Complex Analysis: The Argument Principle in Analysis and Topology

With its emphasis on the argument principle in analysis and topology, this book represents a different approach to the teaching of complex analysis. The three-part treatment provides geometrical insights by covering angles, basic complex analysis, and interactions with plane topology while focusing on the concepts of angle and winding numbers.
Part I takes a critical look at the concept of an angle, illustrating that because a nonzero complex number varies continuously, one may select a con...