Jan 11 |
Complex numbers, exp(z), and Euler's formula |

Jan 13 |
properties of exp(z) |

Jan 15 |
Roots of unity |

Jan 18 |
Holiday |

Jan 20 |
Mobius Transformation |

Jan 22 |
Planner sets |

Jan 25 |
Limit and Continuity(Examples for real valued functions) |

Jan 27 |
Derivatives, Cauchy-Riemann equations,
Analytic functions, Entire functions |

Jan 29 |
Harmonic functions, Singularities |

Feb 01 |
Sequence and Series |

Feb 03 |
Power series, radius of convergence |

Feb 05 |
Uniform convergence, Weierstrass-M test, Taylor's
Theorem |

Feb 08 |
Line and contour integrals |

Feb 10 |
Review for Midterm I |

Feb 12 |
Green's Thorem, Cauchy's Theorem |

Feb 15 |
Fundamental Theorem of Calculus |

Feb 17 |
Cauchy's Integral Formula |

Feb 19 |
General Cauchy's Integral Formula,
Taylor's Theorem |

Feb 22 |
Singularities and Laurent Series.(Examples of Laurent Series) |

Feb 24 |
Residues |

Feb 26 |
Residues and Examples |

Feb 29-Mar 4 |
Spring Breaks |

Mar 7 |
Meromorphic function and Residue theorem |

Mar 9 |
Applications to Residue theorem and Cauchy
principle value |

Mar 11 |
Applications to Residue theorem and Impropre
integral |

Feb 14 |
Applications to Residue theorem and Partial
fraction expansions |

Feb 16 |
Applications to Residue theorem, Partial
fraction expansions, and Trigonometric integrals |

Mar 18 |
More applications |

Mar 21 |
More applications and Jordan's lemma |

Mar 23 |
Applications to Residue therem, Maximum modulus
principle |

Feb 25 |
Maximum modulus principle, Liouville's theorem |

Mar 28 |
Review and Midterm II(Practice Problems) |