| Day | Topics | Preparation |
|---|---|---|
| Mon. 8/31 | Introduction. Solution of a 2 by 2 system in excruciating detail. |
Sec. 1.1-2 |
| Wed. 9/2 | Solution and geometry of 3 by 3 systems. Reduced Row Echelon Form (RREF). |
Sec. 1.2 |
| Fri. 9/4 | Vectors: scalar products and sums. Gaussian elimination: final words. | Sec. 1.3 |
| Wed. 9/9 | The span of a set of vectors. | Sec. 1.3-4 |
| Fri. 9/11 | Matrix equations. | Sec. 1.4 |
| Mon. 9/14 | Matrix equations.
A traffic problem leading to a linear system. |
Sec. 1.5-6 |
| Wed. 9/16 | Linear independence. | Sec. 1.7 |
| Fri. 9/18 | Linear transformations. | Sec. 1.8-9 |
| Mon. 9/21 | Linear transformations. | Sec. 1.8-9 |
| Wed. 9/23 | Matrix multiplication. | Sec. 2.1 |
| Fri. 9/25 | The inverse of a matrix. | Sec. 2.2 |
| Mon. 9/28 | Invertible matrices: key concepts. | Sec. 2.3 |
| Wed. 9/30 | The Invertible Matrix Theorem Determinants . |
Sec. 2.3 3.1 |
| Fri. 10/2 | Determinants. | Sec. 3.1-2 |
| Mon. 10/5 | Exam. | Sec. 1.1-9, 2.1-3 |
| Wed. 10/7 | Properties of determinants | Sec. 3.1-2 |
| Fri. 10/9 | Cramer's rule, volume. | Sec. 3.3 |
| Mon. 10/12 | Fields, vector spaces. Subspaces, column space of a matrix. |
Sec. 4.1 |
| Wed. 10/14 | Nullspace of a matrix. Kernel of a linear transformation. |
Sec. 4.2 |
| Fri. 10/16 | Basis of a vector space. | Sec. 4.3 |
| Mon. 10/19 | Coordinate systems. | Sec. 4.4 |
| Wed. 10/21 | The basis theorem. | Sec. 4.5 |
| Fri. 10/23 | The rank theorem.
Linear recursion. |
Sec. 4.6,8 |
| Mon. 10/26 | Change of basis. | Sec. 4.7 |
| Wed. 10/28 | Change of basis. | Sec. 4.7 |
| Fri. 10/30 | Markov chains and predicting the future! | Sec. 4.9. |
| Mon. 11/2 | Exam. | Ch. 3.1-3, Ch. 4.1-7 |
| Wed. 11/4 | Two population problems. | Sec. 5.1 |
| Fri. 11/6 | Eigenvalues and eigenvectors. | Sec. 5.1-2 |
| Mon. 11/9 | Diagonalization. | Sec. 5.3 |
| Fri. 11/13 | Diagonalization and linear transformations. | Sec. 5.4 |
| Mon. 11/16 | Complex eigenvalues. | Sec. 5.5 |
| Wed. 11/18 | Discrete dynamical systems. | Sec. 5.6 |
| Fri. 11/20 | . | . |
| Mon. 11/23 | EXAM. | Sec. 4.4-7; 4.9; 5.1-6 |
| Mon. 11/30 | Inner product and orthogonality. | Sec. 6.1 |
| Wed. 12/2 | Orthogonal projection and orthonormal basis. | Sec. 6.2 |
| Fri. 12/4 | Geometry of orthogonal projections. | Sec. 6.3 |
| Mon. 12/7 | Gram-Schmidt and QR factorization. | Sec. 6.4 |
| Wed. 12/9 | Least squares problems. | Sec. 6.5 |
| Fri. 12/11 | .. | . |