# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 185A: Complex Variables

**Approved:**2003-10-01 (revised 2022-06-02, J. Hunter, J.Schultens, and B.Temple)

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Search by ISBN on Amazon: 978-0073383170

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) | Sections | Comments/Topics |

1-3 | Chapter 1 | Complex number system |

4 | Chapter 2 (pages 37-43) | Functions of a Complex Variable |

5 | Chapter 2 (pages 44-51) | Limits, Theorems on Limits, Limits involving the Points at Infinity |

6-7 | Chapter 2 (pages 52-67) | Differentiation, Cauchy-Riemann equations |

8 | Chapter 2 (pages 68-75) | Polar coordinates, Analytic functions |

9-11 | Chapter 3 | Elementary Functions |

12-13 | Chapter 4 (pages 115-134) | Contour Integrals |

14 | Chapter 4 (pages 140-147) | Antiderivatives |

15 | Chapter 4 (pages 148-153) | Cauchy-Goursat Theorem |

16-17 | Chapter 4 (pages 154-171) | Cauchy Integral Formula, Derivatives of Analytic Functions |

18 | Chapter 4 (pages 172-178) | Liouville's Theorem, Maximum Modulus Theorem |

19-20 | Chapter 5 (pages 179-201) | Taylor Series, Laurent Series |

21 | Chapter 5 (pages 208-220) | Convergence of Power Series, Integration and Differentiation of Power Series, Uniqueness |

22 | Chapter 5 (pages 221-226) | Multiplication and Division of Power Series, Analytic Continuation |

23-24 | Chapter 6 (pages 227-237) | Residues, Residue Theorems |

25-26 | Chapter 6 (pages 238-258) | Zeros, Poles of Order m, Removable Singular Points |

**Learning Goals:**

**Assessment:**