老師授課主題

課本參考章節

Introduction of ODE 
Introduction of ODE 
Big Picture for ODE 
1.8 Linear Equations 
1st order linear system 
1.8 Linear Equations
1.9 Integrating Factors for Linear Equations

1st order linear system: 量的分析 
3.6 SecondOrder Linear Equations
4.1 Forced Harmonic Oscillators
4.2 Sinusoidal Forcing

2nd order linear equation with constant coefficeints 
3.6 SecondOrder Linear Equations 
Practical Problem 
1.1 Modeling via Differential Equations 
Two more “derivation” of math models from:

PredatorPrey problem

Deposit and Withdraw problem

2.1 Modeling via Systems 
1.2 ODE Big Picture 
1.2 Analytic Technique: Separation of Variables 
1.2 Mixed Problem
1.3 Slope Field 
1.2 Analytic Technique: Separation of Variables
1.3 Qualitative Technique: Slope Fields 
1.3 Slope Field
1.4 Numerical Technique 
1.3 Qualitative Technique: Slope Fields
1.4 Numerical Technique: Euler’s Method 
1.5 IVP解: 存在性與唯一性
1.6 質分析, phase line(for autonomous system) 
1.5 Existence and Uniqueness of Solutions
1.6 Equilibria and the Phase Line 
1.7 Bifurcation and one supplement for 1.6(real problem) 
1.6 Equilibria and the Phase Line
1.7 Bifurcations 
Complete Chapter 1 
1.1 Modeling via Differential Equations 
Chapter 2: 1st order system and 2nd order equation 
2.1 Modeling via Systems 
2.2 Geometry of the system(by vector field)
2.3 Damped harmonic oscillator 
2.2 The Geometry of Systems
2.3 The Damped Harmonic Oscillator 
2.4 Special systems(solutions can be solved explicitly)
2.5 Euler’s method for 1st order system 
2.4 Additional Analytic Methods for Special Systems
2.5 Euler’s Method for Systems 
2.6 存在與唯一性(for 1st order system)
2.7 (假的) 3Dsystem (流行病傳染問題)
2.8 (真的) 3Dsystem (氣象預報簡化系統: Lorenz equation) 
2.6 Existence and Uniqueness for Systems
2.7 The SIR Model of an Epidemic
2.8 The Lorenz Equations 
3.1 線性理論 
3.1 Properties of Linear Systems and the Linearity Principle 
3.2 StraightLine Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues 
3.2 StraightLine Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues 
3.2 StraightLine Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues
3.4 complex valued eigenvalues 
3.2 StraightLine Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues
3.4 Complex Eigenvalues 
3.5 Special cases of Linear systems 
3.5 Special Cases: Repeated and Zero Eigenvalues 
To complete 3.5 
3.5 Special Cases: Repeated and Zero Eigenvalues 
3.5 to complete
3.6 2nd order linear system and 2D linear system 
3.5 Special Cases: Repeated and Zero Eigenvalues
3.6 SecondOrder Linear Equations 
To complete 3.6 
3.6 SecondOrder Linear Equations 
3.7 Trace – Determinant Plane 
3.7 The TraceDeterminant Plane 
To complete chapter 3
3.7 Part II: TD plane
3.8 3D linear system 
3.7 The TraceDeterminant Plane
3.8 Linear Systems in Three Dimensions 
Nonlinear 2nd order ode:

Pendulum motion

Pendulum motion and spring motion

Differences of phase portraits between linear and Nonlinear 2nd order equations


Continue nonlinear 2nd order ode 

Special case for solving problems 
