Applied Linear Algebra
Fall 2011 MATH 4242 Applied Linear Algebra (26167)
Day/Time: 05:00 P.M. - 06:15 P.M. , M,W (09/06/2011 -
12/14/2011)
Location: Vincent 6 (subject to change)
Instructor: Chenyan Wu
Contact Information: cywu "at" math.umn.edu
Office Hours: MW 4-5pm
Textbook: Applied Linear Algebra by Peter J. Olver and
Chehrzad Shakiban
Course Description: This course basically covers Chapters 1, 2, 3, 5, 7 and 8 of the textbook.
You should have already taken a one-semester course in Linear Algebra. The following knowledge is assumed: systems of linear equations, Gaussian elimination, determinants, vector spaces, linear independence, basis and dimension. However I will review these briefly.
New topics include the Cramer's rule, the row, column spaces, linear transformations, inner product, orthogonality, the Gram-Schmidt algorithm, eigenvalues and eigenvectors, diagonalization, hermitian matrices, the singular value decomposition, quadratic forms, positive definite matrices and the Jordan canonical forms. The lectures follow the text fairly closely.
Homework: Assignments will be posted below, but they will not be collected or graded. In the lectures we will go over the harder problems and you are welcome to ask me to explain other problems.
Quizzes: There are 3 Quizzes. Please see schedule below.
Exams: There are 2 midterms and 1 final. The final is projected to take place on Dec. 19 5-7pm. For dates of Midterms please see schedule below.
Grading: The final grade is produced using the following recipe:
- Only your best two quizzes contribute to the final score; the worst of the 3 is dropped. Each quiz contributes 10%, so in total they account for 20% of the final score.
- Each Midterm contributes 20%.
- The final contributes 40%.
- The final grade will be curved in this
class.
Other Policies: - Hand-held calculators can be used during quizzes and exams in this course.
Schedule of Lectures (Tentative)
|
Day |
Topic |
Homework |
Solutions (Taken offline) |
| Sept. 7 | 1.1 - 1.4 | 1.1.2, 1.2.3, 1.2.7, 1.2.23, 1.2.24, 1.3.1, 1.3.4, 1.3.14, 1.4.3, 1.4.9 | |
| Sept. 12 | 1.5, 1.6, 1.8, 1.9 | 1.5.2, 1.5.3, 1.5.4, 1.5.7, 1.5.23, 1.5.24, 1.6.25, 1.8.1, 1.8.7, 1.9.1 | |
| Sept. 14 | Quiz on Chapter 1 | ||
| Sept. 19 | 2.1 |
2.1.1, 2.1.7,
2.2.1, 2.2.4, 2.2.10, 2.2.16, 2.2.27 2.3.3, 2.3.4, 2.3.8, 2.3.22, 2.4.3, 2.4.8, 2.4.21 |
For solution to 2.2.16 click . |
| Sept. 21 | 2.2, 2.3 | ||
| Sept. 26 | 2.3, 2.4 | ||
| Sept. 28 | 2.5 |
2.5.20, 2.5.26, 2.5.41, 2.5.46 |
|
| Oct. 3 | Quiz on Chapter 2. Lecture on 3.1 | 3.1.3, 3.1.11, 3.1.13, 3.1.20 |
Solution
to quiz 2 and homework solution: |
| Oct. 5 | 3.2 - 3.3 | 3.2.5, 3.2.7, 3.2.12, 3.2.18, 3.2.26,
3.2.31, 3.3.1, 3.3.16, 3.3.20, 3.3.35 |
|
| Oct. 10 | 3.4 |
3.4.1, 3.4.2, 3.4.3, 3.4.4, 3.4.7, 3.4.8,
3.4.10, 3.4.23, 3.4.24, 3.5.1 |
|
| Oct. 12 | 3.6 + Review |
3.6.29, 3.6.30, 3.6.32, 3.6.39 |
|
| Oct. 17 | Midterm (on Chapters 1,2 and 3) |
||
| Oct. 19 | 5.1, 5.2 | 5.1.1, 5.1.3, 5.1.5, 5.1.15, 5.1.22,
5.1.23, 5.1.26 |
|
| Oct. 24 | 5.2, 5.3 | 5.2.1, 5.2.3, 5.2.6, 5.2.8, 5.2.11,
5.3.1, 5.3.4, 5.3.13, 5.3.20 |
|
| Oct. 26 | 5.3, 5.6 | 5.6.1, 5.6.2, 5.6.4, 5.6.8 |
|
| Oct. 31 | Quiz on the covered parts of Chapter 5 +
Lecture on 5.6 |
5.6.20, 5.6.23, 5.6.24 |
|
| Nov. 2 | 7.1 | 7.1.2, 7.1.3, 7.1.5, 7.1.6, 7.1.14,
7.1.15, 7.1.19, 7.1.21 |
|
| Nov. 7 | 7.2 | 7.2.2, 7.2.7, 7.2.8, 7.2.12, 7.2.20,
7.2.25, 7.2.26, 7.2.30 |
|
| Nov. 9 | 7.3 |
7.3.3, 7.3.7, 7.3.8, 7.3.10, 7.3.14,
7.3.21 |
|
| Nov. 14 | 7.5 |
7.5.1, 7.5.5, 7.5.6, 7.5.9, 7.5.11, 7.5.12, 7.5.24, 7.5.25, 7.5.27 | |
| Nov. 16 | Review | ||
| Nov. 21 | Midterm on Chapters 1-3, 5, 7 |
||
| Nov. 23 | Happy Thanksgiving! |
||
| Nov. 28 | 8.2 |
8.2.1, 8.2.4, 8.2.5, 8.2.8, 8.2.9,
8.2.17, 8.2.20-23, 8.2.26, 8.2.35, 8.2.38, 8.2.41 |
|
| Nov. 30 | 8.3 |
8.3.1, 8.3.3, 8.3.4, 8.3.8, 8.3.11,
8.3.15, 8.3.17, 8.3.18, 8.3.21, 8.3.24 |
|
| Dec. 5 | 8.4 |
8.4.1, 8.4.2, 8.4.6, 8.4.10, 8.4.14,
8.4.16, 8.4.23, 8.4.24, 8.4.28, 8.4.38, 8.4.40, 8.4.41 |
|
| Dec. 7 | 8.5 |
8.5.1, 8.5.3, 8.5.7, 8.5.19 |
|
| Dec. 12 | 8.6 |
8.6.1, 8.6.6, 8.6.7, 8.6.9, 8.6.10,
8.6.12, 8.6.16, 8.6.19 |
|
| Dec. 14 | We can do least square or more on orthogonality. If you want other material, please suggest! Fancy stuff or Review. You decide. | ||
| Dec. 19 | Final Exam (of course on everything covered in the course) |