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課程名稱 |
偏微分方程導論
Introduction to Partial Differential Equations |
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開課學期 |
102-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳俊全 |
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課號 |
MATH2206 |
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課程識別碼 |
201 25000 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期二7,8(14:20~16:20)星期五1,2(8:10~10:00) |
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上課地點 |
新102新102 |
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備註 |
教學改善計畫課程，有教學助理實施小班輔導。
總人數上限：120人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1022Intro_PDE |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. PDE problems from physics and mathematics
2. First order equations
3. Wave equation, causality and energy
4. Diffusion equation, maximum principle, heat kernel
5. Fourier series
6. Boundary problems
7. Harmonic functions, Poisson's foumula, Green's function
8. Eigenvalue problems |
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課程目標 |
Course Goal：
This course provides an introduction to the basic theory of partial differential equations. |
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課程要求 |
Course prerequisite:
Calculus, advanced calculus, linear algebra |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
Walter A. Strauss
Partial Differential Equations-An Introduction, Second Edition |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
homework |
25% |
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2. |
midterm exam |
35% |
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3. |
final exam |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/18,2/21 |
Introduction: examples of important PDE; transport equation. |
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第2週 |
2/25,2/28 |
Method of characteristic curves: 1st order linear and quasi-linear equations.
Vibrating string and the wave equation. |
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第3週 |
3/04,3/07 |
Wave equation: general solution; bi-characteristics; initial value problem on the whole line;
Causality: domain of dependence; domain of influence |
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第4週 |
3/11,3/14 |
Kinetic engergy and potential energy of the wave equation: lemmas for interchange of differentiation and integration.
Diffusion: flux and Fick's law. |
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第5週 |
3/18,3/21 |
Diffusion: Fick's law, Fourier law, Laplacian and the diffusion equation; maximum principle, uniqueness of the Dirichlet problem. |
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第6週 |
3/25,3/28 |
Invariance properties of diffusion equation: translation, derivatives, linear combination, integral, and scaling.
Fundamental solution: importance, how to solve it, Gaussian distribution. |
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第7週 |
4/01,4/04 |
Mathematical analysis of the solution formula for the diffusion equation on the whole line. |
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第8週 |
4/08,4/11 |
diffusion on half-line and reflections of waves |
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第9週 |
4/15,4/18 |
the Duhamel principle: waves and diffusion with source |
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第10週 |
4/22,4/25 |
the Duhamel principle: waves and diffusion with source |
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第11週 |
4/29,5/02 |
midterm |
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第12週 |
5/06,5/09 |
wave and diffusion on finite interval; method of separation of variables |
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