## 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,Patrick D. Shanahan Limited preview - 2011 |

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

A First Course in Complex Analysis with Applications Dennis G. Zill,Patrick Shanahan Limited preview - 2003 |

### Common terms and phrases

analytic function angle Answers to selected arg(w arg(z boundary conditions branch Cauchy-Goursat theorem Cauchy-Riemann equations color in Figure complex exponential function complex function complex logarithm complex mapping complex power conformal mapping deﬁned Deﬁnition derivative Dirichlet problem disk evaluate Example Exercises f is analytic Figure for Problem ﬁnd Find the image ﬁow ﬁrst ﬁuid ﬂow follows function f harmonic inﬁnite integral formula isin Laplace’s equation Laurent series level curves line segment linear fractional transformation linear mapping loge magniﬁcation modulus multiple-valued function nth root obtain odd-numbered problems begin one-to-one parametrization polygonal region polynomial power series principal value proof radius of convergence real and imaginary real axis real functions real number real variable rotation satisﬁes Section selected odd-numbered problems shown in black shown in color shown in Figure simple closed contour Solution solve streamlines Suppose trigonometric unit circle upper half-plane vector ﬁeld velocity ﬁeld w-plane zero