Function Theory of One Complex Variable

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9780471804680: Function Theory of One Complex Variable
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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

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From the Publisher:

Rather than using the traditional approach of presenting complex analysis as a self-contained subject, the authors demonstrate how it can be connected with calculus, algebra, geometry, topology, and other parts of analysis. They emphasize how complex analysis is a natural outgrowth of multivariable real calculus by comparing and contrasting complex variable theory with real variable theory. The text relates the subject matter to concepts that students already know and motivates these ideas with numerous examples. Special topics in later chapters deal with current research including the Bergman kernel function, Hp spaces, and the Bell-Ligocka approach to proving smoothness to the boundary of biholomorphic mappings. Features many examples as well as 75 illustrations, which is provided through exercise sets.

About the Author:

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.

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Greene, Robert E., Krantz, Steven G.
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