Tu-Th 9:30 - 10:45 a.m. RODM 226

**Instructor:** Prof. O. Merino, Tyler 220, (401) 874 4442,
merino@math.uri.edu

**Text:** Complex Variables, by Stephen D. Fisher (2nd Edition).
Dover Publications Inc.

**Evaluation:** 75% homework, 25% final exam.

Homework will be collected on tuesdays. Homework on starred topics
in the table below counts as 1/2 of other homework assignments.

**On the course:** This is an introduction to the complex
plane and to functions of a complex variable.

**Prerequisite:** MTH 243 or equivalent.

Date |
Section |
Topics |
Problems |

Jan 21 | 1.1 * | Complex Numbers and Complex Plane | 1f, 3d, 5d, 6f, 11, 13b |

Jan 23 | 1.2 * | Some Geometry | 2, 3, 5, 13, 15, 25, 26 |

Jan 28 | 1.3 * | Subsets of the Plane | 1 -- 8 |

Jan 30, Feb 4 | 1.4 | Functions and Limits | 1, 3, 5, 11, 13, 14, 15, 17, 19, 31, 32, 34, 40 |

Feb 6, 11 | 1.5 | Exp, Log, and Trig Functions | 2 -- 28 even |

Feb 13, 20 | 1.6 | Line Integrals and Green's Theorem | 1 -- 8, 10, 11, 12 |

Feb 25, 27 | 2.1 | Analytic and Harmonic fns, CR eqs | 1a, 1g, 2, 4, 6, 8, 10, 14, 16, 18, 20a |

Mar 4, 6 | 2.2 | Power Series | 1 -- 5, 7 -- 11, 15, 16, 22a, 22b |

Mar 10- 15 | SPRING BREAK | SPRING BREAK | |

Mar 18, 20 | 2.3 | Cauchy's Theorem | 1, 2, 3, 5, 6, 8 -- 12, 14, 18a, 18c |

Mar 25, 27 | 2.4 | Consequences of Cauchy's Thm. | 1, 2, 4, 6, 9, 10, 12, 14, 17, 20 ,25 |

Apr 1, 3 | 2.5 | Isolated Singularities | 1, 2, 5, 6, 7, 8, 10, 12, 22a, 22b, 22c |

Apr 8, 10 | 2.6 | The Residue Theorem and Apps. | 1, 2, 4, 5, 9, 10, 13, 14, 16, 17, 20, 22 |

Apr 15, 17 | 3.1 | Zeros of an analytic function | 1, 2, 3, 4, 7, 8, 12, 14, 15, 17a, 17c, 20 |

Apr 22, 24 | 3.3 * | Linear Fractional Transformations | 4a -- 4e, 5a, 5b, 7a -- 7d, 8a, 8b |

Apr 29 | 3.4 * | Conformal Mapping | 1, 4, 5, 7a, 7c, 7d, 15 |

May 1 | 3.2 * | Maximum Modulus and Mean Value | 1, 2, 3, 6, 7, 16 |

May 6 | Last day of class |

Changes to schedule and homework assignments:

Section 1.5: Skipped pages 50-51. Instead, more time was spent discussing logarithm, $z^(1/2)$ and $z^\alpha$. Problems 26, 28 were dropped and replaced by: Find domain of (a) sin(z)/cos(z), and (b) sqrt(1-z)

Section 2.6: we used two weeks to cover it. Homework week 1 is as in table except for 13,14,16,17 of page 167. Also, we discussed winding number (not in text).

Section 3.1: not discussed and no homework assigned due to class cancellation (weather related). The hw assignment consists of more residue theorem problems: 13,14,16,17 of page 167.

Section 3.2: not discussed (ran out of time!)