An Introduction to Mathematical Analysis

Dealing chiefly with functions of a single real variable, this text is geared toward advanced undergraduates and graduate students. It features the topics usually discussed in a rigorous first course in analysis: limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. No previous knowledge of calculus is assumed.
A distinguished educator and researcher, author Robert A. Rankin wrote many influential papers on number theory and the theory of functions. This text is the product of countless lectures over a two-decade period to students at the Universities of Cambridge, Birmingham, and Glasgow. The author's experience as an instructor prompted his inclusion of numerous examples at the end of nearly every section. In addition to testing understanding of preceding theories and providing practice in carrying out techniques, the examples encourage imaginative thinking. Those marked with an asterisk feature hints for solution.