Section | Section title | Suggested problems |
---|---|---|

1.1 | Complex Numbers and the Complex Plane | 1b,d,f,g 2b,c 4 5b,f 11 13a |

1.1.1 | A Formal View of the Complex Numbers | No problems assigned. |

1.2 | Some Geometry | 2 7 21 24 35 36 |

1.3 | Subsets of the Plane | 2 3 8 10 18a 19a,b |

1.4 | Functions and Limits | 1 2 11 15 19 36 37 |

1.5 | The Exponential, Logarithm, and Trigonometric Functions | 2 4 8 9 11 17 19 23 24 25 27 28 |

1.6 | Line Integrals and Green's Theorem | 1 2 4 5 7 15 |

2.1 | Analytic and Harmonic Functions; the Cauchy-Riemann Equations | 1 6 14 16 17 20c,e |

2.2 | Power Series | 2 3 5 14 18 19 22 |

2.3 | Cauchy's Theorem and Cauchy's Formula | 1 2 4 7 8 9 10 14 17 18a |

2.3.1 | The Cauchy-Goursat Theorem | No problems assigned. |

2.4 | Consequences of Cauchy's Formula | 1 2 3 5 7 9 10 11 13 17 18 20 21 24a |

2.5 | Isolated Singularities | 3 4 6 7 8 9 13 14 15 21 22b,c |

2.6 | The Residue Theorem and its Application to the Evaluation of Definite Integrals | 2 3 5 9 10 13 16 17 21 23a 26b |

3.1 | The Zeros of an Analytic Function | 5 7 11 15 17a,c 20 |

3.2 | Maximum Modulus and Mean Value | 1 2 5 7 10 16 |

3.3 | Linear Fractional Transformations | 4a,bc,e 5a,c,e 7a,d 8b |

3.4 | Conformal Mapping | 1 3a 7a,b 10 |

3.5 | The Riemann Mapping Theorem and Schwarz-Christoffel Transformations | 1 2 5 7 8 9 |

4.1 | Harmonic Functions | 1a,b,e 2 6 12 16 |