Lecture Plan
This may be updated from time to time.
| Week | Date | Section |
|---|---|---|
| 1 | W 24 Aug | 1.1. Systems of linear equations |
| F 26 Aug | 1.2. Row reduction and echelon forms | |
| 2 | M 29 Aug | 1.3. Vector equations |
| W 31 Aug | 1.4. The matrix equation Ax=b | |
| F 02 Sep | 1.5. Solution sets of linear systems | |
| 3 | M 05 Sep | Labor Day |
| W 07 Sep | 1.7. Linear independence | |
| F 09 Sep | 1.8. Introduction to linear transformations | |
| 4 | M 12 Sep | 1.9. The matrix of a linear transformation |
| W 14 Sep | 2.1. Matrix operations | |
| F 16 Sep | 2.2. Inverse of a matrix | |
| 5 | M 19 Sep | 2.3. Characterizations of invertible matrices |
| W 21 Sep | 3.1. Introduction to determinants | |
| F 23 Sep | 3.2. Properties of determinants | |
| 6 | M 26 Sep | Review |
| T 27 Sep | First prelim exam | |
| W 28 Sep | 3.3. Determinants as area or volume; linear transformations | |
| (skip subsections on Cramer's rule and formula for A-1) | ||
| F 30 Sep | 4.1. Vector spaces and subspaces | |
| 7 | M 03 Oct | 4.2. Null spaces, column spaces, and linear transformations |
| W 05 Oct | 4.3. Linearly independent sets; bases | |
| F 07 Oct | 4.4. Coordinate systems | |
| 8 | M 10 Oct–T 11 Oct Fall Break | |
| W 12 Oct | 4.5. The dimension of a vector space | |
| F 14 Oct | 4.6. Rank | |
| 9 | M 17 Oct | 5.1. Eigenvectors and eigenvalues |
| W 19 Oct | 5.2. The characteristic equation | |
| F 21 Oct | 5.3. Diagonalization | |
| 10 | M 24 Oct | 5.4. Eigenvectors and linear transformations |
| W 26 Oct | Review | |
| R 27 Oct | Second prelim exam | |
| F 28 Oct | Appendix B. Complex numbers | |
| 11 | M 31 Oct | 5.5. Complex eigenvalues |
| W 02 Nov | 5.6. Discrete dynamical systems | |
| F 04 Nov | 5.7. Applications to differential equations | |
| 12 | M 07 Nov | 6.1. Inner product, length, and orthogonality |
| W 09 Nov | 6.2. Orthogonal sets | |
| F 11 Nov | 6.3. Orthogonal projections | |
| 13 | M 14 Nov | 6.4. The Gram-Schmidt process |
| W 16 Nov | 6.5. Least-squares problems | |
| (skip subsection on alternative calculations) | ||
| 6.6. Least-squares lines (skip other subsections) | ||
| F 18 Nov | 6.7. Inner product spaces | |
| 14 | M 21 Nov | 7.1. Diagonalization of symmetric matrices |
| W 23 Nov | Perron-Frobenius theorem (not in book and not on exam) | |
| F 25 Nov | Thanksgiving Break | |
| 15 | M 28 Nov | 7.2. Quadratic forms |
| W 30 Nov | 7.4. The singular value decomposition | |
| (skip subsection on applications) | ||
| F 02 Dec | Review | |
| M 12 Dec | Final exam | |