| 课 |
主题 |
教材章节 |
重要日程 |
| 1 |
线性方程组的几何性质
The Geometry of Linear Equations |
1.1-2.1 |
|
| 2 |
矩阵消去法
Elimination with Matrices |
2.2-2.3 |
|
| 3 |
矩阵运算与反矩阵
Matrix Operations and Inverses |
2.4-2.5 |
|
| 4 |
LU与DLU分解
LU and LDU Factorization |
2.6 |
|
| 5 |
转置与排列
Transposes and Permutations |
2.7 |
|
| 6 |
向量空间及其子空间
Vector Spaces and Subspaces |
3.1 |
|
| 7 |
核空间:求解 Ax = 0
The Nullspace: Solving Ax=0 |
3.2 |
|
| 8 |
矩形PA与Ax=b
Rectangular PA=LU and Ax=b |
3.3-3.4 |
|
| 9 |
列简化梯形式
Row Reduced Echelon Form |
3.3-3.4 |
|
| 10 |
复习
Review |
|
|
| 11 |
第一次期中考: 1-3章
Exam 1: Chapters 1-3 |
|
第一次期中考
Exam 1 |
| 12 |
基底与矩阵
Basis and Dimensions |
3.5 |
|
| 13 |
四维子空间
The Four Dimensional Subspaces |
3.6 |
|
| 14 |
图形与网络
Graphs and Networks |
8.2 |
|
| 15 |
正交性
Orthogonality |
4.1 |
|
| 16 |
投影与子空间
Projections and Subspaces |
4.2 |
|
| 17 |
最小平方逼进法
Least Squares Approximations |
4.3 |
|
| 18 |
Gram-Schmidt法与A=QR
Gram-Schmidt and A=QR |
4.4 |
|
| 19 |
行列式的性质
Properties of Determinants |
5.1 |
|
| 20 |
方程式与行列式
Formulas for Determinants |
5.2 |
|
| 21 |
行列式的应用
Applications for Determinants |
5.3 |
|
| 22 |
固有值与固有向量
Eigenvalues and Eigenvectors |
6.1 |
|
| 23 |
对角化
Diagonalization |
6.2 |
|
| 24 |
复习
Review |
|
|
| 25 |
第二次期中考: 1-5章
Exam 2: Chapters 1-5 |
|
第二次期中考
Exam 2 |
| 26 |
Markov矩阵
Markov Matrices |
8.3 |
|
| 27 |
Fourier级数与复数矩阵
Fourier Series and Complex Matrices |
8.5, 10.2 |
|
| 28 |
微分方程
Differential Equations |
6.3 |
|
| 29 |
对称矩阵
Symmetric Matrices |
6.4 |
|
| 30 |
正定矩阵
Positive Definite Matrices |
6.5 |
|
| 31 |
相似矩阵
Similar Matrices |
6.6 |
|
| 32 |
奇异值分解法
Singular Value Decomposition |
6.7 |
|
| 33 |
线性转换
Linear Transformations |
7.1-7.2 |
|
| 34 |
基底选择
Choice of Basis |
7.3-7.4 |
|
| 35 |
复习
Review |
|
|
| 36 |
第三次期中考：1-7章, 8.3
Exam 3: Chapters 1-7, 8.3 |
|
第三次期中考
Exam 3 |
| 37 |
快速Fourier转换
Fast Fourier Transform |
10.3 |
|
| 38 |
线性代数在工程学上之应用
Linear Algebra in Engineering |
|
|
| 39 |
课程回顾
Course Review |
|
|
| 40 |
|
|
期末考
Final Exam |
