Non-linear 2nd order ode:–Pendulum motion –Pendulum motion and spring motion –Differences of phase portraits between linear and Nonlinear 2nd order equations

Non-linear 2nd order ode:--Pendulum motion --Pendulum motion and spring motion --Differences of phase portraits between linear and Nonlinear 2nd order equations

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課程內容	課程影音	課程下載
課程介紹	線上觀看	MP4下載
Introduction of ODE	線上觀看	MP4下載
Big Picture for ODE	線上觀看	MP4下載
1st order linear system	線上觀看	MP4下載
1st order linear system: 量的分析	線上觀看	MP4下載
2nd order linear equation with constant coefficients	線上觀看	MP4下載
Practical Problem	線上觀看	MP4下載
Two more “derivation” of math models from: --Predator-Prey problem --Deposit and Withdraw problem	線上觀看	MP4下載
1.2 ODE Big Picture	線上觀看	MP4下載
1.2 Mixed Problem 1.3 Slope Field	線上觀看	MP4下載
1.3 Slope Field 1.4 Numerical Technique	線上觀看	MP4下載
1.5 IVP解: 存在性與唯一性 1.6 質分析, phase line(for autonomous system)	線上觀看	MP4下載
1.7 Bifurcation and one supplement for 1.6(real problem)	線上觀看	MP4下載
Complete Chapter 1	線上觀看	MP4下載
Chapter 2: 1st order system and 2nd order equation	線上觀看	MP4下載
2.2 Geometry of the system(by vector field) 2.3 Damped harmonic oscillator	線上觀看	MP4下載
2.4 Special systems(solutions can be solved explicitly) 2.5 Euler’s method for 1st order system	線上觀看	MP4下載
2.6 存在與唯一性(for 1st order system) 2.7 (假的) 3D-system (流行病傳染問題) 2.8 (真的) 3D-system (氣象預報簡化系統: Lorenz equation)	線上觀看	MP4下載
3.1 線性理論	線上觀看	MP4下載
3.2 Straight-Line Solutions 3.3 Phase Portraits for Linear Systems with Real Eigenvalues	線上觀看	MP4下載
3.2 Straight-Line Solutions 3.3 Phase Portraits for Linear Systems with Real Eigenvalues 3.4 complex valued eigenvalues	線上觀看	MP4下載
3.5 Special cases of Linear systems	線上觀看	MP4下載
To complete 3.5	線上觀看	MP4下載
3.5 to complete 3.6 2nd order linear system and 2D linear system	線上觀看	MP4下載
To complete 3.6	線上觀看	MP4下載
3.7 Trace – Determinant Plane	線上觀看	MP4下載
To complete chapter 3 3.7 Part II: T-D plane 3.8 3D linear system	線上觀看	MP4下載
Non-linear 2nd order ode: --Pendulum motion --Pendulum motion and spring motion --Differences of phase portraits between linear and Nonlinear 2nd order equations	線上觀看	MP4下載
Continue nonlinear 2nd order ode	線上觀看	MP4下載
Special case for solving problems	線上觀看	MP4下載

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