国立交通大学 偏微分方程 二 Partial Differential Equations 97学年度 应用数学系 林琦焜老师

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资源信息： 中文名: 国立交通大学 偏微分方程(二) 英文名: Partial Differential Equations 别名: 数学物理方程 版本: 97学年度 应用数学系 林琦焜老师 发行日期: 2008年 地区: 台湾 对白语言: 普通话,英语 文字语言: 繁体中文 概述:

开拓视野新学习 数学交流新气象 本课程是由交通大学应用数学系提供。 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. 授课教师 应用数学系 林琦焜老师 授课时数 每週3小时 授课学分 3学分 授课学期 97学年度 授课对象 研究所学生 预备知识 Calculus, Advanced Calculus, Linear Algebra,Ordinary differential equation,Complex Analysis and Real analysis 课程纲要

课程目标/概述 本课程属研究所程度的微分方程课程，授课偏重於数学与物理间的连结，并且让学生藉由此课程了解直观地PDE概念。 课程章节 章节 主题 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 课程书目 * 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 单元主题 内容纲要 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 国立交通大学 偏微分方程(一)