Burn Numbers and Functions

Steps into Analysis
3. Auflage 2015
ISBN: 978-1-316-02897-1
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 0 Seiten

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this third edition of Numbers and Functions, Professor Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of more than 800 problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, of which most are supplied with brief answers, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. Carefully corrected and updated throughout, this new edition also includes extra questions on integration and an introduction to convergence. 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.

Autoren/Hrsg.

Burn, R. P.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Preface to first edition; Preface to second edition; Preface to third edition; Glossary; Part I. Numbers: 1 Mathematical induction; 2. 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, Taylor's Theorem; 10. Integration: the fundamental theorem of calculus; 11. Indices and circle functions; 12. Sequences of functions; Appendix 1. Properties of the real numbers; Appendix 2. Geometry and intuition; Appendix 3. Questions for student investigation and discussion; Bibliography; Index.

Über Autor(innen)

Burn, R. P.
R. P. Burn is an Honorary University Fellow at the University of Exeter. His other titles include Groups: A Path to Geometry (1985) and A Pathway into Number Theory (1982).