## A Guide to Complex VariablesThis quick and easy-to-use guide provides a solid grounding in the fundamental area of complex variables. Copious figures and examples are used to illustrate the principal ideas, and the exposition is lively and inviting. In addition to important ideas from the Cauchy theory, the author also includes the Riemann mapping theorem, harmonic functions, the argument principle, general conformal mapping, and dozens of other central topics. An undergraduate taking a first look at the subject, or a graduate student preparing for their qualifying exams, will find this book to be both a valuable resource and a useful companion to more exhaustive texts in the field. For mathematicians and non-mathematicians alike. |

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### Contents

The Complex Plane | 1 |

Complex Line Integrals | 19 |

Applications of the Cauchy Theory | 33 |

Laurent Series | 43 |

The Argument Principle | 71 |

The Geometric Theory | 83 |

Harmonic Functions | 95 |

Infinite Series and Products | 111 |

Analytic Continuation | 125 |

Glossary of Terms from Complex Variable Theory and Analysis | 143 |

175 | |

About the Author | 182 |

### Common terms and phrases

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