# 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 Analysis

**Approved:**2003-10-01 (revised 2013-03-01, )

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

Search by ISBN on Amazon: 978-0716728771

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1-2 |
1.1-1.3 |
Complex number system |

3-4 |
1.4 |
Review continuous functions |

5-6 |
1.5 |
Basic properties of analytic functions |

7 |
1.6 |
Differentiation of elementary functions |

8 |
2.1 |
Contour Integrals |

9-10 |
2.2-2.3 |
Cauchy’s Theorem |

11-12 |
2.4 |
Cauchy’s Integral Formula |

13-14 |
2.5 |
Maximum Modulus Principle and harmonic functions |

15 |
3.1 |
Convergent series of analytic functions |

16-17 |
3.2 |
Power series and Taylor’s Thm |

18-19 |
3.3 |
Laurent series and classification of singularities |

20-21 |
4.1 |
Calculation of residues |

22-23 |
4.2 |
Residue Thm |

24-25 |
4.3 |
Evaluation of definite integrals |

26-27 |
4.4 |
Evaluation of infinite series |

**Learning Goals:**

Complex analysis appears in many areas of the natural sciences and has wide applications. Students will be challenged to improve their problem solving skills within the broad context of Calculus. Mastery of this course also supports the development of clear analytical thinking.

**Assessment:**