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課程名稱 |
應用數學一
Applied Mathematics (Ⅰ) |
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開課學期 |
111-1 |
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授課對象 |
理學院 大氣科學系 |
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授課教師 |
梁禹喬 |
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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 |
必修 |
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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B105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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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 |
This course gives students overviews of linear first and second order ordinary differential equations (OEDs) and linear algebra. The math skills will be applied to atmospheric sciences problems.
First order ODEs:
- responses to (complex) exponential, oscillating, delta function inputs
- integrating factor
- separable euqations
Second order ODEs:
- fundamental equation of mechanics
- forced harmonic motion
- unforced damped motion
- impulse response, exponential response
- method of undetermined coefficients
- variation of parameters
Linear algebra:
- row and column view of matrix multiplication
- independence, basis, and dimension
- four fundamental subspaces
- factorization
(i) A = LU: LU elimination
(ii) A = QR: orthogonalization (Gram-Schmidt)
(iii) S = Q𝜦QT: eigenvalues
(iv) A = X𝜦XT, diagonalization
(v) A = U𝜮VT, singular value decomposition
Solving linear system:
- matrix exponential
- phase plane: source, sink, saddle
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課程目標 |
This course aims to train students with the basics of ODEs and linear algebra, and their applications on atmospheric sciences problems. |
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課程要求 |
Calculus basics |
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預期每週課後學習時數 |
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Office Hours |
備註： Thursday 11:20 AM - 12:00 |
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指定閱讀 |
待補 |
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參考書目 |
Textbooks
Differential Equations and Linear Algebra:
- website: https://math.mit.edu/~gs/dela/
- youtube: https://www.youtube.com/playlist?list=PLMsYJgjgZE8iBpOBZEsS8PuwNBkwMcjix
Introduction to Linear Algebra:
- website: https://math.mit.edu/~gs/linearalgebra/
- youtube: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8
Linear Algebra and Learning from Data:
- website: https://math.mit.edu/~gs/learningfromdata/
- youtube: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/05,9/08 |
introduction to ODEs and linear algebra; the calculus you need; first-order ODEs |
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第2週 |
9/12,9/15 |
responses to exponential, oscillating, delta function inputs |
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第3週 |
9/19,9/22 |
integrating factor |
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第4週 |
9/26,9/29 |
logistic equation; separable equations |
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第5週 |
10/03,10/06 |
second-order ODEs; fundamental equation of mechanics; forced harmonic motion |
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第6週 |
10/10,10/13 |
unforced damped motion; impulse responses |
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第7週 |
10/17,10/20 |
exponential response; resonance; method of undetermined coefficients |
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第8週 |
10/24,10/27 |
variation of parameters; mid term |
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第9週 |
10/31,11/03 |
introduction to linear algebra; independence , basis, and dimension |
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第10週 |
11/07,11/10 |
LU decomposition/elimination |
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第11週 |
11/14,11/17 |
four fundamental subspaces |
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第12週 |
11/21,11/24 |
orthogonalization; Gram-Schmidt |
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第13週 |
11/28,12/01 |
Eigenvalues; diagonalization |
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第14週 |
12/05,12/08 |
singular value decomposition |
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第15週 |
12/12,12/15 |
solving linear system; matrix exponential |
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第16週 |
12/19,12/22 |
phase plane: source, sink, saddle |
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第17週 |
12/26,12/29 |
final exam |
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