3.1 線性理論
| Week | Course Content | Course Video |
|---|---|---|
| 課程介紹 | Watch Online | |
| Introduction of ODE | Watch Online | |
| Big Picture for ODE | Watch Online | |
| 1st order linear system | Watch Online | |
| 1st order linear system: 量的分析 | Watch Online | |
| 2nd order linear equation with constant coefficients | Watch Online | |
| Practical Problem | Watch Online | |
| Two more “derivation” of math models from: --Predator-Prey problem --Deposit and Withdraw problem | Watch Online | |
| 1.2 ODE Big Picture | Watch Online | |
| 1.2 Mixed Problem 1.3 Slope Field | Watch Online | |
| 1.3 Slope Field 1.4 Numerical Technique | Watch Online | |
| 1.5 IVP解: 存在性與唯一性 1.6 質分析, phase line(for autonomous system) | Watch Online | |
| 1.7 Bifurcation and one supplement for 1.6(real problem) | Watch Online | |
| Complete Chapter 1 | Watch Online | |
| Chapter 2: 1st order system and 2nd order equation | Watch Online | |
| 2.2 Geometry of the system(by vector field) 2.3 Damped harmonic oscillator | Watch Online | |
| 2.4 Special systems(solutions can be solved explicitly) 2.5 Euler’s method for 1st order system | Watch Online | |
| 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) | Watch Online | |
| 3.1 線性理論 | Watch Online | |
| 3.2 Straight-Line Solutions 3.3 Phase Portraits for Linear Systems with Real Eigenvalues | Watch Online | |
| 3.2 Straight-Line Solutions 3.3 Phase Portraits for Linear Systems with Real Eigenvalues 3.4 complex valued eigenvalues | Watch Online | |
| 3.5 Special cases of Linear systems | Watch Online | |
| To complete 3.5 | Watch Online | |
| 3.5 to complete 3.6 2nd order linear system and 2D linear system | Watch Online | |
| To complete 3.6 | Watch Online | |
| 3.7 Trace – Determinant Plane | Watch Online | |
| To complete chapter 3 3.7 Part II: T-D plane 3.8 3D linear system | Watch Online | |
| Non-linear 2nd order ode: --Pendulum motion --Pendulum motion and spring motion --Differences of phase portraits between linear and Nonlinear 2nd order equations | Watch Online | |
| Continue nonlinear 2nd order ode | Watch Online | |
| Special case for solving problems | Watch Online |
COURSE
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