Part of the Graduate Texts in Mathematics book series (GTM, volume 245)


The first section of this chapter introduces the complex plane, fixes notation, and discusses some useful concepts from real analysis. Some readers may initially choose to skim this section. The second section contains the definition and elementary properties of the class of holomorphic functions - the basic object of our study.


Complex Number Complex Plane Limit Point Cauchy Sequence Real Analysis 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jane P. Gilman
    • 1
  • Irwin Kra
    • 2
    • 3
  • Rubí E. Rodríguez
    • 4
  1. 1.Department of Mathematics and Computer ScienceRutgers UniversityNewarkUSA
  2. 2.Math for AmericaNew YorkUSA
  3. 3.Department of MathematicsState University of New York at Stony BrookStony BrookUSA
  4. 4.Pontificia Universidad Católica de ChileSantiagoChile

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