偏微分方程(二) Partial Differential Equations II | 應用數學系林琦焜老師

Partial Differential Equations II

偏微分方程(二)

課程首頁
課程影音
課程綱要
課程行事曆

本課程屬研究所程度的微分方程課程，授課偏重於數學與物理間的連結，並且讓學生藉由此課程了解直觀地PDE概念。

課程用書：Fritz John, Partial Differential Equations (4th Edition), Applied Mathematical Sciences Vol.1 Springer-Verlag 1982.

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授課老師	應用數學系林琦焜老師
課程學分	3學分
授課年度	97學年度
授課對象	研究所學生
預備知識	Calculus, Advanced Calculus, Linear Algebra, Ordinary differential equation, Complex Analysis and Real analysis
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
	第五章 Hyperbolic Equations in Higher Dimensions 5-1 The Wave Equation in n-Dimensional Space	線上觀看
	第五章 Hyperbolic Equations in Higher Dimensions 5-2 Higher-Order Hyperbolic Equations with Constant Coefficients	線上觀看
	第五章 Hyperbolic Equations in Higher Dimensions 5-3 Symmetric Hyperbolic System	線上觀看
	第六章 Higher-Order Elliptic Equations with Constant Coefficients 6-1 The Fundamental Solution for Odd n	線上觀看
	第六章 Higher-Order Elliptic Equations with Constant Coefficients 6-2 The Dirichlet Problem	線上觀看
	第六章 Higher-Order Elliptic Equations with Constant Coefficients 6-3 Sobolev Space	線上觀看
	第七章 Parabolic Equations 7-1 The Heat Equation	線上觀看
	第七章 Parabolic Equations 7-2 The Initial-Value Problem for General Second-Order Parabolic Equations	線上觀看
	第八章 H. Lewys Example of a Linear Equation without Solutions 8-1 Brief introduction of Functional Analysis	線上觀看
	第八章 H. Lewys Example of a Linear Equation without Solutions 8-2 Semigroups of linear operator	線上觀看
	第八章 H. Lewys Example of a Linear Equation without Solutions 8-3 Perturbations and Approximations	線上觀看
	第八章 H. Lewys Example of a Linear Equation without Solutions 8-4 The abstract Cauchy Problem	線上觀看
	第八章 H. Lewys Example of a Linear Equation without Solutions 8-5 Application to linear partial differential equations	線上觀看
	第八章 H. Lewys Example of a Linear Equation without Solutions 8-6 Applications to nonlinear partial differential equations	線上觀看
	第八章 H. Lewys Example of a Linear Equation without Solutions 8-6 Applications to nonlinear partial differential equations	線上觀看

目前顯示第 1 至第 15 個資料列，總計 15 個資料列

課程目標

本課程屬研究所程度的微分方程課程，授課偏重於數學與物理間的連結，並且讓學生藉由此課程了解直觀地PDE概念。

課程章節

章節	主題內容
第五章	Hyperbolic Equations in Higher Dimensions
第六章	Higher-Order Elliptic Equations with Constant Coefficients
第七章	Parabolic Equations
第八章	H. Lewys Example of a Linear Equation without Solutions

課程書目

Fritz John, Partial Differential Equations (4th Edition), Applied Mathematical Sciences Vol.1 Springer-Verlag 1982.
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983.

評分標準

項目	百分比
平時作業	60%
期中報告	20%
期末報告	20%

本課程行事曆提供課程進度與考試資訊參考。

章節	主題內容
第五章 Hyperbolic Equations in Higher Dimensions	5-1 The Wave Equation in n-Dimensional Space 5-2 Higher-Order Hyperbolic Equations with Constant Coefficients 5-3 Symmetric Hyperbolic System
第六章 Higher-Order Elliptic Equations with Constant Coefficients	6-1 The Fundamental Solution for Odd n 6-2 The Dirichlet Problem 6-3 Sobolev Space
第七章 Parabolic Equations	7-1 The Heat Equation 7-2 The Initial-Value Problem for General Second-Order Parabolic Equations
第八章 H. Lewys Example of a Linear Equation without Solutions	8-1 Brief introduction of Functional Analysis 8-2 Semigroups of linear operator 8-3 Perturbations and Approximations 8-4 The abstract Cauchy Problem 8-5 Application to linear partial differential equations 8-6 Applications to nonlinear partial differential equations