Complex Analysis: A Modern First Course In Function Theory

This book concisely addresses the classical results of the field, emphasizes the beauty, power, and counterintuitive nature of the subject, and moves the notion of power series front and center, giving readers a primary tool to deal with problems from modern function theory.

• Uniquely defines analyticity in terms of power series (as opposed to differentiability), making power series a central concept and tool to solve problems
• Features many “counterintuitive” concepts as a learning tool, such as addressing Liouville’s Theorem, the factorization of analytic function, the Open Mapping Theorem, and the Maximum Principle in quick succession early on in the book in an attempt to prepare readers for the development of the Cauchy integral theory
• Classroom tested for 10+ years by the author at the University of Scranton as well as colleagues at Rose-Hulman Institute of Technology and Adams State College
• Presents sequences and series early on, distinguishes complex analysis from real analysis and calculus, and emphasizes geometry when analyzing complex functions
• Contains appendices for basic notation of sets and functions as well as necessary topics from advanced calculus, such as Leibnitz’s Rule and Fubini’s Theorem
• An Instructor’s Manual containing all solutions is available via request to the Publisher.

Written with a reader-friendly approach and provides a wide range of exercises and numerous figures throughout, allowing readers to gain intuition for solving problems.