Analytic function theory, Volume I / Einar Hille

Written in a pleasant and unhurried style, this book departs in many respects from currently held ideas as to what a college text should be. The author neither accepts the narrow utilitarian outlook of those who are convinced of the superiority of vegetables over flowers, nor does he have much sympathy for the true believer who feels that anything written, say, more than twenty years ago belongs to the heathen past and should be relegated to oblivion lest it corrupt the impressionable young. While all the standard topics are covered, the presentation is often guided by aesthetic and, especially, historical considerations. There are a large number of historical footnotes supplying biographical details of many major—and also minor—contributors to the theory of functions, and the author makes every possible effort to communicate to the reader his sense of the historical continuity of the subject.
The chapter headings of the present volume are: (1) Number systems. (2) The complex plane. (3) Fractions, powers, and roots. (4) Holomorphic functions. (5) Power series. (6) Some elementary functions. (7) Complex integration. (8) Representation theorems. (9) The calculus of residues. There are also three appendices, containing supplementary material on point sets, polygons, and Riemann-Stieltjes integration. A second volume, covering more advanced topics, is to follow fairly soon. (MathSciNet)

Bibliogr. Index