## Introduction to complex analysisStraightforward in concise, this introductory volume treats the theory rigorously but uses a minimum of sophisticated machinery and assumes no prior knowledge of topology. Priestley presents the major theorems as early as possible, so that those meeting complex analysis for the first time can appreciate the power and elegance of the subject by seeing applications of results, both practical and theoretical. A valuable resource for pure and applied mathematicians, this book is also suitable for graduate students and, as a reference, for engineers. |

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### Contents

Holomorphic functions and power series | 13 |

Prelude to Cauchys theorem | 28 |

Cauchys theorem | 49 |

Copyright | |

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### Common terms and phrases

bounded branch point Cauchy-Riemann equations Cauchy's integral formula Cauchy's residue theorem Cauchy's theorem Chapter circle circline circular arcs closed path complex analysis complex numbers complex-valued conformal mapping constant continuous function contour integration Convolution theorem Corollary cut plane deduce defined definition Deformation theorem denote derivatives disc D(a eH(G evaluate example Exercise exists f z)dz feH(G Fourier transform given Hence holomorphic branch holomorphic functions holomorphic in G holomorphic inside implies improper integral infinite integral formula integrals round inverse points Inversion theorem Jordan's inequality Laplace transform Laurent expansion Lebesgue integrals Lemma Let G limit point line segments logarithm Mobius transformation multibranches multifunction Note obtain open disc open set open set G parameter interval power series Proof prove real axis real numbers region G reie shown in Fig simple pole singularity Solution subset theorem Let Theorem Suppose topological unique