| Day | Topics | Preparation |
|---|---|---|
| Mon. 8/27 | Introduction. Solution of a 2 by 2 system in excruciating detail. |
Sec. 1.1-2 |
| Wed. 8/29 | Solution of 3 by 3 systems. | Sec. 1.1-2 |
| Fri. 8/31 | Geometry of linear systems. Terminology. |
Sec. 1.2 |
| Wed. 9/5 | Observations on RREF. | Sec. 1.2 |
| Fri. 9/7 | Matrix algebra and matrix equations. | Sec. 1.3, 2.4 |
| Mon. 9/10 | Matrix multiplication amd inverses. Linear transformations. |
Sec. 2.3-4 Sec. 2.1 |
| Wed. 9/12 | Linear transformations and geometry. | Sec. 2.1-2 |
| Fri. 9/14 | Dot product, orthogonality, projection. | Sec. 2.2, Appendix A |
| Mon. 9/17 | EXAM | Ch. 1-2. |
| Wed. 9/19 | Projections and reflections. | Sec. 2.2 |
| Fri. 9/21 | Kernel and image of a linear transformation. | Sec. 3.1 |
| Mon. 9/24 | Subspaces of R^n . | Sec. 3.2 |
| Wed. 9/26 | Linear independence and bases for a subspace of R^n . | Sec. 3.2 |
| Fri. 9/28 | Bases and dimension. | Sec. 3.2-3 |
| Mon. 10/1 | The rank-nullity theorem. | Sec. 3.3 |
| Wed. 10/3 | Change of coordinates on R^m . | Sec. 3.4 |
| Fri. 10/5 | Change of coordinates for a linear transformation. | Sec. 3.4 |
| Mon. 10/8 | Change of coordinates on a subspace of R^m.
Similar matrices . |
Sec. 3.4 |
| Wed. 10/10 | Linear spaces and bases: Many examples. | Sec. 4.1 |
| Fri. 10/12 | Bases and dimension. Space of solutions to a linear homogeneous differential equation. |
Sec. 4.1 |
| Mon. 10/15 | Linear transformation on a linear space. | Sec. 4.2 |
| Wed. 10/17 | The matrix for a linear transformation. | Sec. 4.3 |
| Fri. 10/19 | Linear transformations on matrix spaces. | Sec. 4.4 |
| Mon. 10/22 | Solution space of a homogeneous linear differential eqn.
Complex numbers. |
. |
| Wed. 10/24 | Classes cancelled due to fire. | . |
| Fr. 10/26 | Classes cancelled due to fire. | . |
| Mon. 10/29 | Determinants. | Sec. 6.1-2 |
| Wed. 10/31 | EXAM. | Ch. 3, 4 |
| Fri. 11/2 | Determinants. | Sec. 6.1-2 |
| Mon. 11/5 | A dynamical system. | Sec. 7.1 |
| Wed. 11/7 | Eigenvalues and eigenvectors. | Sec. 7.1-2 |
| Fri. 11/9 | Thinking algebraically about eigenvalues and vectors. | Sec. 7.2-4 |
| Wed. 11/14 | Polynomials and roots. Geometric multiplicity. | Sec. 7.1-2 |
| Fri. 11/16 | Similar matrices and diagonalization. | Sec. 7. |
| Mon. 11/19 | Complex eigenvalues: rotation-scaling. | Sec. 7.5-6 |
| Wed. 11/21 | Phase Potraits: HW party. | Sec. 7.1-6 |
| Mon. 11/26 | Test prep. | Ch. 6,7 |
| Wed. 11/28 | EXAM | Ch. 6-7 |
| Fri. 11/30 | Orthonormal basis for a space.
Orthogonal projection. |
Sec. 5.1 |
| Mon. 12/3 | Gram-Schmidt and QR factorization. | Sec. 5.2 |
| Wed. 12/5 | Orthogonal transformations. | Sec. 5.3 |