Author | Narasimhan, Raghavan. author |
---|---|
Title | Complex Analysis in One Variable [electronic resource] / by Raghavan Narasimhan, Yves Nievergelt |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2001 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0175-5 |
Descript | XIV, 381 p. online resource |
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 Picardโs Theorem -- 5 Inhomogeneous Cauchy-Riemann Equation and Rungeโs Theorem -- 6 Applications of Rungeโs 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 Picardโs Theorem -- 5 The Inhomogeneous CauchyโRiemann Equation and Rungeโs Theorem -- 6 Applications of Rungeโs 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