LEC # | TOPICS |
---|---|

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 |

## Calendar

## Course Info

##### Instructors

##### Departments

##### As Taught In

Fall
2004

##### Level

##### Learning Resource Types

*notes*Lecture Notes

*grading*Exams with Solutions