Complex Analysis

This Wikibook aims to be a comprehensive text on complex analysis, the study of complex numbers and complex functions.

Contributors include Samuel Cormier-Iijima and Tachyon01. Add your name here if you contribute!

See also: Calculus/Complex_analysis

Table of Contents

Chapter 1: Complex Numbers

• 1.1 Introduction
• 1.2 The Topology of the Complex Plane and Stereographic Projection

Chapter 2: Complex Functions

• 2.1 Complex Functions
• 2.2 Limits and Continuous Functions
• 2.3 Complex Derivatives
• 2.4 Holomorphic and Harmonic Functions

Chapter 3: Elementary Functions

• 3.1 Polynomial Functions
• 3.2 Exponential and Trigonometric Functions
• 3.3 Logarithmic Functions
• 3.4 Inverse Trigonometric Functions

Chapter 4: Residue Theory

• The Basics
• Partial Fractions
• A More "Complex" Solution
• Some Consequences

References

In English

• Alder, Michael D..An Introduction to Complex Analysis for Engineers. , 1997.
• Ahlfors, Lars Valerian. Complex Analysis: An Introduction to the theory of analytic functions of one complex variable. 2.ed. New York: McGraw-Will, 1966. ISBN 000700656X
• Boas, Ralph Philip. An invitation to complex analysis. 1.ed. New York: Random House, 1988. ISBN 0394350766
• Conway, John B.. Functions of One Complex Variable: Graduate Texts in Mathematics. 2.ed. Berlin: Springer, 1978. v. 1. ISBN 0387903283
• Henrici, Peter. Applied and Computational Complex Analysis. Wiley, 1974. v. 1. ISBN 0471372447
• Knopp, K.. Theory of Functions. New York: Dover, 1945. v. 2.
• Lang, Serge. Complex Analysis: Graduate Texts in Mathematics. New York: Springer, 1993.
• Rudin, Walter. "Real and Complex Analysis". 3.ed. McGraw Hill. ISBN 0070542341

In other languages

• Ávila, Geraldo Severo de Souza. Variáveis Complexas e Aplicações. 2.ed. Rio de Janeiro: LTC, 2000.
• Cartan, Henri Paul. Théorie Élémentaire Des Fonctions Analytiques d'Une Ou Plusieurs Variables Complexes. 2.ed. Paris: Hermann, 1967.
• Churchill, R. V.. Variáveis Complexas e suas Aplicações. São Paulo: Mac-Graw-Hill do Brasil e Editora da Universidade de São Paulo, 1975.
• Fernandez, Cecília S., Bernardes Jr., Nilson C.. Introdução às Funções de uma Variável Complexa. Rio de Janeiro: , 2006. ISBN 8585818336
• Lima, Elon Lages. Curso de Análise. Rio de Janeiro: IMPA, 1989. v. 2.
• Lins Neto, Alcides. Funções de uma variável complexa. Rio de Janeiro: IMPA, 1996.