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課程名稱 |
應用數學一
Applied Mathematics (Ⅰ) |
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開課學期 |
110-1 |
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授課對象 |
理學院 大氣科學系 |
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授課教師 |
陳宜良 |
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課號 |
AtmSci2011 |
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課程識別碼 |
209 27110 |
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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 |
星期一3,4(10:20~12:10)星期四3(10:20~11:10) |
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上課地點 |
大氣A104大氣A104 |
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備註 |
限本系所學生(含輔系、雙修生)
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1101AtmSci2011_ |
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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 |
Course Description Applied Mathematics I includes Linear Algebra and Ordinary Differential
Equations. It provides basic mathematical training for all science and engineering students.
The contents include
[Linear Algebra]
1. Vector Space and solving systems of linear equations (2 weeks)
2. Linear Transformation (2)
3. Determinant (1)
4. Eigenvalues and Eigenvectors, Singular Value Decomposition (2)
[Ordinary Differential Equations]
1.First-order Single Differential Equations (1.5)
2. Second-order Linear Differential Equations (1.5)
3. Nonlinear Systems in Two Dimensions (2)
4. Linear Systems with Constant Coefficients, Jordan form (1)
5. Methods of Laplace Transform (1)
6. Bifurcation and chaos (1.5)
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課程目標 |
1. Provides background for fluid mechanics, data analysis, dynamical system for atmospheric science.
2. Enhance students' mathematical maturity.
3. Fluently on mathematical calculation. |
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課程要求 |
Calculus I,II |
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預期每週課後學習時數 |
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Office Hours |
每週四 14:30~16:30
每週一 14:30~16:30 備註： Location: AS B104. |
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指定閱讀 |
I-Liang Chern, Lecture Note on Linear Algebra 2021.
I-Liang Chern, Lecture Note on Mathematical Modeling and Ordinary Differential Equations (2021) |
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參考書目 |
Linear Algebra:
Gilbert Strang, Linear Algebra and its applications
Theodore Shifrin and Malcolm Adams, Linear Algebra, a geometric approach, 2nd edition.
Sheldon Axler, Linear Algebra done Right.
ODE:
Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems.
K.K. Tung, Topics in mathematical modeling |
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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. |
Mid Term Exam |
30% |
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2. |
Final Exam |
30% |
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3. |
Homeworks or Quizs |
40% |
6 times. |
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週次 |
日期 |
單元主題 |
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第1週 |
9/23 |
R^n space |
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第2週 |
9/27,9/30 |
Subspace, System of linear equations |
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第3週 |
10/04,10/07 |
System of linear equations and applications |
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第4週 |
10/11,10/14 |
Linear transformations |
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第5週 |
10/18,10/21 |
Orthogonality, Least-squares method |
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第6週 |
10/25,10/28 |
Determinant, Eigenvalue problems, |
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第7週 |
11/01,11/04 |
Spectral Theory for symmetric operators |
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第8週 |
11/08,11/11 |
Singular Value Decomposition
First order single differential equation |
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第9週 |
11/15,11/18 |
First order single differential equation
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第10週 |
11/22,11/25 |
First order single differential equation
Mid term exam on 11/25
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第11週 |
11/29,12/02 |
Second order linear differential equations |
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第12週 |
12/06,12/09 |
Second order linear differential equations |
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第13週 |
12/13,12/16 |
Nonlinear differential equations |
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第14週 |
12/20,12/23 |
Hamiltonian systems, dissipative systems, 7.1, 7.2, 9.2, (9.5) |
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第15週 |
12/27,12/30 |
Linear equations with constant coefficients, Laplace transformation, Chaos |
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第16週 |
1/03,1/06 |
Climate Modeling |
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第17週 |
1/10,1/13 |
Final exam on 1/13. |
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