偏微分方程導論 Introduction to Partial Differential Equations

Introduction to Partial Differential Equations

偏微分方程導論

課程首頁
課程影音
課程綱要
課程行事曆

Mathematical models as PDE ─ qualitative and quantative analysis.
Three classical types of linear PDEs and the corresponding theory.
A short topic on nonlinear PDE.

課程用書：

PDE, An Introduction, 2nd ed. by Walter A. Strauss;Publisher: Wiley

為求學習成效完美，請購買課本！

授課教師	應用數學系李榮耀老師
課程學分	3學分
授課年度	103學年度
授課對象	大學二年級學生
預備知識	常微分方程 (Differential Equations)
課程提供	課程影音課程綱要課程行事曆

每頁顯示個資料列

搜尋:

週次	課程內容	課程影音	課程下載
第一週	PDE導論. Fundamental differences between PDE and ODE.	線上觀看	MP4下載
第二週	First and second order linear wave equations; Transport equations Characteristic lines; Travelling wave solutions. Wave equations with dispersion, dissipation, and nonlinearity.	線上觀看	MP4下載
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 p	線上觀看	MP4下載
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 fo	線上觀看	MP4下載
第四週	Initial-boundary value problem for a finite-line linear wave equation (II).	線上觀看	MP4下載
第五週	Linear superposition and sub-problems. Method of Separation of Variables. Fourier series representations of solutions.	線上觀看	MP4下載
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.	線上觀看	MP4下載
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.	線上觀看	MP4下載
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.	線上觀看	MP4下載
第九週	Boundary value problem for a Poisson’s equation in a circle.	線上觀看	MP4下載
第十週	Well-posed problems for linear PDE systems (I).	線上觀看	MP4下載
第十一週	Well-posed problems for linear PDE systems (II).	線上觀看	MP4下載
第十二週	Well-posed problems for linear PDE systems (III).	線上觀看	MP4下載
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 solution	線上觀看	MP4下載
第十四週	Nonlinear problems (II) - kdV equation and the solitary solutions.	線上觀看	MP4下載
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.	線上觀看	MP4下載
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.	線上觀看	MP4下載
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.	線上觀看	MP4下載

目前顯示第 1 至第 18 個資料列，總計 18 個資料列

課程目標

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

章節	章節內容
PDE導論 Fundamental differences between PDE and ODE.	1.1* What is a Partial Differential Equation? 1.2* First-Order Linear Equations
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
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
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
Initial-boundary value problem for a finite-line linear wave equation (II).	3.2 Reflections of Waves Supplement to lecture notes
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
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
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
Boundary value problem for a Poisson’s equation in a circle.	6.3* Poisson’s Formula Chapter 5 Fourier Series
Well-posed problems for linear PDE systems (I).	1.5 Well-Posed Problems 6.1* Laplace’s Equation
Well-posed problems for linear PDE systems (II).	1.5 Well-Posed Problems 6.3* Poisson’s Formula
Well-posed problems for linear PDE systems (III).	2.1* The Wave Equation
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
Nonlinear problems (II) - kdV equation and the solitary solutions	14.1 Shock Waves 14.2 Solitary waves and Solitons Supplement to lecture notes
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
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)
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%

本課程行事曆提供課程進度與考試資訊參考。

授課日期	上課日期	參考課程進度
2015/02/25	PDE導論 Fundamental differences between PDE and ODE.	1.1* What is a Partial Differential Equation? 1.2* First-Order Linear Equations
2015/03/02	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
2015/03/04	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
2015/03/11	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
2015/03/18	Initial-boundary value problem for a finite-line linear wave equation (II).	3.2 Reflections of Waves Supplement to lecture notes
2015/03/25	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
2015/04/01	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
2015/04/08	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
2015/04/15	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
2015/04/22	Boundary value problem for a Poisson’s equation in a circle.	6.3* Poisson’s Formula Chapter 5 Fourier Series
2015/04/29	Well-posed problems for linear PDE systems (I).	1.5 Well-Posed Problems 6.1* Laplace’s Equation
2015/05/06	Well-posed problems for linear PDE systems (II).	1.5 Well-Posed Problems 6.3* Poisson’s Formula
2015/05/13	Well-posed problems for linear PDE systems (III).	2.1* The Wave Equation
2015/05/20	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
2015/05/27	Nonlinear problems (II) - kdV equation and the solitary solutions	14.1 Shock Waves 14.2 Solitary waves and Solitons Supplement to lecture notes
2015/06/03	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
2015/06/10	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)
2015/06/17	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)