Complex Analysis in One Variable

Complex Analysis in One Variable by Raghavan Narasimhan, Yves Nievergelt.

This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Thus, covering spaces are used explicitly in dealing with Cauchy's theorem, real varia...

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Bibliographic Details
Main Authors: Narasimhan, Raghavan (Author), Nievergelt, Yves (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2001.
Edition:2nd ed. 2001.
Series:Springer eBook Collection.
Subjects:
Functions of real variables.
Functions of complex variables.
Algebraic geometry.
Mathematical analysis.
Analysis (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I Complex Analysis in One Variable
  • 1 Elementary Theory of Holomorphic Functions
  • 2 Covering Spaces and the Monodromy Theorem
  • 3 The Winding Number and the Residue Theorem
  • 4 Picard’s Theorem
  • 5 Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem
  • 6 Applications of Runge’s Theorem
  • 7 Riemann Mapping Theorem and Simple Connectedness in the Plane
  • 8 Functions of Several Complex Variables
  • 9 Compact Riemann Surfaces
  • 10 The Corona Theorem
  • 11 Subharmonic Functions and the Dirichlet Problem
  • II Exercises
  • 0 Review of Complex Numbers
  • 1 Elementary Theory of Holomorphic Functions
  • 2 Covering Spaces and the Monodromy Theorem
  • 3 The Winding Number and the Residue Theorem
  • 4 Picard’s Theorem
  • 5 The Inhomogeneous Cauchy—Riemann Equation and Runge’s Theorem
  • 6 Applications of Runge’s Theorem
  • 7 The Riemann Mapping Theorem and Simple Connectedness in the Plane
  • 8 Functions of Several Complex Variables
  • 9 Compact Riemann Surfaces
  • 10 The Corona Theorem
  • 11 Subharmonic Functions and the Dirichlet Problem
  • Notes for the exercises
  • References for the exercises.

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