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Zusatztext Review of previous edition: '? written in a very comprehensible but exact way ? an excellent guide through the basic course of mathematical analysis at university.' European Mathematical Society Newsletter Informationen zum Autor 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). Klappentext Revised and updated 3rd edition. Helps the transition from school to university-level calculus. Zusammenfassung In this updated 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 over 800 problems to concepts! definitions and proofs of classical real 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.
