Analysis I : Convergence

The main topic of these two English-language volumes are Functions in R and C, including the theory of Fourier series, Fourier integrals and part of holomorphic functions. Based on a course given by the author, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. The French edition in four volumes, published from 1998, has met with resounding success.