Mathematics 54
Professor A. Ogus
Spring 2005
Syllabus
| Week of | Tues | Thur | Topics |
| 1/17 | 1.1, 1.2 | 1.2 |
Linear equations and Gauss elimination.
|
| 1/24 | 1.3 | 1.4 |
Matrix arithmetic. Inverses and elementary matrices.
|
| 1/31 | 3.1,3.2 | 3.3 |
Euclidean space. Vector Spaces.
|
| 2/07 | 3.4, 3.5 | 3.5, 3.6 |
Subspaces and spans. Linear independence and bases.
|
| 2/14 | 3.7 | 3.7, 3.8 |
Basis, dimension, and rank. Coordinates.
|
| 2/21 | 4.1, 4.2 | 4.2, 4.3 |
Linear transformations. Inner products, orthogonal projections and least squares.
|
| 2/28 | 4.4 | Exam:chapters 1 and 3 |
Least Squares. Orthogonal basis.
|
| 3/07 | 4.4, 5.1 | 5.2 |
Gram-Schmidt. Determinants. Eigenvectors and eigenvalues.
|
| 3/14 | 5.2 | 5.3 |
Diagonalization.
|
| 3/21 |
Spring Break.
|
||
| 3/28 | 5.3, 5.4 | 5.4 |
Symmetric matrices. Jordan form for 2x2 matrices.
|
| 4/04 | 3.2, 3.3 | Exam:chapters 4 and 5 |
Review of 2nd order ODE (Change of Book!).
|
| 4/11 | 7.4* | 7.5 |
Systems of ODE.
|
| 4/18 | 7.6, 7.8 | 10.1 |
Complex and multiple eigenvalues. Boundary Value problems.
|
| 4/25 | 10.2 | 10.3,10.4 |
Fourier Series. Odd and Even functions
|
| 5/02 | 10.4,10.5 | 10.5 |
Partial differential equations. Separation of Variables.
|
| 5/10 | 10.5,10.6** |
More on the Heat equation.
|
The above schedule is provisional and subject to change as the course progresses, so keep in touch. Please make arrangements now to be in town for the scheduled midterms; it's just not possible for me to arrange special midterms for the convenience of individuals in such a large class. According to university regulations, incompletes can only be given when, due to circumstances beyond your control, you are unable to take one of the exams, and cannot be used to allow more time to catch up because you have fallen behind. Notice that we are in Exam group 13, with our final exam scheduled for 5/18/05 at 8:00 am. Be sure to that you have no conflicts.
The grading will be weighted approximately as follows: midterms 30%, class work 25%, final 45%. Calculators and notes are not permitted during examinations; please do not bring cram sheets to the examination rooms. Linear algebra is conceptually very clear and simple, and I hope that everything you need to know will fit easily in your head.
*This section was omitted from the paperback version. Here are the necessary pages.
**This section was omitted from the paperback version. Here are the necessary pages.