課程大綱 Syllabus |
學生學習目標 Learning Objectives |
單元學習活動 Learning Activities |
學習成效評量 Evaluation |
備註 Notes |
序 No. | 單元主題 Unit topic |
內容綱要 Content summary |
1 | Linear Equations |
1. Introduction to linear systems
2. Gauss-Jordan elimination
3. Matrix algebra |
1. Introduction to linear systems
2. Gauss-Jordan elimination
3. Matrix algebra |
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學習如何利用矩陣解線性方程 |
2 | Linear Equations |
1. Introduction to linear systems
2. Gauss-Jordan elimination
3. Matrix algebra |
1. Introduction to linear systems
2. Gauss-Jordan elimination
3. Matrix algebra |
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學習如何利用矩陣解線性方程 |
3 | Linear Equations |
1. Introduction to linear systems
2. Gauss-Jordan elimination
3. Matrix algebra |
1. Introduction to linear systems
2. Gauss-Jordan elimination
3. Matrix algebra |
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學習如何利用矩陣解線性方程 |
4 | Linear Transformations |
1. Linear transformations
2. The inverse of Linear transformations |
1. Linear transformations
2. The inverse of Linear transformations |
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學習線性轉換的要領 |
5 | Linear Transformations |
1. Linear transformations
2. The inverse of Linear transformations |
1. Linear transformations
2. The inverse of Linear transformations |
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學習線性轉換的要領 |
6 | Linear Transformations |
1. Linear transformations
2. The inverse of Linear transformations |
1. Linear transformations
2. The inverse of Linear transformations |
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學習線性轉換的要領 |
7 | Subspaces and Dimensions |
1. Image and kernel of a linear transformation
2. Bases and linear independence
3. The dimensions |
1. Image and kernel of a linear transformation
2. Bases and linear independence
3. The dimensions |
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學習子空間與基底的概念 |
8 | Subspaces and Dimensions |
1. Image and kernel of a linear transformation
2. Bases and linear independence
3. The dimensions |
1. Image and kernel of a linear transformation
2. Bases and linear independence
3. The dimensions |
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學習子空間與基底的概念 |
9 | Subspaces and Dimensions |
1. Image and kernel of a linear transformation
2. Bases and linear independence
3. The dimensions |
1. Image and kernel of a linear transformation
2. Bases and linear independence
3. The dimensions |
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學習子空間與基底的概念 |
10 | Midterm |
examination |
examination |
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測試期中學習成效 |
11 | Orthogonality and Least Squares |
1. Orthogonal projection
2. Gram-Schmidt process and QR factorization
3. Least squares and data fitting |
1. Orthogonal projection
2. Gram-Schmidt process and QR factorization
3. Least squares and data fitting |
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學習正交投影與QR分解之概念與應用 |
12 | Orthogonality and Least Squares |
1. Orthogonal projection
2. Gram-Schmidt process and QR factorization
3. Least squares and data fitting |
1. Orthogonal projection
2. Gram-Schmidt process and QR factorization
3. Least squares and data fitting |
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學習正交投影與QR分解之概念與應用 |
13 | Determinants |
1. Introduction to determinants
Cramer's rule |
1. Introduction to determinants
Cramer's rule |
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學習行列式值概念與應用 |
14 | Determinants |
1. Introduction to determinants
Cramer's rule |
1. Introduction to determinants
Cramer's rule |
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學習行列式值概念與應用 |
15 | Eigenvalues and Eigenvectors |
1. Finding the eigenvalues of a matrix
2. Finding the eigenvectors of a matrix
3. Diagonalization
4. Stability |
1. Finding the eigenvalues of a matrix
2. Finding the eigenvectors of a matrix
3. Diagonalization
4. Stability |
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學習特徵值與特徵向量之求法及其應用 |
16 | Eigenvalues and Eigenvectors |
1. Finding the eigenvalues of a matrix
2. Finding the eigenvectors of a matrix
3. Diagonalization
4. Stability |
1. Finding the eigenvalues of a matrix
2. Finding the eigenvectors of a matrix
3. Diagonalization
4. Stability |
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學習特徵值與特徵向量之求法及其應用 |
17 | Eigenvalues and Eigenvectors |
1. Finding the eigenvalues of a matrix
2. Finding the eigenvectors of a matrix
3. Diagonalization
4. Stability |
1. Finding the eigenvalues of a matrix
2. Finding the eigenvectors of a matrix
3. Diagonalization
4. Stability |
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學習特徵值與特徵向量之求法及其應用 |
18 | Final exam |
examination |
examination |
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測試期末學習成效 |