Analysis

Building on the basic concepts through a careful discussion of covalence, (while adhering resolutely to sequences where possible), the main part of the book concerns the central topics of continuity, differentiation and integration of real functions. Throughout, the historical context in which the subject was developed is highlighted and particular attention is paid to showing how precision allows us to refine our geometric intuition. The intention is to stimulate the reader to reflect on the underlying concepts and ideas.

Introduction: why we study Analysis * Convergent sequences and series * Completeness and Convergence * Functions defined by Power Series * Functions and Limits * Continuous functions * Continuity on intervals * Differentiable Real Functions * Mean values and Taylor Series * The Riemann Integral * Integration techniques * What Next? Extensions and developments * Appendix * Index.