測試文章(表格)屬於分類五,長標題文章會遭遇的排版問題長標題文章會遭遇的排版問題

By 開放教育推動中心 | 2017-01-09 JUNE 7, 2017 |
課程目標/概述

  • Mathematical models as PDE – qualitative and quantative analysis.
  • Three classical types of lineat PDEs and the corresponding theory.
  • A short topics on nonlinear PDE.

 

課程章節

授課週次

老師授課主題

課本參考章節
第一週
  • PDE導論
  • Fundamental differences between PDE and ODE.
  • 1.1* What is a Partial Differential Equation?
  • 1.2* First-Order Linear Equations
第二週
  • First and second order linear wave equations;
  • Transport equations
  • Characteristic lines;
  • Travelling wave solutions.
  • Wave equations with dispersion, dissipation, and nonlinearity
  • 2.1* The Wave Equation
第二週
  • Classical linear wave equations with travelling wave solutions.
  • Dispersive linear wave equations.
  • Dissipative linear wave equations.
  • Nonlinear wave equations with shock wave solutions.
  • Nonlinear wave equations with solitary wave solutions.
  • Initial value problem for a whole-line linear wave equation and the dAlembert solution (I)
  • 1.1* What is a Partial Differential Equation?
  • 2.1* The Wave Equation
  • Supplement to lecture notes
第三週
  • Classification of 3 types of second order linear PDEs (I).
  • Initial value problem for a whole-line linear wave equation and the dAlembert solutions (II).
  • Initial-boundary value problem for a half-line linear wave equation.
  • Initial-boundary value problem for a finite-line linear wave equation (I) – method of Reflection and method of Separation of Variables.
  • 2.1* The Wave Equation
  • 3.2 Reflections of Waves
  • 1.6 Types of Second-Order Equations
第四週
  • Initial-boundary value problem for a finite-line linear wave equation (II).
  • 3.2 Reflections of Waves
  • Supplement to lecture notes
第五週
  • Linear superposition and sub-problems
  • Method of Separation of Variables
  • Fourier series representations of solutions
  • 4.1* Separation of Variables, The Dirichlet Condition
  • Chapter 5 Fourier Series
第六週
  • Classification of 3 types of second order linear PDEs (II).
  • Initial value problem for a whole-line linear heat equation solved by the Fundamental solution
  • 2.4* Diffusion on the Whole Line
  • 4.1* Separation of Variables, The Dirichlet Condition
第七週
  • Initial-boundary value problem for a finite-line linear heat equations solved by method of Separation of Variables.
  • Initial value problem for an infinite-line linear heat equation solved by Fourier transform and inverse Fourier transform.
  • 4.1* Separation of Variables, The Dirichlet Condition
  • Chapter 5 Fourier Series
  • 12.3 Fourier Transform
第八週
  • Boundary value problem for a Laplace’s equation in a rectangle solved by method of Separation of Variables.
  • Boundary value problem for a Laplace’s equation in a circle solved by method of Separation of Variables.
  • 6.1* Laplace’s Equation
  • 6.2* Rectangles and Cubes 161
  • 6.3* Poisson’s Formula
  • Chapter 5 Fourier Series
第九週
  • Boundary value problem for a Poisson’s equation in a circle.
  • 6.3* Poisson’s Formula
  • Chapter 5 Fourier Series
第十週
  • Well-posed problems for linear PDE systems (I).
  • 1.5 Well-Posed Problems
  • 6.1* Laplace’s Equation
第十一週
  • Well-posed problems for linear PDE systems (II).
  • 1.5 Well-Posed Problems
  • 6.3* Poisson’s Formula
第十二週
  • Well-posed problems for linear PDE systems (III).
  • 2.1* The Wave Equation
第十三週
  • Nonlinear problems (I) –
  • The effect of a combination of nonlinearity and dispersion;
  • The effect of a combination of nonlinearity and dissipation;
  • The effect of a combination of nonlinearity, dispersion, and dissipation.
  • Shock waves, steady-state solutions, travelling wave solutions, soliton solutions, N-soliton solutions, and wavetrains.
  • 14.1 Shock Waves
  • 14.2 Solitary waves and Solitons
  • Supplement to lecture notes
第十四週
  • Nonlinear problems (II) –
  • kdV equation and the solitary solutions
  • 14.1 Shock Waves
  • 14.2 Solitary waves and Solitons
  • Supplement to lecture notes
第十五週
  • Nonlinear Problems (III) – : Three famous universal nonlinear PDEs – kdV, s-G, and NLS equations.
  • Completely integrable systems
  • s-G equation and the travelling wave solutions.
  • NLS equation and the solitary wave solutions.
  • 14.2 Solitary waves and Solitons
  • Supplement to lecture notes
第十六週
  • Nonlinear Problems (IV) – Introduction of Riemann surfaces of genus N (1) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.
  • Supplement to lecture notes – Extension I of sec14.2 – the underlying theory of solutions of universal nonlinear PDEs (KdV, s-G, and NLS)
第十七週
  • Nonlinear Problems (V) – Introduction of Riemann surfaces of genus N (2) for the underlying theory of solutions of universal nonlinear PDEs such as kdV, s-G, and NLS.
  • Supplement to lecture notes – Extension II of sec14-the underlying theory of solutions of universal nonlinear PDEs (KdV, s-G, and NLS)

 

課程書目

PDE, An Introduction, 2nd ed. by Walter A. Strauss

 

評分標準

項目 百分比

四次考試(最佳3次每次30%,剩餘1次10%)

100%