems, Taylor's theorem; 11. Indices and circle functions; 12. Sequences of functions.

Produkt-Details

• Erscheint lt. Verlag: 11.6.1992
• Zusatzinfo: 25 Line drawings, unspecified
• Verlagsort: Cambridge
• Sprache: englisch
• Maße: 160 x 238 mm
• Gewicht: 692 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-13: 9780521410861 / 9780521410861
• Zustand: Neuware