Complex Analysis in one Variable

Complex Analysis in one Variable by NARASIMHAN.

This book is based on a first-year graduate course I gave three times at the University of Chicago. As it was addressed to graduate students who intended to specialize in mathematics, I tried to put the classical theory of functions of a complex variable in context, presenting proofs and points of v...

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Bibliographic Details
Main Author: NARASIMHAN (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1985.
Edition:1st ed. 1985.
Series:Springer eBook Collection.
Subjects:
Functions of complex variables.
Mathematical analysis.
Analysis (Mathematics).
Applied mathematics.
Engineering mathematics.
Topology.
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:
  • 1 Elementary Theory of Holomorphic Functions
  • 1 Some basic properties of ?-differentiable and holomorphic functions
  • 2 Integration along curves
  • 3 Fundamental properties of holomorphic functions
  • 4 The theorems of Weierstrass and Montel
  • 5 Meromorphic functions
  • 6 The Looman-Menchoff theorem
  • Notes on Chapter 1
  • References : Chapter 1
  • 2 Covering Spaces and the Monodromy Theorem
  • 1 Covering spaces and the lifting of curves
  • 2 The sheaf of germs of holomorphic functions
  • 3 Covering spaces and integration along curves
  • 4 The monodromy theorem and the homotopy form of Cauchy’s theorem
  • 5 Applications of the monodromy theorem
  • Notes on Chapter 2
  • References : Chapter 2
  • 3 The Winding Number and the Residue Theorem
  • 1 The winding number
  • 2 The residue theorem
  • 3 Applications of the residue theorem
  • Notes on Chapter 3
  • References : Chapter 3
  • 4 Picard’s Theorem
  • Notes on Chapter 4
  • References : Chapter 4
  • 5 The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem
  • 1 Partitions of unity
  • 2 The equation % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq % GHciITcaWG1baabaGaeyOaIyRabmOEayaaraaaaiabg2da9iabew9a % Mbaa!3DAD!$$ [ frac{{ partial u}} {{ partial bar z}} = phi ]$$
  • 3 Runge’s theorem
  • 4 The homology form of Cauchy’s theorem
  • Notes on Chapter 5
  • References : Chapter 5
  • 6 Applications of Runge’s Theorem
  • 1 The Mittag-Leffler theorem
  • 2 The cohomology form of Cauchy’s theorem
  • 3 The theorem of Weierstrass
  • 4 Ideals in ? (?)
  • Notes on Chapter 6
  • References : Chapter 6
  • 7 The Riemann Mapping Theorem and Simple Connectedness in the Plane
  • 1 Analytic automorphisms of the disc and of the annulus
  • 2 The Riemann mapping theorem
  • 3 Simply connected plane domains
  • Notes on Chapter 7
  • References : Chapter 7
  • 8 Functions of Several Complex Variables
  • Notes on Chapter 8
  • References : Chapter 8
  • 9 Compact Riemann Surfaces
  • 1 Definitions and basic theorems
  • 2 Meromorphic functions
  • 3 The cohomology group H1(.

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