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課程名稱 |
線性代數與應用
Linear Algebra and Its Applications |
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開課學期 |
107-1 |
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授課對象 |
共同教育中心 統計碩士學位學程 |
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授課教師 |
陳正剛 |
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課號 |
IE5034 |
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課程識別碼 |
546 U6040 |
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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 |
星期二7,8,9(14:20~17:20) |
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上課地點 |
普502 |
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備註 |
工程與環境統計領域選修課程之一。
限學士班四年級以上 或 限碩士班以上
總人數上限：60人
外系人數限制：50人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1071IE5034_ |
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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 |
A movie entitled "Linear Algebra and Its Applications" directed by Argon Chen based on a screenplay adapted from the original novel by Prof. Gilbert Strang. The story is clean and beautiful. Though the story has been so often told, it's usually told too abstractly. "less on rigor and much more on understanding" is how the author of the original novel wishes to deliver the story to you and is also the way this movie is directed. |
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課程目標 |
Students should feel excited and touched by the following subjects:
1. Introduction - Importance of Linear Algebra
2. Ax=b , Matrix, Gaussian Elimination and Application
3. Vector Spaces and Linear Equation
4. Applications: Graphs and Networks
5. Orthogonality and Least Squares
6. Applications: Multiple Regression
7. Application: Linear Programming and Karmarkar Method (if time allowed)
8. Determinant and its Applications
9. Eigenvalues and Eigenvectors
10. A^k and Difference Equations
11. e^A and Differential Equations
12. Similarity Transformation and Spectral Theorem
13. Positive Definite Matrices and Minimum Principles
14. Applications: Multivariate Analysis and Principal Component Analysis
15. Singular Value Decomposition and its Applications |
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課程要求 |
Calculus |
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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 |
Linear Algebra and Its Applications by Gilbert Strang
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參考書目 |
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/ |
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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 |
9/11 |
Introduction |
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第2週 |
9/18 |
Guassian Elimination and LDU |
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第3週 |
9/25 |
N/A |
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第4週 |
10/02 |
Vector Space |
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第5週 |
10/09 |
Complete Solution and 4 Fundamental Sub-spaces |
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第6週 |
10/16 |
Four Spaces and Applications to Graph |
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第7週 |
10/23 |
Linear Transformation |
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第8週 |
10/30 |
Orthogonality, Projection and Least Squares |
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第9週 |
11/06 |
Gram-Schmidt and Hilbert Space |
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第10週 |
11/13 |
Mid-term exam |
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第11週 |
11/20 |
Determinant |
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第12週 |
11/27 |
Eigenvalues and Eigenspace |
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第13週 |
12/04 |
Eigens and Similar transformation |
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第14週 |
12/11 |
Similar matrices and Spectral Theorem |
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第15週 |
12/18 |
Quadratic Functions and Positive Definiteness |
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第16週 |
12/25 |
SVD |