# 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 185B: Complex Analysis

**Approved:**2003-10-01, D. Coutand & B. Nachtergaele

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

Search by ISBN on Amazon: 0-7167-2877-X

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1-2 |
5.1 |
Basic theory of conformal mappings |

3-4 |
5.2 |
Fractional linear transformations |

5-7 |
5.3 |
Applications of conformal mappings |

8-10 |
6.1 |
Analytic continuations and Riemann surfaces |

11-12 |
6.2 |
Rouche’s Thm and Principle of the Argument |

13-14 |
6.3 |
Mapping properties of analytic functions |

15-17 |
7.1 |
Infinite products and the Gamma function |

18-20 |
7.2 |
Asymptotic expansions and the Method of Steepest Descent |

21-22 |
7.3 |
Stirling’s formula etc. |

23-24 |
8.1 |
Basic properties of the Laplace Transform |

25 |
8.2 |
Complex Inversion Formula |

26-27 |
8.3 |
Applications of the Laplace Transform |

**Additional Notes:**

**Learning Goals:**