# Complex Analysis in one Variable

• Raghavan Narasimhan
Book

1. Front Matter
Pages i-xvi
2. Raghavan Narasimhan
Pages 1-52
3. Raghavan Narasimhan
Pages 53-69
4. Raghavan Narasimhan
Pages 70-88
5. Raghavan Narasimhan
Pages 89-99
6. Raghavan Narasimhan
Pages 100-118
7. Raghavan Narasimhan
Pages 119-143
8. Raghavan Narasimhan
Pages 144-155
9. Raghavan Narasimhan
Pages 156-165
10. Raghavan Narasimhan
Pages 166-192
11. Raghavan Narasimhan
Pages 193-215
12. Raghavan Narasimhan
Pages 216-262
13. Back Matter
Pages 263-268

### Introduction

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 view which relate the subject to other branches of mathematics. Complex analysis in one variable is ideally suited to this attempt. Of course, the branches of mathema­ tics one chooses, and the connections one makes, must depend on personal taste and knowledge. My own leaning towards several complex variables will be apparent, especially in the notes at the end of the different chapters. The first three chapters deal largely with classical material which is avai­ lable in the many books on the subject. I have tried to present this material as efficiently as I could, and, even here, to show the relationship with other branches of mathematics. Chapter 4 contains a proof of Picard's theorem; the method of proof I have chosen has far-reaching generalizations in several complex variables and in differential geometry. The next two chapters deal with the Runge approximation theorem and its many applications. The presentation here has been strongly influenced by work on several complex variables.

### Keywords

Complex analysis Convexity Meromorphic function Monodromy Residue theorem Riemann surface corona theorem differential geometry function functional analysis holomorphic function integral integration residue sheaves

#### Authors and affiliations

• Raghavan Narasimhan
• 1
1. 1.Department of MathematicsThe University of ChicagoChicagoUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-1106-6
• Copyright Information Birkhäuser Boston 1985
• Publisher Name Birkhäuser, Boston, MA
• eBook Packages
• Print ISBN 978-0-8176-3237-3
• Online ISBN 978-1-4757-1106-6
• Buy this book on publisher's site