## A First Course in Complex Analysis with ApplicationsThe new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill's clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis. |

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### Contents

Chapter 1 Complex Numbers and the Complex Plane | 1 |

Chapter 2 Complex Functions and Mappings | 45 |

Chapter 3 Analytic Functions | 127 |

Chapter 4 Elementary Functions | 157 |

Chapter 5 Integration in the Complex Plane | 211 |

Chapter 6 Series and Residues | 271 |

Chapter 7 Conformal Mappings | 351 |

Appendixes | 407 |

Answers to Selected OddNumbered Problems | 423 |

Indexes | 445 |

### Other editions - View all

A First Course in Complex Analysis with Applications Dennis G. Zill,Zill,Patrick D. Shanahan Limited preview - 2011 |

A First Course in Complex Analysis with Applications Dennis G. Zill,Patrick D. Shanahan Limited preview - 2008 |

A First Course in Complex Analysis with Applications Dennis Zill,Patrick Shanahan No preview available - 2009 |

### Common terms and phrases

analysis analytic angle answer applications argument begin boundary bounded branch called Cauchy principal value centered Chapter circle closed complex function complex mapping complex number complex plane compute Concepts conformal mapping Consider consists constant containing continuous contour converges curve deﬁned Deﬁnition denote derivative describe determine differentiable Dirichlet problem discussion disk domain entire equation evaluate Example Exercises exists expression ﬁeld Figure Figure for Problem ﬁnd ﬁow ﬁrst flow follows formula function f given gives half-plane harmonic integral interval inverse limit line segment logarithm modulus obtain origin parametrization pole positive potential power series Problem proof properties prove radius radius of convergence real axis real number region represent respectively result Section shown shown in color shown in Figure similar simple Solution solve Suppose symbol Theorem transform upper variable vector vertical write zero