## Complex analysis: an introduction to the theory of analytic functions of one complex variable |

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#### Review: Complex Analysis: An Introduction to The Theory of Analytic Functions of One Complex Variable (International Series in Pure & Applied Mathematics)

User Review - GoodreadsUsed it during my complex analysis class. Great choice, but you still have to search additional information. Read full review

#### Review: Complex Analysis: An Introduction to The Theory of Analytic Functions of One Complex Variable (International Series in Pure & Applied Mathematics)

User Review - GoodreadsA beautiful exposition of complex analysis. One warning, though: you should have a good understanding of complex algebra and calculus before reading this text, as it is dense. Read full review

### Contents

COMPLEX NUMBERS | 1 |

The Geometric Representation of Complex Numbers | 12 |

COMPLEX FUNCTIONS | 21 |

Copyright | |

24 other sections not shown

### Common terms and phrases

algebraic analytic continuations analytic function angle arbitrary assume boundary bounded Cauchy's theorem Chap choose closed curve coefficients compact set complex numbers conclude condition conformal mapping conjugate consider constant corresponding defined definition denote derivative differential equation direct analytic continuations end points entire function equal exists finite number follows formula function elements function f(z geometric global analytic function harmonic function hence homotopic imaginary inequality infinite initial branch integral inverse lemma linear transformation meromorphic function metric space multiple neighborhood notation obtain open sets poles polygon polynomial positive power series proof prove radius of convergence rational function real axis rectangle region 12 residue Riemann surface roots satisfies sequence simple simply connected simply connected region single-valued singularity solution subharmonic subset Suppose tion topological uniform convergence uniformly upper half plane vanishes variable whole plane z-plane