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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 |
98-2 |
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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 |
必帶 |
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上課時間 |
星期二7,8(14:20~16:20)星期四1,2(8:10~10:00) |
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上課地點 |
新204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。時段：四1。
總人數上限：120人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/982PDE_intro |
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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 students basic theory and practical applications 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 |
另約時間 |
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指定閱讀 |
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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. |
期中考 |
35% |
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2. |
期末考 |
40% |
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3. |
作業及小考 |
25% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/23,2/25 |
Introduction |
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第2週 |
3/02,3/04 |
models described by PDE |
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第3週 |
3/09,3/11 |
first order equation and characteristic curve |
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第4週 |
3/16,3/18 |
general nonlinear 1st order equation |
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第5週 |
3/23,3/25 |
wave equation in one space dimension,
wave speed, energy,
domain of dependence, domain of influence |
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第6週 |
3/30,4/01 |
scaling and self-similar solutions for heat equation, heat kernel |
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第7週 |
4/06,4/08 |
delta function, further properties of heat kernel, comparison of wave and heat equations |
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第8週 |
4/13,4/15 |
boundary value problem and reflection method |
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第9週 |
4/20,4/22 |
Duhamel principle |
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第10週 |
4/27,4/29 |
heat and wave equations with sources,
operator method |
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第11週 |
5/04,5/06 |
separation of variables and Fourier series |
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第12週 |
5/11,5/13 |
Fourier series and Hilbert space, L2 theory, Bessel's inequality, Parseval's equality |
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第13週 |
5/18,5/20 |
completeness,convergence theorems for Fourier series |
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第14週 |
5/25,5/27 |
separation of variables: Dirichelt, Neumann and Robin conditions |
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第15週 |
6/01,6/03 |
Laplace's equation, radially symmetric harmonic function (Newton potential), Green's identity, Green's function |
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第16週 |
6/08,6/10 |
Green's function on half-space and sphere, maximum principle,
Dirichlet principle, mean value property, separation of variables on rectangle and sphere |
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第17週 |
6/15,6/17 |
waves in three and two dimensions, diffusions in higher dimensions |
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