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General |
MATH 670 , Fall 2007: Notes and Summary
| 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 |
