Mathematics 54
Professor M. Gu
Fall
2007
Tentative Schedule
| Week of | Tuesday | Thursday | Topics |
| 8/28 | 1.1/1.2 |
1.2/1.3 |
Linear equations, Gauss elimination. Matrix algebra. |
| 9/03 | 2.1/2.2 |
2.2/2.3 |
Linear transformations. Inverses. |
| 9/10 | 2.4/3.1 |
3.1/3.2 |
Matrix Product. Images and kernels. Linear Dependence. |
| 9/17 | 3.3/3.4 |
3.4/4.1 |
Subspaces. Dimension. Coordinates. Linear Space. |
| 9/24 | 4.2/4.3 |
4.3/Review |
Linear transformations. Matrices. Orthogonal Projections. |
| 10/01 |
Exam: Chapters 1-4 |
5.1/5.2 | Orthogonal projections. Orthonormal Bases, Gram-Schmidt. |
| 10/08 | 5.2/5.3 | 5.4/5.5 | Orthogonal transformations. Least Squares. |
| 10/15 | 5.5/6.1 |
6.2/6.3 |
Inner product spaces. Determinants. |
| 10/22 | 6.3/7.1 |
7.2/7.3 |
Eigenvalues and eigenvectors. Diagonalization. |
| 10/29 | 7.3/7.4 |
7.5/*4.1--4.2 |
Complex eigenvvalues. Nagle Book Begins. |
| 11/05 | 4.3/4.4 |
4.5/Review |
Linear Second Order ODE. |
| 11/12 |
Exam: Linear Algebra |
9.1, 9.4 | Linear Systems of ODEs. Normal form. |
| 11/19 | 9.5/9.6 |
Holiday |
Linear Systems with constant coefficients. Complex eigenvalues |
| 11/26 | 10.1/10.2 |
10.2/10.3 |
Separation of variables. Fourier Series. |
| 12/03 | 10.4/10.5 |
10.5/Review |
Odd and even functions. The Heat equation. |
*At this point we switch textbooks.
The above schedule is provisional and will frequently change as the course progresses.