Function theory of one complex variable

A new approach that treats complex analysis in a broad context This book presents a new approach to one of mathematics' oldest fields. It departs from the tradition of teaching complex analysis as a self-contained subject and, instead, treats the subject as a natural development from calculus. It also shows how complex analysis is used in other areas, exploring connections with calculus, algebra, geometry, topology, and other parts of analysis. The authors provide the ideal framework for a first-year graduate course in complex analysis—building upon ideas the student is already familiar with and simplifying the transition to advanced topics. The book is also for those using complex numbers and functions in applied fields, including engineering, physics, and other areas. Function Theory of One Complex Variable Compares and contrasts complex variable theory with real variable theory Clarifies analytical ideas belonging to complex analysis by separating them from topological issues Discusses some of the current research in the field, including a number of interesting topics not discussed in other textbooks Features many examples as well as 75 illustrations Provides especially thorough exercise sets ROBERT E. GREENE is a professor in the Department of Mathematics at the University of California at Los Angeles. STEVEN G. KRANTZ is a professor in the Department of Mathematics at Washington University in St. Louis, Missouri. This book offers an excellent modern introduction to complex analysis, one of the core components of mathematics. It establishes the basic analytical ideas before moving on to more topological subjects, easing the transition from familiar ideas of calculus to the more advanced ones distinctive to complex analysis.Exercises address such topics as the Bergman kernel and the boundary behavior of conformed mappings.-- Explores a number of topics relevant to current research. 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 Robert E. Greene, Steven G. Krantz. A Wiley-interscience Publication. Includes Bibliographical References (p. 491-492) And Index.