常微分方程
Ordinary Differential Equations
學期
108-1
學分
3
學分
當期課號
5377
永久課號
IAM5500
開課單位
應用數學系
授課教師
李明佳
校區
光復
類別
選修
上課時間表
| 節 | 週二 | 週四 |
|---|---|---|
2 09:00–09:50 | 常微分方程 SA211 | |
8 16:30–17:20 | 常微分方程 SA211 2 節連堂 | |
9 17:30–18:20 |
* 根據陽明交大上課時間表所列
概述
微分方程及動態系統相關研究課題的預備知識
先修科目
大學部高等微積分、微分方程、線性代數
評分方式
研讀教科書、上台報告、發問討論
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1~18週 研讀論文、上台報告、發問討論 |
| 第 18 週 | introduction linear differential equations linear systems: sink and source two-dimensional linear differential equaionts hyperbolic linear differential equation stability of hyperbolic linear ODEs the implicit function theorem transformation and the inverse function theorem fundamental theorem for ODEs continuity and differentiability on parameters and initial condition differential inequality fundamental matrices flows of ODEs, the nonwandering set and the chain recurrent set asymptoical stability and topological equivalence Lyapunov functions on R^k the Hartman and Grobman theorem for nonlinear ODEs proof of the Hartman and Grobman theorem hyperblic periodic orbits the Poincare map the Poincare-Bendixson theore gradient flows on R^k gradient-like flows saddle-node and other bifurcation the Andronov-Hopf bifurcation center manifold theorem manifold and tangent bundles Riemannian metric and norm, and immersed and embedding manifolds the C^r topology the quotient topology and quotient space Lorenz attractor attracting set for flows Conley's fundamental theorem of dynamical systems flow expansiveness and structural stability of Anosov |
教科書
Textbook: Clark Robinson, Dynamical systems: stability, symbolic dynamics, and chaos, 2nd Edition, Boca Raton, FL, CRC Press, 1999. References: Jack Hale, Ordinary differential equations, R. E. Krieger Pub. Co., Huntington, New York, 1980. Philip Hartman,Ordinary differential equations, SIAM, Philadelphia, PA, 2002.
Office Hours
- 地點
- 科學一館337
- 時間
- 3EF
- 聯絡方式
- 分機:56463