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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 |
102-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
薛克民 |
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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 |
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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@(~)星期四7,8(14:20~16:20) |
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上課地點 |
天數102天數202 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1022MATH7421_ |
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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 |
One major aim of this course is to introduce state-of-the-art mathematical methods for
analyzing real-world problems arising from applied and natural sciences. Sample topics
to be discussed include:
1. Dimensional analysis, scaling, and differential equations
2. Perturbation methods
3. Calculus of variations
4. Eigenvalue problems, integral equations, and Green's functions
5. Discrete models |
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課程目標 |
待補 |
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課程要求 |
修課同學需具備初步常微分及偏微分方程式之知識 |
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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 |
Read a brief introduction of the asymptotic methods by A. Harper (available
at the ceiba bulletin). |
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參考書目 |
1. J. D. Logan, Applied Mathematics, 3rd Edition, Wiley 2006
2. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and
Engineers, McGraw-Hill, 1978
3. An introduction to asymptotic analysis (lecture notes given by S.J.A. Malham, available
at ceiba bulletin)
4. Mathematical modelling in applied sciences (lecture notes given by N. Bellomo, E. D.
Angelis, and M. Delitala, available at ceiba bulletin) |
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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. |
Midterm exam |
30% |
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2. |
Final exam |
30% |
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3. |
Homework |
40% |
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週次 |
日期 |
單元主題 |
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第18週 |
06/19 |
Final Exam |
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第1-1週 |
02/17 |
Course overview |
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第1-2週 |
02/20 |
Perturbation methods for algebraic equations |
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第2-1週 |
02/24 |
Asymptotic expansion of integrals I:
Introduction & Watson's lemma |
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第2-2週 |
02/27 |
Laplace' method |
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第3-1週 |
03/03 |
Laplace method (Cont.) |
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第3-2週 |
03/06 |
Method of stationary phase |
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第4-1週 |
03/10 |
Method of stationary phase (Cont.) |
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第4-2週 |
03/13 |
Method of steepest descent |
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第5-1週 |
03/17 |
Method of steepest descent (Cont.) |
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第5-2週 |
03/20 |
Dimensional analysis \& similarity |
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第6-1週 |
03/24 |
Perturbation methods for duffing equations |
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第6-2週 |
03/27 |
Lindstedt-Poincare technique for Duffing equation |
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第7-1週 |
03/31 |
Method of renormalization \& multiple scales
for Duffing equation |
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第7-2週 |
04/03 |
溫書假 |
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第8-1週 |
04/07 |
Exercise session: Airy integral |
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第8-2週 |
04/10 |
Boundary-layer problem |
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第9-1週 |
04/14 |
出國開會 |
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第9-2週 |
04/17 |
出國開會 |
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第10-1週 |
04/21 |
Boundary-layer problem (nonlinear case) |
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第10-2週 |
04/24 |
Midterm exam |
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第11-1週 |
04/28 |
Boundary layer theory: A nonlinear problem |
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第12-1週 |
05/05 |
WKB theory |
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第12-2週 |
05/08 |
WKB & Liouville-Green transformation |
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第13-1週 |
05/12 |
Periodic homogenization theory |
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第14-1週 |
05/19 |
Calculus of variations |
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第15-1週 |
05/26 |
Difference equations |
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第15-2週 |
05/29 |
Difference equations |
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第16-1週 |
06/02 |
端午節 |
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