## 2015-09-07

### 偏微分方程導論--李榮耀 / 交大

# 播放清單 (請按影片的右上角選取)

source: nctuocw        2015年8月24日

Mathematical models as PDE ─ qualitative and quantative analysis. Three classical types of linear PDEs and the corresponding theor

Lec01 偏微分方程導論 第一週課程 Fundamental differences between PDE and ODE. 1:40:50
Lec02 偏微分方程導論 第二週課程 (1/2) First and second order linear wave equations;Transport equations、Characteristic lines;Travelling wave solutions.、Wave equations with dispersion, dissipation, and nonlinearity. 51:59
Lec03 偏微分方程導論 第二週課程 (2/2) 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 Alembert solution (I). 1:35:26
Lec04 偏微分方程導論 第三週課程 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 .2:23:31
Lec05 偏微分方程導論 第四週課程 Initial-boundary value problem for a finite-line linear wave equation (II).2:21:03
Lec06 偏微分方程導論 第五週課程 Linear superposition and sub-problems.
Method of Separation of Variables.
Fourier series representations of solutions. 1:11:24
Lec07 偏微分方程導論 第六週課程 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. 2:14:44
Lec08 偏微分方程導論 第七週課程 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. 2:04:36
Lec09 偏微分方程導論 第八週課程 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.2:24:46
Lec10 偏微分方程導論 第九週課程 Boundary value problem for a Poisson’s equation in a circle.1:10:31
Lec11 偏微分方程導論 第十週課程 Well-posed problems for linear PDE systems (I).2:10:16
Lec12 偏微分方程導論 第十一週課程 Well-posed problems for linear PDE systems (II)2:24:49
Lec13 偏微分方程導論 第十二週課程 Well-posed problems for linear PDE systems (III).1:44:22
Lec14 偏微分方程導論 第十三週課程 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. 2:17:18
Lec15 偏微分方程導論 第十四週課程 Nonlinear problems (II) - kdV equation and the solitary solutions. 59:48
Lec16 偏微分方程導論 第十五週課程 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. 2:00:19
Lec17 偏微分方程導論 第十六週課程 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. 2:41:25
Lec18 偏微分方程導論 第十七週課程 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. 2:39:25