This volume connects complex analysis with calculus, algebra, geometry, topology, and analysis. Exercises and illustrations are provided throughout the text. Also included is information on Bergman Kernal and two boundary behaviour of conformal mappings.The book should be of interest to scientists, engineers, physicists and chemists who use complex numbers and functions in their research, and to first-year graduate students.
Table of Contents:
Fundamental Concepts; Complex Line Integrals; Applications of the Cauchy Integral; Meromorphic Functions and Residues; The Zeros of a Holomorphic Function; Holomorphic Functions as Geometric Mappings; Harmonic Functions; Infinite Series and Products; Applications of Infinite Sums and Products; Analytic Continuation; Topology; Rational Approximation Theory; Special Classes of Holomorphic Functions; Extension of Conformal Maps to the Boundary; Hilbert Spaces of Holomorphic Functions, the Bergman Kernal, and Biholomorphic Mappings, Special Functions and the Prime Number Theorem.
