商品編號: unc0043d
  商品名稱: 偏微分方程(二) 全16講 台灣國立交通大學 DVD 只於電腦播放
  光碟片數: 1片
  銷售價格: $200元
您可能感興趣: Max 
unc0285d--上海交通大學 IT項目管理 普通話 簡體中文 DVD 只於電腦播放
unc0012c--人類健康的未來:七個顛覆你思想的演講 The Future of Human Health 7 Very Short Talks That Will Blow Your Mind 斯坦福大學開放課程 英文版 CD只能於電腦播放
unc0325d--吉林大學 概率統計D 48講 孫毅主講 簡體中文 普通話 DVD
unc0133d-4--耶魯大學開放課程:有關食物的心理學,生物學和政治學 The Psychology, Biology and Politics of Food 英文版 DVD 只於電腦播放
unc0041d-2--傅立葉分析及應用 全30講 台灣國立交通大學 繁體中文 2DVD 只於電腦播放
偏微分方程(二) 全16講 台灣國立交通大學 DVD 只於電腦播放


This is the continuous course of Partial Differential Equations (I).This is the GRADUATE level partial differential equation. We will focus on the relation between mathematics and physics and show the students how to understand PDEs intuitively.
授課教師 應用數學系 林琦焜老師

授課時數 每週3小時

授課學分 3學分

授課學期 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



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


* 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

第五章Hyperbolic Equations in Higher Dimensions
5-1 The Wave Equation in n-Dimensional Space
(1) The method of sphereical means
(2) Hadmards method of descent
(3) Duhamels principle and the general Cauchy problem
(4) mixed problem
5-2 Higher-Order Hyperbolic Equations with Constant Coefficients
(1) Standard form of the initial-value problem
(2) solution by Fourier transform,
(3) solution of a mixed problem by Fourier transform
5-3 Symmetric Hyperbolic System
(1) The basic energy inequality
(2)Finite difference method
(3) Schauder method
第六章Higher-Order Elliptic Equations with Constant Coefficients
6-1 The Fundamental Solution for Odd n Travelling wave
6-2 The Dirichlet Problem Lax-Milgram theorem, Garding inequality
6-3 Sobolev Space Weak solution and Hibert space
第七章 Parabolic Equations
7-1 The Heat Equation Self-Similarity, Heat kernel, Maximum principle
7-2 The Initial-Value Problem for General Second-Order Parabolic Equations
(1) Finite difference and Maximum principle
(2) Existence of Initial Value Problem
第八章H. Lewys Example of a Linear Equation without Solutions
8-1 Brief introduction of Functional Analysis Hilbert and Banach spaces, projection theorem, Leray-Schauder theorem
8-2 Semigroups of linear operator Generation, representation and spectral properties
8-3 Perturbations and Approximations The Trotter theorem
8-4 The abstract Cauchy Problem Basic theory
8-5 Application to linear partial differential equations Parabolic equation, Wave equation and Schrodinger equation
8-6 Applications to nonlinear partial differential equations KdV equation, nonlinear heat equation, nonmlinear Schrodinger equation