Textbook for the course: Linear Algebra and Its Application by G Strang, Cengage, ISBN 978-0030105678, 4th edition, 2006
Exams, Homework, and Grades: There will be two midterm exams and a final exam (all exams will be closed book). Homework will be assigned and graded. Part of the homework problems will require the use of Matlab. No late homework will be graded. The two lowest homework grades will be dropped in computing the total homework grade.
Final grade = 50% final exam + 20% 1st midterm + 20% 2nd midterm + 10% hw
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Class Meeting |
Section |
Topics |
|
1 |
1.1-1.3 |
Geometry of linear equations and Gaussian elimination |
|
2 |
1.4-1.5 |
Matrices, matrix multiplication, triangular factors |
|
3 |
1.5-1.6 |
Row exchange and inverse |
|
4 |
1.7-2.1 |
Applications, vector spaces and subspaces |
|
5 |
2.2 |
Solving Ax=b |
|
6 |
2.3 |
Linear independence |
|
7 |
2.4 |
The four fundamental subspaces |
|
8 |
2.5 |
Graphs and networks |
|
9 |
2.6 |
Linear transformation and review |
|
10 |
First exam |
|
|
11 |
3.1 |
Orthogonal vectors and subspaces |
|
12 |
3.2 |
Orthogonal projection onto lines |
|
13 |
3.3 |
Least square method |
|
14 |
3.4 |
Gram-Schmidt |
|
15 |
3.5, 4.1, 4.2 |
Fast Fourier transformation and properties of determinant |
|
16 |
4.2-4.3 |
Properties of determinant and formulas |
|
17 |
4.4-5.1 |
Application of determinant and eigenvalues |
|
18 |
5.2 |
Diagonalization of a matrix |
|
19 |
5.3 |
Difference equation and powers of matrices |
|
20 |
5.4, 5.6 |
Differential equations and similarity transformations |
|
21 |
Second exam |
|
|
22 |
6.1-6.2 |
Minima, maxima and saddle points |
|
23 |
6.2 |
Positive definite matrices |
|
24 |
6.3 |
Singular value decomposition |
|
25 |
6.4-6.4 |
Minimum principle and the finite element method |
|
26 |
7.1-7.2 |
Matrix norm |
|
27 |
7.4 |
Iterative method for Ax=b |
|
28 |
Review and catchup |