## Schedule

Lecture |
Date |
Topic |
Reading* |
Notes |

1 | Jan 21 | Complex numbers | 1-6 | |

2 | Jan 23 | Euler's formula | 7-12 | HW 1 due |

3 | Jan 26 | Functions | 13-14 | |

4 | Jan 28 | Limits | 15-16 | |

5 | Jan 30 | Continuity | 17-18 | HW 2 due |

6 | Feb 2 | Differentiation: The Cauchy-Riemann equations | 19-21 | |

7 | Feb 4 | Sufficient conditions for differentiability | 22-23 | |

8 | Feb 6 | Analytic functions and polar coordinates | 24-26 | HW 3 due |

9 | Feb 9 | Exponentials and logarithms | 30-34 | |

10 | Feb 11 | Power and trigonometric functions | 35-38 | |

Feb 13 | Midterm I |
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Feb 16 | Holiday (No class) |
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11 | Feb 18 | Contour Integrals | 40-44 | |

12 | Feb 20 | Examples and path independence | 45-49 | HW 4 due |

13 | Feb 23 | Cauchy-Goursat Theorem | 50-51 | |

14 | Feb 25 | Cauchy-Goursat and Antiderivatives | 52-53 | |

15 | Feb 27 | Cauchy's Integral Formula | 54-56 | HW 5 due |

16 | Mar 2 | Cauchy's Integral Formula and Harmonic functions | 57,27 | |

17 | Mar 4 | Liouville's Theorem, maximum modulus principle | 57-59 | |

18 | Mar 6 | Sequences and Series | 60-61 | HW 6 due |

19 | Mar 9 | Taylor Series | 62-64 | |

20 | Mar 11 | Laurent Series | 65-67 | |

21 | Mar 13 | Some examples, uniform convergence of power series | 68-69 | HW 7 due |

22 | Mar 16 | Integration, differentiation of series, etc. | 70-73 | |

Mar 18 | Cauchy-Residue Theorem | 74-77 | ||

Mar 20 | Midterm II |
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Mar 23 | Spring Recess (No class) |
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Mar 25 | Spring Recess (No class) |
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Mar 27 | Spring Recess (No class) |
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23 | Mar 30 | Types of singularities, residues at poles | 78-80 | |

24 | Apr 1 | Zeros of analytic functions | 81-82 | |

25 | Apr 3 | Poles and singularities | 83-84 | HW 8 due |

26 | Apr 6 | Applications to improper integrals | 85-87 | |

27 | Apr 8 | Jordan's Lemma and indented paths | 88-89 | |

28 | Apr 10 | Branch cuts and trigonometric integrals | 90-92 | HW 9 due |

29 | Apr 13 | Argument principle and Rouche's theorem | 93-94 | |

30 | Apr 15 | Linear transformations, the mapping w=1/z | 96-98 | |

31 | Apr 17 | Fractional linear transformations | 99-102 | HW 10 due |

32 | Apr 20 | The mappings exp(z) and sin(z) | 103-106 | |

33 | Apr 22 | Mappings by square roots and polynomials | 107-109 | |

34 | Apr 24 | Riemann surfaces | 110-111, G-XVI.1** | HW 11 due |

35 | Apr 27 | Conformal mappings and inverse function theorem | 112-114 | |

36 | Apr 29 | Analytic continuation and the Gamma function | G-XIV.1** | |

37 | May 1 | The Riemann-Zeta function | G-XIV.3** | HW 12 due |

May 6 | Final exam review I | |||

May 8 | Final exam review I | |||

May 12 |
Final Exam: 7pm-10pm |

*The numbers in the reading column refer to chapters in the course textbook

Brown and Churchill.

**Complex variables and Applications**, 9th Edition, 2013.**Numbers of the form G-# refer to chapters in the book

Theodore W. Gamelin, Complex Analysis, Springer, 2001,

which is available on SpringerLink.