1 |
Number Systems and Algebra of Complex Numbers |

2 |
Elementary Complex Functions, Part 1 |

3 |
Elementary Complex Functions, Part 2 |

4 |
Branch Points and Branch Cuts |

5 |
Analytic Functions |

6 |
Complex Integrals |

7 |
Cauchy's Formula, Properties of Analytic Functions |

8 |
Taylor Series, Laurent Series |

9 |
Laurent Series (cont.) |

10 |
Properties of Laurent Series, Singularities |

11 |
Singularities (cont.) |

12 |
Residue Theorem |

13 |
In-class exam 1 |

14 |
Evaluation of Real Definite Integrals, Case I |

15 |
Evaluation of Real Definite Integrals, Case II |

16 |
Evaluation of Real Definite Integrals, Case III |

17 |
Evaluation of Real Definite Integrals, Case IV |

18 |
Theorems for Contour Integration |

19 |
Series and Convergence |

20 |
Ordinary Differential Equations |

21 |
Singular Points of Linear Second-Order ODEs |

22 |
Frobenius Method |

23 |
Frobenius Method - Examples |

24 |
Frobenius Method (cont.) and a "particular type" of ODE |

25 |
Bessel Functions |

26 |
Properties of Bessel Functions |

27 |
Modified Bessel Functions |

28 |
In-class exam 2 |

29 |
Differential Equations Satisfied by Bessel Functions |

30 |
Introduction to Boundary-Value Problems |

31 |
Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions |

32 |
Boundary Value Problems for Nonhomogeneous PDEs |

33 |
Sturm-Liouville Problem |

34 |
Fourier Series |

35 |
Fourier Sine and Cosine Series |

36 |
Complete Fourier Series |

37 |
Review of Boundary Value Problems for Nonhomogeneous PDEs |

38 |
In-class exam 3 |