線性代數
Linear Algebra
| 節 | 週四 | 週五 |
|---|---|---|
2 09:00–09:50 | 線性代數 AB103（光復） | |
5 13:20–14:10 | 線性代數 AB103（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
說明線性代數之基本觀念及相關之定理與運算,使學習者建立運用線性代數解決有關工程與管理問題之基礎。
無
無備註
課堂講解為主,並輔助以助教習作課程,相關教學資料提供於教學平台http://e3.nctu.edu.tw/。
(1) 考試題庫:各次考試的考題皆從作業或課本的例題中選取,作業的題目和參考答案公布於e3 (2) 上課出席:10%(點名、隨堂考) (3) 分章考:60% 甲、每上完一章,考一次,一學期考6次 (Chap 1-Chap 6)(每次10% * 6 = 60%), 乙、各班分章考日期,由上課老師自行決定、也由上課老師自行出題 丙、每次的分章考只考5題,考50分鐘。 (4) 期末考:30% 甲、一學期考一次期末考(30%),考整本書(Chap 1- Chap 7),各班考題都相同 乙、期末考共考10題、Chap 7出2題,Chap 1-Chap6出8題 丙、Chap 1-Chap 6的考題是從分章考的題目中抽選,修改數字後出題 (5) 助教演習課(額外加分):若同學的考試成績不理想,但演習課全期出席次數滿 10次,授課老師得在其學期成績給予加分,最多以5分為限。(備註:若沒有設置演習課助教,則取消此項加分) (6) 學期成績:各班及格人數的總平均為78分(不及格的人數不列入平均)
System of Linear Equations
1. Introduction to Systems of Linear Equations 2. Gaussian Elimination 3. Applications of Systems of Linear Equations
- 講授：
- 3
Matrices
1. Matrix Operations 2. The Inverse of a Matrix 3. Elementary Matrices 4. Applications of Matrix Operations
- 講授：
- 5
Determinants
1. The Determinant of a Matrix 2. Evaluation of a Determinant 3. Properties of Determinants 4. Applications of Determinants
- 講授：
- 3
Vector Spaces
1. Vector Spaces 2. Subspaces of Vector Spaces 3. Spanning Sets and Linear Independence 4. Basis and Dimension 5. Rank of a Matrix 6. Coordinates and Change of Basis 7. Coordinates and Change of Basis
- 講授：
- 11
Inner Product Spaces
1. Length and Dot Product 2. Inner Product Spaces 3. Orthogonal Basis 4. Least Square Analysis
- 講授：
- 11
Linear Transformations
1. Introduction to Linear Transformation 2. Kernel and Range 3. Matrices for Linear Transformations 4. Transition Matrices and Similarity
- 講授：
- 7
Eigenvalues and Eigenvectors
1. Eigenvalues and Eigenvectors 2. Diagonalization 3. Symmetrical Matrices and Orthogonal Diagonalization
- 講授：
- 7
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1.1 Introduction to Systems of Linear Equations; 1.2 Gaussian Elimination 1.3 Applications of Systems of Linear Equations 2/21 2/22 |
| 第 2 週 | 2/28 和平紀念日放假一日 3/1 和平紀念日彈性放假一日 2/28 和平紀念日放假一日 3/1 和平紀念日彈性放假一日 |
| 第 3 週 | 2.1 Operations with Matrices; 2.2 Properties of Matrix Operations; 2.3 The Inverse of a Matrix ● Exam (Chap 1) 3/7 3/8 |
| 第 4 週 | 2.4 Elementary Matrices; 2.5 Markov Chains 2.6 Applications of Matrix Operations 3.1 The Determinant of a Matrix 3/14 3/15 |
| 第 5 週 | 3.2 Evaluation of a Determinant Using Elementary Operations 3.3 Properties of Determinants; 3.4 Applications of Determinants; ● Exam (Chap 2) 3/21 3/22 |
| 第 6 週 | 4.1 Vectors in Rn; 4.2 Vector Spaces; 4.3 Subspaces of Vector Spaces; 4.4 Spanning Sets and Linear Independence; ● Exam (Chap 3) 3/28 3/29 |
| 第 7 週 | 4/4 兒童節放假一日 4/5 民族掃墓節放假一日 4/4 兒童節放假一日 4/5 民族掃墓節放假一日 |
| 第 8 週 | 4.5 Basis and Dimension; 4/11 4/12 |
| 第 9 週 | 4.6 Rank of a Matrix; 4.7 Coordinates and Change of Basis 4/18 4/19 |
| 第 10 週 | 5.1 Length and Dot Product; 5.2 Inner Product Spaces 5.3 Orthogonal Basis ● Exam (Chap 4) 4/25 4/26 |
| 第 11 週 | 5.4 Least Square Analysis 5/2 5/3 |
| 第 12 週 | 5.5 Applications of Inner Product; 6.1 Introduction to Linear Transformation 5/9 5/10 |
| 第 13 週 | 6.2 Kernel and Range; ● Exam (Chap 5) 5/16 5/17 |
| 第 14 週 | 6.3 Matrices for Linear Transformations; 6.4 Transition Matrices and Similarity 5/23 5/24 |
| 第 15 週 | 6.4 Transition Matrices and Similarity; 6.5 Applications of Linear Transformations; 5/30 5/31 |
| 第 16 週 | 7.1 Eigenvalues and Eigenvectors; 7.2 Diagonalization 6/7 端午節放假一日 6/6 6/7 |
| 第 17 週 | 7.3 Symmetrical Matrices and Orthogonal Diagonalization; 7.4 Applications of Eigenvalues & Eigenvectors ● Exam (Chap 6) 6/13 6/14 |
| 第 18 週 | 6/20 Final Exam (Chap 1 - Chap 7) 6/21 學期成績公布 6/20 6/21 |
R. Larson, B.H. Edwards and D.C. Falvo, Elementary Linear Algebra, Cengage, 8th Edition, 2015 (高立圖書).
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