SES # | TOPICS | KEY DATES |
---|---|---|
1 | The geometry of linear equations | |
2 | Elimination with matrices | |
3 | Matrix operations and inverses | |
4 | LU and LDU factorization | |
5 | Transposes and permutations | Problem set 1 due |
6 | Vector spaces and subspaces | |
7 | The nullspace: Solving Ax = 0 | |
8 | Rectangular PA = LU and Ax = b | Problem set 2 due |
9 | Row reduced echelon form | |
10 | Basis and dimension | |
11 | The four fundamental subspaces | Problem set 3 due |
12 | Exam 1: Chapters 1 to 3.4 | |
13 | Graphs and networks | |
14 | Orthogonality | Problem set 4 due |
15 | Projections and subspaces | |
16 | Least squares approximations | |
17 | Gram-Schmidt and A = QR | Problem set 5 due |
18 | Properties of determinants | |
19 | Formulas for determinants | |
20 | Applications of determinants | Problem set 6 due |
21 | Eigenvalues and eigenvectors | |
22 | Diagonalization | |
23 | Markov matrices | Problem set 7 due |
24 | Review for exam 2 | |
25 | Exam 2: Chapters 1-5, 6.1-6.2, 8.2 | |
26 | Differential equations | |
27 | Symmetric matrices | |
28 | Positive definite matrices | |
29 | Matrices in engineering | Problem set 8 due |
30 | Similar matrices | |
31 | Singular value decomposition | Problem set 9 due |
32 | Fourier series, FFT, complex matrices | |
33 | Linear transformations | |
34 | Choice of basis | Problem set 10 due |
35 | Linear programming | |
36 | Course review | |
37 | Exam 3: Chapters 1-8 (8.1, 2, 3, 5) | |
38 | Numerical linear algebra | |
39 | Computational science | |
40 | Final exam |
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2010
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