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:


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)