Partial Differential Equations I
偏微分方程(一)
本課程是由 國立陽明交通大學應用數學系 提供。
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 |
| 週次 | 課程內容 | 課程影音 | 課程下載 |
|---|---|---|---|
| 第一章 The Single First-Order Equation 1-1 Introduction | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-2 Examples | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-3 Analytic Solution and Approximation methods in a simple example | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-4 Quasilinear Equation | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-5 The Cauchy Problem for the Quasilinear-linear Equations | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-6 Examples | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-7 The general first-order equation for a function of two variables | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-8 The Cauchy Problem | 線上觀看 | MP4下載 | |
| 第一章 The Single First-Order Equation 1-9 Solutions generated as envelopes | 線上觀看 | MP4下載 | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-1 Characteristics for Linear and Quasilinear Second-Order Equations | 線上觀看 | MP4下載 | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-2 Propagation of Singularity | 線上觀看 | MP4下載 | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-3 The Linear Second-Order Equation | 線上觀看 | MP4下載 | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-4 The One-Dimensional Wave Equation | 線上觀看 | MP4下載 | |
| 第二章 Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-5 System of First-Order Equations | 線上觀看 | MP4下載 | |
| 第二章Second-Order Equations: Hyperbolic Equations for Functions of Two Independent Variables 2-6 A Quasi-linear System and Simple Waves | 線上觀看 | MP4下載 | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-1 Natation of Laurent Schwartz | 線上觀看 | MP4下載 | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-2 The Cauchy Problem | 線上觀看 | MP4下載 | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem | 線上觀看 | MP4下載 | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-4 The Lagrange-Green Identity | 線上觀看 | MP4下載 | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-5 The Uniqueness Theorem of Holmgren | 線上觀看 | MP4下載 | |
| 第三章 Characteristic Manifolds and Cauchy Problem 3-6 Distribution Solutions | 線上觀看 | MP4下載 | |
| 第四章 The Laplace Equation 4-1 Greens Identity, Fundamental Solutions, and Poissons Equation | 線上觀看 | MP4下載 | |
| 第四章 The Laplace Equation 4-2 The Maximal Principle | 線上觀看 | MP4下載 | |
| 第四章 The Laplace Equation 4-3 The Dirichlet Problem, Greens Function, and Poisson Formula | 線上觀看 | MP4下載 | |
| 第四章 The Laplace Equation 4-4 Perrons method | 線上觀看 | MP4下載 | |
| 第四章 The Laplace Equation 4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods | 線上觀看 | MP4下載 |
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 |
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 |
| 第一章 The Single First-Order Equation | 1-1 Introduction 1-2 Examples 1-3 Analytic Solution and Approximation methods in a simple example 1-4 Quasilinear Equation 1-5 The Cauchy Problem for the Quasilinear-linear Equations 1-6 Examples 1-7 The general first-order equation for a function of two variables 1-8 The Cauchy Problem 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 2-2 Propagation of Singularity 2-3 The Linear Second-Order Equation 2-4 The One-Dimensional Wave Equation 2-5 System of First-Order Equations 2-6 A Quasi-linear System and Simple Waves |
| 第三章 Characteristic Manifolds and Cauchy Problem | 3-1 Natation of Laurent Schwartz 3-2 The Cauchy Problem 3-3 Real Analytic Functions and the Cauchy-Kowalevski Theorem 3-4 The Lagrange-Green Identity 3-5 The Uniqueness Theorem of Holmgren 3-6 Distribution Solutions |
| 第四章 The Laplace Equation | 4-1 Greens Identity, Fundamental Solutions, and Poissons Equation 4-2 The Maximal Principle 4-3 The Dirichlet Problem, Greens Function, and Poisson Formula 4-4 Perrons method 4-5 Solution of the Dirichlet Problem by Hilbert-Space Methods |
課程專區
選單