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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 |
105-1 |
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授課對象 |
工學院 工業工程學研究所 |
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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 |
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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 |
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/1051IE5034 |
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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 |
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. Ak and Difference Equations
11. eA 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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課程目標 |
I am trying to tell you a STORY of Linear Algebra
The story is clean and beautiful
- A mathematician’s statement?
- Linear algebra is one of very few mathematical subjects that can really make you feel that way
- This is exactly one of this class’s goals: tell you something exciting and beautiful.
Things learned from the story are needed and used
- The subject has been taught too abstractly.
- Crucial importance of the story was often missed
- An essential sophomore course but not really appreciated
- We are here trying to pick up this subject again and hopefully this time we can have different perspectives not only on this subject but also on any subject that uses linear algebra.
Less on rigor and much more on understanding.
- Explain rather than deduce
- Ideas come with examples
- Ability to reason mathematically will naturally develop
- The story moves simply and naturally from a line or a plane to the n-dimensional space. That step is mathematics at its best and every one of you should be able to take it.
Read the Novel and Watch the Movies Directed by Me or Prof. Strang!!!
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課程要求 |
高中數學
微積分
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預期每週課後學習時數 |
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Office Hours |
備註： Evaluation (*subject to minor changes)
Mid-term 30%*
Final 30%*
Term report 25%*
Homework 15% |
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指定閱讀 |
Gilbert Strang, Linear Algebra and Its Applications, Thomson |
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參考書目 |
Professor Strang’s Class Lecture Videos
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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