**Lectures:** Tuesday&Thursday 11:00AM-12:30PM (Berkeley Time) at Dwinelle 182

**Professor:** Semeon Artamonov

**Textbook:** T. W. Gamelin "Complex Analysis" (ISBN 978-0387-95069-3)

**Office Hours:** Wednesday 10:00AM-11:00AM, Thursday 1:00-3:00 PM at 1055 Evans Hall

**GSI: **(Aug. 22-Aug. 31) Nick Ryder 12-2PM MWF & 3:30PM-5:30PM TuTh in Evans 961

(From Sep. 1) Benjamin Filippenko 3:00PM-5:00PM in Evans 961 (everyday)

Homework problems are from the Textbook unless specified otherwise.

**Due Aug. 30**Chapter I, Sec. 1, ex. 2, 6, 10; Chapter I, Sec. 2, ex. 1c, 1g, 5.**Due Sep. 6**Chapter I, Sec. 3, ex. 1, 6; Sec. 5, ex. 4; Sec. 6, ex. 1, 4; Chapter II, Sec. 1, ex. 10, 15, 19.**Due Sep. 13**Chapter II, Sec. 2, ex. 5; Sec. 3, ex. 3, 4; Sec. 4, ex. 8; Extra Problems (by the link).**Due Sep. 20**Chapter II, Sec. 5, ex. 2, 7; Sec. 6, ex. 1, 7; Sec. 7, ex. 2, 8, 11, 12.**Due Sep. 27**Chapter III, Sec. 1, ex. 2, 5, 7; Sec. 2, ex. 2, 5, 6; Extra Problems (by the link)**Due Oct. 4**Chapter III, Sec. 3, ex. 2; Sec. 4, ex. 2; Sec. 5, ex. 3, 7; Chapter IV, Sec. 1, ex. 4, 6, 8; Sec. 2, ex. 5.**Due Oct. 11**Chapter IV, Sec. 3, ex. 1, 2; Sec. 4, ex. 1f, 1g, 1h; Sec. 5, ex. 2; Sec. 6, ex. 2; Extra Problems (by the link)**Due Oct. 18**Chapter V, Sec. 1, ex. 7; Sec. 2, ex. 3, 8, 9; Sec. 3, ex. 1b, 1e, 1i; Extra Problems (by the link)**Due Oct. 25**Chapter V, Sec. 4. ex. 1d, 1f, 3; Sec. 5, ex. 1c; Sec. 6, ex. 3; Sec. 7, ex. 1a, 1f, 1i; Sec. 7, ex. 9, 11; Extra Problem**Due Nov. 1**Chapter VI, Sec. 1, ex. 1, 3, 5.**Due Nov. 8**Chapter VI, Sec. 2, ex. 1g, 1e, 1i, 3, 12; Sec. 3, ex. 1 (for (g),(e),(i)); Sec. 4, ex. 1c, 1f, 2c, 3**Due Nov. 15**Chapter VII, Sec. 1, ex. 1e, 1g, 1h, 3b, 3e; Sec. 2, ex. 5; Sec. 3. ex. 4; Sec. 4, ex. 8.**Due Nov. 27**Chapter VIII, Sec. 1, ex. 1; Sec. 2, ex. 2, 8; Sec. 3, ex. 2; Sec. 4, ex. 4, 6.

Thursday, August 23 | Complex Numbers and Polar Representation | Chapter I, Sec. 1-2 |

Tuesday, August 28 | Stereographic projection, Exp and Log | Chapter I, Sec. 3,5,6 |

Thursday, August 30 | Limits, Continuity, and Analytic Functions | Chapter II, Sec.1-2 |

Tuesday, September 4 | Complex Derivatives and Cauchy-Riemann Equations | Chapter II, Sec. 2-3 |

Thursday, September 6 | Inverse Mappings and Jacobian | Chapter II, Sec. 4 |

Tuesday, September 11 | Harmonic Functions and Conformal Mappings | Chapter II, Sec. 5-6 |

Thursday, September 13 | Fractional Linear Transformations | Chapter II, Sec. 7 |

Tuesday, September 18 | Midterm I | |

Thursday, September 20 | Line Integrals and Green's Theorem | Chapter III, Sec. 1-2 |

Tuesday, September 25 | Conjugates, Mean Value Property, Maximum Principle | Chapter III, Sec. 3-5 |

Thursday, September 27 | Complex Line Integrals and Fundamental Theorem of Calculus | Chapter IV, Sec. 1-2 |

Tuesday, October 2 | Cauchy's Theorem and Cauchy's Integral Formula | Chapter IV, Sec. 3-4 |

Thursday, October 4 | Liouville's Theorem and Morera's Theorem | Chapter IV, Sec. 5-6 |

Tuesday, October 9 | Complex Series and Sequences, Series of Complex Functions | Chapter V, Sec. 1-2 |

Thursday, October 11 | Power Series and Power Series Expansions of Analytic Functions | Chapter V, Sec. 3-4 |

Tuesday, October 16 | Power Series Expansions (continued) | Chapter V, Sec. 4-5 |

Thursday, October 18 | Manipulation of Power Series and Zeros of an Analytic Function | Chapter V, Sec. 6-7 |

Tuesday, October 23 | Laurent Series and Isolated Singularities | Chapter VI, Sec. 1-2 |

Thursday, October 25 | Midterm II | |

Tuesday, October 30 | Isolated Singularities (continued) | Chapter VI, Sec. 2-3 |

Thursday, November 1 | Partial Fractions Decomposition | Chapter VI, Sec. 4 |

Tuesday, November 6 | The Residue Theorem, Integrals of Rational Functions | Chapter VII, Sec. 1-2 |

Thursday, November 8 | Integrals of Trigonometric Functions, Integrals with Branch Points | Chapter VII, Sec. 3-4 |

Tuesday, November 13 | The Argument Principle and Rouche's Theorem | Chapter VIII, Sec. 1-2 |

Thursday, November 15 | Hurwitz's Theorem, Open Mapping and Inverse Function Theorem | Chapter VIII, Sec. 3-4 |

Tuesday, November 20 | Class cancelled due to weather | |

Thursday, November 22 | No class, Happy Thanksgiving! | |

Tuesday, November 27 | The Schwarz Lemma and Conformal Self-Maps of the Unit Disc | Chapter IX, Sec. 1-2 |

Thursday, November 29 | The Riemann Mapping Theorem | Chapter XI, Sec. 1-2 |