This book is intended as a text for a two-semester course at the advanced undergraduate or first-year graduate level. The present volume develops both the real and complex theory together. The contents and scope of the book are best made clearer in detail by listing chapter headings, followed by parenthetical comments on contents. (1) The Spaces ℝ, ℝ k , and ℂ (real numbers, the real space ℝ k , and the complex space ℂ); (2) Point-Set Topology (bounded sets, classification of points, open and closed sets, nested intervals and the Bolzano-Weierstrass theorem, compactness and connectedness); (3) Limits and Convergence (convergence results for sequences, topological results for sequences, properties of infinite series, manipulations of series in ℝ); (4) Functions: Definitions and Limits (functions as mappings, some elementary complex functions, limits of functions); (5) Functions: Continuity and Convergence (continuity, uniform continuity, sequences and series of functions); (6) The De...
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