## A First Course in Complex Analysis with ApplicationsA First Course In Complex Analysis With Applications Limits Theoretical Coverage To Only What Is Necessary, And Conveys It In A Student-Friendly Style. Its Aim Is To Introduce The Basic Principles And Applications Of Complex Analysis To Undergraduates Who Have No Prior Knowledge Of This Subject. Contents Of The Book Include The Complex Number System, Complex Functions And Sequences, As Well As Real Integrals; In Addition To Other Concepts Of Calculus, And The Functions Of A Complex Variable. This Text Is Written For Junior-Level Undergraduate Students Who Are Majoring In Math, Physics, Computer Science, And Electrical Engineering. |

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### Contents

Chapter 7 | 34 |

Complex Functions and Mappings | 49 |

Analytic Functions | 141 |

Elementary Functions | 175 |

Integration in the Complex Plane | 235 |

Formulas | 277 |

Chapter 6 | 301 |

Proof of Theorem 2 1 APP2 | 453 |

Table of Conformal Mappings APP9 | 459 |

Answers for Selected OddNumbered Problems ANS1 | 493 |

### 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 Answers to selected arg(z branch Cauchy-Goursat theorem Cauchy-Riemann equations color in Figure complex exponential function complex function complex logarithm complex mapping complex power conformal mapping continuous converges cosh cosine defined Definition differential equation Dirichlet problem disk evaluate Example Exercises extended complex plane Figure for Problem Find the image flow follows function f(z iv(x Laplace's equation level curves limit line segment linear fractional transformation linear function linear mapping loge modulus multiple-valued function nth root odd-numbered problems begin one-to-one parametrization point ZQ polynomial principal square root principal value proof quadratic radius Re(z real and imaginary real axis real functions real number real variable region rotation satisfies Section selected odd-numbered problems shown in black shown in color shown in Figure simple closed contour sinh Solution solve square root function trigonometric unit circle upper half-plane vector field velocity field vertical line z-plane zero