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課程名稱 |
應用數學方法
Methods of Applied Mathematics |
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開課學期 |
105-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
謝天長 |
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課號 |
MATH7421 |
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課程識別碼 |
221 U6150 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一8(15:30~16:20)星期三8,9(15:30~17:20) |
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上課地點 |
天數304天數304 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH7421_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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 |
"Methods in Applied Mathematics" consists of modeling, analysis and computations. This course is an entry level course on applied mathematics. I will focus on basic skills on modeling and analysis. Its contents include (1) dimensional analysis and scaling, (2) perturbation methods and asymp-totic analysis, (3) basic calculus of variation. |
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課程目標 |
This course will be the basis of most applied mathematics courses, including PDEs, numerical PDEs. |
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課程要求 |
Undergraduate Linear Algebra, Advanced Calculus, ODEs and basic PDEs. |
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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 |
The lecture notes by Professor I-Liang Chern.
Textbook: J. David Logan, Applied Mathematics (2nd or 3rd edition) |
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參考書目 |
C. C. Lin and L. A. Segel, Mathematics applied to deterministic
problems in the natural sciences, 1974.
Bender and Orszag,Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill |
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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. |
Homeworks |
70% |
Type your homeworks in latex. Upload pdf files. |
2. |
Projects |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/20,2/22 |
Introduction to Applied Mathematics |
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第2週 |
2/27,3/01 |
Dimensional Analysis and Scaling |
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第3週 |
3/06,3/08 |
Dimensional Analysis and Scaling
Review ODE |
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第4週 |
3/13,3/15 |
Review ODE |
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第5週 |
3/20,3/22 |
Introduction to 2-dimensional Dynamical Systems
Perturbation methods for algebraic equations |
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第6週 |
3/27,3/29 |
Some applications of dimensional analysis
Regular perturbation methods for ODE |
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第8週 |
4/10,4/12 |
Regular Perturbation method for ODE
The Poincare-Lindstedt method
Asymptotic expansion |
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第9週 |
4/17,4/19 |
Singular perturbation method --- outer solution, inner solution and matching |
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第10週 |
4/24,4/26 |
Initial Layers, Boundary Layer, Internal Layer |
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第11週 |
5/01,5/03 |
Boundary Layers and Internal Layers |
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第12週 |
5/08,5/10 |
Shock wave
WKB method |
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第13週 |
5/15,5/17 |
Application of WKB method:
From Maxwell's equation to Geometric optics,
Semi-classical limit of Schrodinger equation --- from Quantum mechanics to classical mechanics
Laplace's method for asymptotic expansion of an integral |
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第14週 |
5/22,5/24 |
Introduction to the Calculus of Variations |
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