課程資訊
課程名稱
 應用數學專題一
Special Topics on Applied Mathematics (Ⅰ) 
開課學期
 101-1 
授課對象
 理學院  數學系  
授課教師
 陳宜良 
課號
 MATH7417 
課程識別碼
 221 U5760 
班次
  
學分
 3 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期五2,3,4(9:10~12:10) 
上課地點
 天數304 
備註
 總人數上限：30人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1011method_in_appl_m 
課程簡介影片
 
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課程概述

Usually, ``Methods in Applied Mathematics" consists of modeling, analysis and computations. This course is an entry level course on ap-plied 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. 

課程目標
 This course will be the basis of most applied mathematics courses,
including PDEs, numerical PDEs. 
課程要求
 undergraduate Linear Algebra, Advanced Calculus, ODEs and basic
PDEs. 
預期每週課後學習時數
  
Office Hours
 備註： office hour Friday afternoon, 4:30-5:30 
指定閱讀
  Textbook: J. David Logan, Applied Mathematics (2nd or 3rd edition)
  
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  
評量方式
(僅供參考)
  
No.
項目
百分比
說明
1. 
 Homeworks 
70% 
 type your homeworks in latex. Upload pdf files. 
2. 
 Projects 
30% 
  
 
課程進度
週次
日期
單元主題
第1週
 9/11  Course description and Introduction of Applied Mathematics

The two files are updated on 9/21 
第2週
 9/18  Dimensional Analysis and Scaling 
第3週
 9/25  Dimensional Analysis and Scaling 
第4週
 10/02  Dimensional Analysis and Scaling 
第5週
 10/09  No class. (I attend an International Conference.) 
第6週
 10/16  (a) Regular Perturbation
(b) Singular Perturbation
(c) Boundary Layer
(d) The WKB method
(e) Asymptotic expansion 
第7週
 10/23  (a) Regular Perturbation
(b) Singular Perturbation
(c) Boundary Layer
(d) The WKB method
(e) Asymptotic expansion 
第8週
 10/30  (a) Regular Perturbation
(b) Singular Perturbation
(c) Boundary Layer
(d) The WKB method
(e) Asymptotic expansion 
第9週
 11/06  (a) Regular Perturbation
(b) Singular Perturbation
(c) Boundary Layer
(d) The WKB method
(e) Asymptotic expansion 
第10週
 11/13  a) Regular Perturbation
(b) Singular Perturbation
(c) Boundary Layer
(d) The WKB method
(e) Asymptotic expansion 
第11週
 11/20  (a) Variational problems
(b) Function spaces and derivative of functionals
(c) Lagragian mechanics vs. Hamiltonian mechanics
(d) Direct method of Calculus of Variation
(e) Isoperimetric problems
(f) Selected variational problems 
第12週
 11/27  (a) Variational problems
(b) Function spaces and derivative of functionals
(c) Lagragian mechanics vs. Hamiltonian mechanics
(d) Direct method of Calculus of Variation
(e) Isoperimetric problems
(f) Selected variational problems
This a.pdf is new on 11/23. 
第13週
 12/04  Continuum Mechanics 
第14週
 12/11  12/7 has no class.
The updated version of a.pdf is uploaded. 
第15週
 12/18  12/14 has no class. 
第16週
 12/25  (a) Variational problems
(b) Function spaces and derivative of functionals
(c) Lagragian mechanics vs. Hamiltonian mechanics
(d) Direct method of Calculus of Variation
(e) Isoperimetric problems
(f) Selected variational problems 
第17週
 1/01  (a) Variational problems
(b) Function spaces and derivative of functionals
(c) Lagragian mechanics vs. Hamiltonian mechanics
(d) Direct method of Calculus of Variation
(e) Isoperimetric problems
(f) Selected variational problems