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微分方程 Differential Equations

課程行事曆

  • 微分方程 Differential Equations

課程行事曆  

本課程行事曆提供課程進度與考試資訊。

授課日期

老師授課主題

課本參考章節
2014/09/15 Introduction of ODE Introduction of ODE
2014/09/17 Big Picture for ODE 1.8 Linear Equations
2014/09/22 1st order linear system

1.8 Linear Equations
1.9 Integrating Factors for Linear Equations

2014/09/24 1st order linear system: 量的分析

3.6 Second-Order Linear Equations
4.1 Forced Harmonic Oscillators
4.2 Sinusoidal Forcing

2014/09/29 2nd order linear equation with constant coefficeints 3.6 Second-Order Linear Equations
2014/10/01 Practical Problem 1.1 Modeling via Differential Equations
2014/10/06

Two more “derivation” of math models from:

  • Predator-Prey problem
  • Deposit and Withdraw problem
2.1 Modeling via Systems
2014/10/08 1.2 ODE Big Picture 1.2 Analytic Technique: Separation of Variables
2014/10/13 1.2 Mixed Problem
1.3 Slope Field
1.2 Analytic Technique: Separation of Variables
1.3 Qualitative Technique: Slope Fields
2014/10/15 期中考  
2014/10/20 1.3 Slope Field
1.4 Numerical Technique
1.3 Qualitative Technique: Slope Fields
1.4 Numerical Technique: Euler’s Method
2014/10/22 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
2014/10/27 1.7 Bifurcation and one supplement for 1.6(real problem) 1.6 Equilibria and the Phase Line
1.7 Bifurcations
2014/10/29 Complete Chapter 1 1.1 Modeling via Differential Equations
2014/11/03 Chapter 2: 1st order system and 2nd order equation 2.1 Modeling via Systems
2014/11/05 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
2014/11/10 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
2014/11/12 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)
2.6 Existence and Uniqueness for Systems
2.7 The SIR Model of an Epidemic
2.8 The Lorenz Equations
2014/11/17 3.1 線性理論 3.1 Properties of Linear Systems and the Linearity Principle
2014/11/19 期中考  
2014/11/24 3.2 Straight-Line Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues
3.2 Straight-Line Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues
2014/11/26 3.2 Straight-Line Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues
3.4 complex valued eigenvalues
3.2 Straight-Line Solutions
3.3 Phase Portraits for Linear Systems with Real Eigenvalues
3.4 Complex Eigenvalues
2014/12/01 3.5 Special cases of Linear systems 3.5 Special Cases: Repeated and Zero Eigenvalues
2014/12/03 運動會  
2014/12/08 To complete 3.5 3.5 Special Cases: Repeated and Zero Eigenvalues
2014/12/10 3.5 to complete
3.6 2nd order linear system and 2D linear system
3.5 Special Cases: Repeated and Zero Eigenvalues
3.6 Second-Order Linear Equations
2014/12/15 To complete 3.6 3.6 Second-Order Linear Equations
2014/12/17 期中考  
2014/12/22 3.7 Trace – Determinant Plane 3.7 The Trace-Determinant Plane
2014/12/24 To complete chapter 3
3.7 Part II: T-D plane
3.8 3D linear system
3.7 The Trace-Determinant Plane
3.8 Linear Systems in Three Dimensions
2014/12/29

Non-linear 2nd order ode:

  • Pendulum motion
  • Pendulum motion and spring motion
  • Differences of phase portraits between linear and Nonlinear 2nd order equations
 
2014/12/31 Continue nonlinear 2nd order ode  
2015/01/05 Special case for solving problems  
2015/01/07 期末考  

 

 


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