Math 63

    Summer 2005 (first half)

    Linear Algebra II

    Professor: Weiqing Gu

    Place: BK 126 & Time:8:45-10:15, 10:30-noon


    Grading

    Homework: 30%

    Exam 1: 30%

    Project: 10%

    Final Exam: 30%


Midterm Exam: Tuesday May 24, 2005. Term project on applications of linear algebra due: Monday May 30, 2005. Final Exam: Friday June 3, 2005.


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Homework Assignments for Math 63 Summer 2005 (first half semester)


The problems below are from the textbook Linear Algebra: A Modern Introduction, by David Poole.

HW #1       Due Tuesday, May 17

READ     Sections 4.3, 4.4, 4.5

DO         Section 4.3 (Review: Eigenvalues and Eigenvectors), p. 293:    15, 16, 22, 23.
DO         Section 4.4 (Diagonalization), p. 306:    8, 13, 23, 27.

HW #2       Due Wednesday, May 18

READ     Sections 4.5, 5.1, 5.2

DO         Section 4.4 (Similar matrices), p. 306:    3, 7, 37, 44.
DO         Section 4.5 (Power Method for calculating dominant eigenvalue-eigenvector pair), p. 316:    1, 5, 24.

HW #3       Due Thursday, May 19 in class.

READ     Sections 5.2, 5.3.

DO         Section 5.1 (Orthogonality and orthogonal matrices), p. 363:    4, 8, 17, 28a)b), 33.
DO         Section 5.2 (Orthogonal projections), p. 382:    2, 5.

HW #4       Due Friday, May 20 in class.

READ     Section 5.4

DO         Section 5.3 (Gram-Schmidt process, QR factorization), p. 382:    4, 9, 13, 15, 18.
DO         Review problems:   Rewrite the problems that you did not get the full points for all the graded assignments so far.

Start reviewing for our EXAM 1, which will be take place on Tuesday, May 24, in class. The Exam 1 is on sections we have covered so far, plus section 5.4.
HW #5       Due Mon, May 23, in class.

READ     Sections 5.5

DO         Section 5.4 (Orthogonal diagonalization of symmetric matrix), p. 397:    2, 8, 13, 15, 16, 21.

Tuesday, May 24: No homework due, because of Exam 1.
HW #6       Due Wed May 25, in class.

READ     Section 4.6

DO         Section 5.5 (Applications to quadratic forms and geometry), p. 422:   32, 35, 41, 48, 50, 53, 67.

HW #7       Due Thursday, May 26, in class.

READ     Sections 6.1

DO         Section 4.6 (Applications to Markov chains, solving ODE systems), p.344:  1, 2, 7, 57, 61, 63.

HW #8       Due Friday, May 27, in class.

READ     Sections 6.2

DO         Section 6.1 (Vector spaces and subspaces), p. 441:    2, 6, 10, 26, 28, 30, 44, 60, 61.

Start preparing for the term project, which will be turned in, Monday May 31, 10:00 pm or Tuesday before lecture.

Preparing Term Poject:        
Find your favorite real world applications related to eigenvalues and eigenvectors.
(a) Describe a real world problem. (You may attach a Xerox copy of the description of the problem with the project write-up.)
(b) Put the problem into mathematical form.
(c) Solve the problem by using the technique of eigenvalues and eigenvectors.
(d)Give answer(s) to the original real world problem.

HW #9       Due 11:45 pm, Sunday, May 29, to my office.

READ     Sections 6.4, 6.6

DO         Section 6.2 (Linear dependence, basis, dimension and their theorems), p. 457:    4, 8, 10, 17a), 22, 28, 46, 48, 50, 58.

Finish Term Project       Due 3:00 pm, Monday, May 30, to my office, Olin 1279.
DO         REWRITE the homework problems that you did not get the full points from Exam 1 to the current graded homework. Due Tuesday, May 31, in class.

HW #10       Due Wednesday June 1, in class:

READ     Sections 6.5

DO         Section 6.4(Linear transformations), p. 478:    2, 3, 14, 18, 24, 25.
DO         Section 6.6 (The matrix of linear transformation), p. 514:    3, 7, 9, 40.

HW #11       Due Thursday June 2, in class.

READ     Section 7.1

DO         Section 6.5 (The Kernel and Range of linear transformations), p.494 :    4, 9, 15.
p.514: 40(moved from last assignment).
Section 7.1 (Inner product spaces), p.549 :    2, 5, 9, 19.
DO (Optional)         a) Make a list of questions that you have for the course so far.
b) Suggest one problem that you think it should be on the final exam.

HW #12       DO         Review for the final exam and write a summary of the materials covered so far.