Lecture |
Date |
What was
covered |
Notes |

1 |
Aug.
30 |
Review of analysis &
topology |
- |

2 |
Sept.
4 |
Review
cont'd, Arzela-Ascoli theorem |
get
assignment 1 |

3 |
Sept.
6 |
Existence
Theorem |
- |

4 |
Sept.
11 |
class
cancelled |
- |

5 |
Sept.
13 |
Uniqueness Theorem |
return
assignment 1 |

6 |
Sept.
18 |
Numerical
Approximation |
get
assignment 2 |

7 |
Sept.
20 |
Continuation (I) |
- |

8 |
Sept.
25 |
Continuation (II) |
return
assignment 2 |

9 |
Sept.
27 |
Continuity
w.r.t. Initial Condition |
get assignment 3 |

10 |
Oct.
2 |
Separable
ODE, Integrals |
- |

11 |
Oct.
4 |
Flows,
Phase Portrait (1) |
- |

12 |
Oct.
9 |
Phase
Portraits (2) |
return
assignment 3/get assignment 4 |

13 |
Oct.
11 |
Phase
Portraits (3) |
- |

14 |
Oct.
16 |
Differential Inequalities
(1) |
return
assignment 4 |

15 |
Oct.
18 |
Differential Inequalities
(2) |
get
assignment 5 |

16 |
Oct.
23 |
Linear ODE
(LODE) - Introduction |
return
assignment 5 |

17 |
Oct.
25 |
MIDTERM |
MIDTERM |

18 |
Oct.
30 |
LODE:
Fundamental Matrix Solution |
get
assignment 6 |

19 |
Nov.
1 |
LODE: Higher-Order Case |
- |

20 |
Nov.
6 |
LODE:
Higher-Order & Complex Case |
return
assignment 6/get assignment 7 |

21 |
Nov.
8 |
Matrix Exponential |
- |

22 |
Nov.
13 |
Matrix Expo:
Generalized Eigenvectors&Jordan Form |
get assignment
8/return
assignment 7 |

23 |
Nov.
15 |
Matrix
Exponential with Laplace Transform |
- |

24 |
Nov.
20 |
Range of the
Matrix Exponential/Stability |
return
assignment 8 |

25 |
Nov.
22 |
no
class |
Thanksgiving |

26 |
Nov.
27 |
Stability: Liapunov (I) |
get assignment
9 |

27 |
Nov.
29 |
Stability:
Liapunov (II) |
- |

28 |
Dec.
4 |
Stability of LODE with Constant
Coeffs |
return
assignment 9/get assignment 10 |

29 |
Dec.
6 |
Stability of
general LODE |
- |

30 |
Dec.
11 |
Stability of
Periodic LODE |
return
assignment 10/Last
Lecture |