Syllabus
The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in on Canvas will always be accurate.
| Lecture | Date | Sections in Text | Brief Description |
|---|---|---|---|
| 1 | 1/3 | 1.1, 6.1 | Systems of linear equations; vectors (part 1) |
| 2 | 1/5 | 1.2 | Row reduction and echelon forms |
| 3 | 1/8 | 1.2, 1.3 | Reduced row echelon form; Vector equations |
| 4 | 1/10 | 1.3, 1.4, 1.5 | Vector equations; Matrix equations, the matrix equation Ax=b and its solutions |
| 5 | 1/12 | 1.5, 1.7 | Homogeneous systems, general solutions, particular solution, linear Independence |
| 1/15 | No class (MLK Day) | ||
| 6 | 1/17 | 1.8 | Introduction to linear transformations |
| 7 | 1/18 (x-hour) | 1.9 | The matrix of a linear transformation |
| 8 | 1/19 | 2.1 | Matrix operations |
| 9 | 1/22 | 2.2 | Inverse of a matrix |
| 10 | 1/24 | 2.3 | Invertible Matrix Theorem |
| 1/25 | Exam 1 | ||
| 11 | 1/26 | 4.1, 4.2 | Introduction to Vector Spaces, null space, column space, notion of a linear transformation |
| 12 | 1/29 | 4.3 | Linearly independent sets; bases |
| 13 | 1/31 | 4.4 | Coordinate systems |
| 14 | 2/2 | 4.5, 4.6 | Dimension; Rank |
| 15 | 2/4 | 4.7, 5.4 | Change of coordinates matrix and composition of linear transformations |
| 16 | 2/7 | 3.1, 3.2 | Determinants and properties of determinants |
| 17 | 2/9 | 5.1, 5.2 | Eigenvalues and the characteristic equation |
| 18 | 2/12 | 5.2, 5.3 | The characteristic equation, diagonalization |
| 19 | 2/14 | 5.3, 5.4 | Diagonalization and linear transformations |
| 2/15 | Exam 2 | ||
| 20 | 2/16 | 4.9, 5.8 | Markov chains; Iteration method for eigenvalues; Google's page rank |
| 21 | 2/19 | 6.1, 6.2 | Inner products and orthogonality |
| 22 | 2/21 | 6.3, 6.4 | Projections; Gram-Schmidt process |
| 23 | 2/23 | 6.5 | Least-squares problems |
| 24 | 2/26 | 7.1 | Diagonalization of symmetric matrices |
| 25 | 2/28 | 7.4 | Application: Singular value decomposition (SVD) |
| 26 | 3/1 | 7.5 | Principal component analysis (PCA) and eigenfaces |
| 27 | 3/4 | Review for the final exam |