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《国立交通大学 偏微分方程(一)》(Partial Differential Equations)97学年度 应用数学系 林琦焜老师

2010-04-21 03:27:41  編輯來源:互聯網  简体版  手機版  評論  字體: ||
 
 
  中文名: 国立交通大学 偏微分方程(一)

  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

  发行时间: 2008年

  地区: 台湾

  对白语言: 普通话,英语

  文字语言: 繁体中文

  简介:

  

  

  
《国立交通大学 偏微分方程(一)》(Partial Differential Equations)97学年度 应用数学系 林琦焜老师


  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。

  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。

  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

  第一章 The Single First-Order Equation

  第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables

  第三章 Characteristic Manifolds and Cauchy Problem

  第四章 The Laplace Equation

  课程书目

   * Partial Differential Equations (4th Edition), Fritz John

   * Applied Mathematical Sciences Vol.1, Springer-Verlag 1982

  课程纲要

  单元主题

  

  内容纲要

  第一章 The Single First-Order Equation

   1-1 Introduction Partial differential equations occur throughout mathematics. In this part we will give some examples

   1-2 Examples

   1-3 Analytic Solution and Approximation methods in a simple example 1-st order linear example

   1-4 Quasilinear Equation The concept of characteristic

   1-5 The Cauchy Problem for the Quasilinear-linear Equations

   1-6 Examples Solved problems

   1-7 The general first-order equation for a function of two variables characteristic curves, envelope

   1-8 The Cauchy Problem characteristic curves, envelope

   1-9 Solutions generated as envelopes

  第二章Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables

   2-1 Characteristics for Linear and Quasilinear Second-Order Equations Characteristic

   2-2 Propagation of Singularity Characteristic curve and singularity

   2-3 The Linear Second-Order Equation classification of 2nd order equation

   2-4 The One-Dimensional Wave Equation dAlembert formula, dimond law, Fourier series

   2-5 System of First-Order Equations Canonical form, Characteristic polynominal

   2-6 A Quasi-linear System and Simple Waves Concept of simple wave

  第三章 Characteristic Manifolds and Cauchy Problem

   3-1 Natation of Laurent Schwartz Multi-index notation

   3-2 The Cauchy Problem Characteristic matrix, characteristic form

   3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem Local existence of solutions of the non-characteristic

   3-4 The Lagrange-Green Identity Gauss divergence theorem

   3-5 The Uniqueness Theorem of Holmgren Uniqueness of analytic partial differential equations

   3-6 Distribution Solutions Introdution of Laurent Schwartzs theory of distribution (generalized function)

  第四章 The Laplace Equation

   4-1 Greens Identity, Fundamental Solutions, and Poissons Equation Dirichlet problem, Neumann problem, spherical symmetry, mean value theorem, Poisson formula

   4-2 The Maximal Principle harmonic and subharmonic functions

   4-3 The Dirichlet Problem, Greens Function, and Poisson Formula Symmetric point, Poisson kernel

   4-4 Perrons method Existence proof of the Dirichlet problem

   4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods Functional analysis, Riesz representation theorem, Dirichlet integra
 
 
 
中文名: 国立交通大学 偏微分方程(一) 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 发行时间: 2008年 地区: 台湾 对白语言: 普通话,英语 文字语言: 繁体中文 简介: [url=/bt/detail_90137.html][img]http://image.wangchao.net.cn/bt/1271791659091.jpg[/img][/url] 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。  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。 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 第一章 The Single First-Order Equation 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 第三章 Characteristic Manifolds and Cauchy Problem 第四章 The Laplace Equation 课程书目 * Partial Differential Equations (4th Edition), Fritz John * Applied Mathematical Sciences Vol.1, Springer-Verlag 1982 课程纲要 单元主题 内容纲要 第一章 The Single First-Order Equation 1-1 Introduction Partial differential equations occur throughout mathematics. In this part we will give some examples 1-2 Examples 1-3 Analytic Solution and Approximation methods in a simple example 1-st order linear example 1-4 Quasilinear Equation The concept of characteristic 1-5 The Cauchy Problem for the Quasilinear-linear Equations 1-6 Examples Solved problems 1-7 The general first-order equation for a function of two variables characteristic curves, envelope 1-8 The Cauchy Problem characteristic curves, envelope 1-9 Solutions generated as envelopes 第二章Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-1 Characteristics for Linear and Quasilinear Second-Order Equations Characteristic 2-2 Propagation of Singularity Characteristic curve and singularity 2-3 The Linear Second-Order Equation classification of 2nd order equation 2-4 The One-Dimensional Wave Equation dAlembert formula, dimond law, Fourier series 2-5 System of First-Order Equations Canonical form, Characteristic polynominal 2-6 A Quasi-linear System and Simple Waves Concept of simple wave 第三章 Characteristic Manifolds and Cauchy Problem 3-1 Natation of Laurent Schwartz Multi-index notation 3-2 The Cauchy Problem Characteristic matrix, characteristic form 3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem Local existence of solutions of the non-characteristic 3-4 The Lagrange-Green Identity Gauss divergence theorem 3-5 The Uniqueness Theorem of Holmgren Uniqueness of analytic partial differential equations 3-6 Distribution Solutions Introdution of Laurent Schwartzs theory of distribution (generalized function) 第四章 The Laplace Equation 4-1 Greens Identity, Fundamental Solutions, and Poissons Equation Dirichlet problem, Neumann problem, spherical symmetry, mean value theorem, Poisson formula 4-2 The Maximal Principle harmonic and subharmonic functions 4-3 The Dirichlet Problem, Greens Function, and Poisson Formula Symmetric point, Poisson kernel 4-4 Perrons method Existence proof of the Dirichlet problem 4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods Functional analysis, Riesz representation theorem, Dirichlet integra
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