R. P. Burn

Numbers and Functions (eBook, ePUB)

Steps into Analysis

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 19. Februar 2015
• Englisch
• ISBN-13: 9781316028490
• Artikelnr.: 52970899

Autorenporträt

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).

Inhaltsangabe

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.