A Primer of Real Analytic Functions (Birkhauser Advanced Textbooks)

This book treats the subject of analytic functions of one or more real variables using, almost solely, the techniques of real analysis. This approach dramatically alters the natural progression of ideas and brings previously neglected arguments to the fore. The first chapter requires only a background in calculus; the treatment is nearly self-contained. As the book progresses, the reader is introduced to more sophisticated topics requiring more background and perseverance. When truly advanced topics are reached, the book shifts to a more expository mode, with goals of introducing the reader to the theorems, providing context and examples, and indicating sources in the literature.