Classical Analysis in the Complex Plane

Burckel walks readers through the classical theory of functions of a single complex variable, covering both the mathematics and its historical background in full. Readers need only an undergraduate-level background to follow the material, which spans the core topics of the field and is handled with careful reasoning and precision.

Many proofs are developed in unusual depth, and the book presents familiar standard arguments alongside newer ones. The exercises, several accompanied by hints, give readers room to practice and to build a firmer understanding of the subject.

Alongside the mathematics, the book traces how central ideas in complex analysis developed over many centuries, so readers can see the subject's growth over time. Historical notes appear throughout the text. Its bibliography contains more than 2,000 entries, covering both well-known publications and lesser-known works that are easy to overlook.

The book is aimed at graduate students, experienced mathematicians, and anyone doing scholarly work in complex analysis. The author's deep familiarity with the field and his enthusiasm for it come through throughout, and he hopes readers will come away with a lasting appreciation for the subject.