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. – NYCU OCW

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.

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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

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