Math 2431, Section 10087 - Fall 2004

Linear Algebra

Teacher Evaluations

The Mathematics Department will collect the evaluations via an online form.
See http://online.math.uh.edu.

I handed in the grades Monday, Dec. 13. You can recover them from the VIP system (hopefully in a few days).
I will not be able to send you the grade (or score) by e-mail.
If you want to see your final exam, or me, please come after the start of the Spring semester. Have a pleasant vacation!

Classes: 9:00-10:00 am MWF, 634 SR1
Course description
- General information
- Syllabus (with links to Matlab manuals): see the department page of syllabi
- Policy
Instructor: Andrew Török
- Office: 672 PGH
- Phone: (713) 743-3478
- E-mail: torok@math.uh.edu
- Office hours: see the home-page
Lab TA's:
- Misko Mitkovski
  - Office: 691 PGH
  - E-mail: misko@math.uh.edu
  - Office hour: Wednesday, 10-11 am
- Maria Leite
  - Office: 626 PGH
  - E-mail: conceisu@math.uh.edu
  - Office hour: Friday, 11-12 am
Extra help:
- Mathlab, 222 Garrison Gym
- Learning Support Services, 321 Social Work Bldg, phone (713) 745-411, http://www.las.uh.edu/LSS/.
Extra lab hours:
- You can use 648 PGH between roughly 10am - 4pm, whenever it is not used for another class (see open hours on the schedule).
- Other computer labs that have Matlab are 108 Technology (you have to bring paper if you want anything printed; available at least 5pm - 9pm most days) and 110 Social Work. See the general information above.
Other books:
- David C. Lay: Linear algebra and its applications
- Otto Bretscher: Linear algebra with applications
- Richard Hill: Elementary Linear Algebra with Applications
- Salas, Hille, Etgen: Calculus, one and several variables (this is the book used at UH for Calculus I-III; look at Chapter 12 for more about planes, lines etc. in R³)
Typos and Errors in the textbook.
MATLAB Files for Linear Algebra and Differential Equations Using MATLAB. This corrects some errors in the software included with the book.

Handouts

Gaussian elimination (Sec. 2.3)

Examinations

Exam I: Monday, September 27
- The exam will cover all material up to and including section 4.2.
- Please bring your student I.D.
- It will be a closed book exam.
- No calculators.
- Review held Wednesday, 9/22. Bring any questions you might have.
- I handed out a list of problems to be discussed during the review.
- A list with some of the topics discussed so far is here.
- Approximate results:
  - average 76
  - min, quartiles, max: 41, 69, 76, 84, 100 (i.e, there are about 25% of students in each of these four intervals).
Exam II: Monday, November 1
- The exam will cover all material up to and including Chapter 5 (with the exception of section 4.4).
- Please bring your student I.D.
- It will be a closed book exam.
- No calculators.
- A list with some of the topics discussed so far is here.
- Review held Wednesday and Friday (10/27 or 10/29). Bring any questions you might have.
  Here is a selection of problems.
- Approximate results
  For Exam II:
  - average 59/100
  - min, quartiles, max: 0, 53, 65, 72, 91.
  For Exam I + Exam II:
  - average 136/200
  - min, quartiles, max: 57, 121, 141, 157, 180.
Exam III: Wednesday, Dec. 1
- The exam will cover all material starting with (and including) section 5.6 (remember, we looked only at problems from that section).
- Review held Monday, November 22, and continued (with Chapter 8) on November 29. Bring any questions you might have.
- Please bring your student I.D.
- No books, but you can bring one sheet of paper (letter size, two sides, reasonable font) with notes.
- No calculators.
- A list with some of the topics of the course is here.
- A list of review problems is here.
- Approximate results
  For Exam III:
  - average 66/100
  - min, quartiles, max: 28, 56, 67, 77, 95.
  For Exam I + Exam II + Exam III:
  - average 207/300
  - min, quartiles, max: 94 (next score 137), 182, 209, 229, 276.
Final Exam: Wednesday, Dec. 8, 8-11 am
- The exam will be comprehensive.
- As a review, you can use the problems for Exams I-III.
  If you have questions, please ask them in class, on 11/29 or 12/03.
- Extra office hours: Monday, Dec. 6, 10-12, and by appointment.
- Please bring your student I.D.
- No books, but you can bring one sheet of paper (letter size, two sides, reasonable font) with notes.
- No calculators.
- Approximate results:
  For the best 10 HW's (after being all rescaled to 10 pts each):
  - average 69/100
  - min, quartiles, max: 12, 59, 73, 87, 96.5
  For Exam I + Exam II + Exam III + (best 10 HW's):
  - average 277/400
  - min, quartiles, max: 153 (next score 189), 242, 279, 306, 370

Assignments

The problems below are from the textbook. Please write the solutions on separate pages (i.e., do not hand in a note-book), and STAPLE them.
The homeworks must be handed in during the Wed. class (unless specified otherwise).

LATE homeworks will receive a 20% penalty. I should receive them during the class following the one when the homework was due.

Some of the problems have the answer or a hint in the textbook. If you have to hand in such a problem, you are welcome to use the hint but have to still write a complete solution.
For problems that require Matlab, you can either hand in the printed Matlab computations, or a hand written copy of them.

HOMEWORKS (M = use Matlab)
HW # Section HAND IN Solve only, do not hand in

1. (due Sept. 1)
SOLUTIONS 1.1 2 (as written in the book), 4, 8, 10
1.3 6, 10, 18
1.4 8, 14
2.2 1, 4, 5 (use any calculator)
2.3 2, 4, 6, 8, 9, 12, 14 22M, 23M
2. (due Sept. 8)
SOLUTIONS 2.4 2 (rank of B!), 4
3.1 2, 4, 8 18M
3.2 4, 8, 12
3. (due Sept. 15)
SOLUTIONS 2.4 8M, 10M
2.5 4M
3.1 14M, 16M
3.2 22M
3.3 2, 4, 6, 8, 10, 14 15
3.4 2, 3
4. (due Sept. 22)
SOLUTIONS 3.5 2, 4, 10, 14M
3.6 1, 2, 4
3.7 2, 4, 7 1, 3, 12M
3.8 2, 4, 7, 8 10M, 12M
[for the general Cramer's rule, see # 16 in sec. 8.1]
5. (due Sept. 29)
SOLUTIONS 4.1 2, 4, 6, 8 11, 12, 18M
4.2 2, 4, 6, 10, 12, 18M 8, 16M, 19M
6. (due Oct. 6)
SOLUTIONS 4.3 6(M), 8(M), 12(M), 14, 16
4.5 2, 4 1, 6, 9, 10
4.6 2M, 6, 8
7. (due Oct. 13)
SOLUTIONS 4.7 2, 4 5, 7
4.8 2, 4, 6, 8, 10M
4.9 2, 4, 6M
8. (due Oct. 20)
SOLUTIONS 4.4 1, 3, 5, 7
5.1 2, 4, 6, 8, 10, 12, 16 (use Thm. 5.1.4)
5.2 4, 8, 10, 12, 14, 20 11
9. (due Oct. 27)
SOLUTIONS 5.3 8M 1, 4 (verify 8, from HW8), 7 (do by hand too)
5.4 2, 6, 8M, 10M
5.5 1, 2, 4
10. (due Nov. 10)
SOLUTIONS 5.6 2, 6 (do not read sec. 5.6!)
6.1 12, 15, 16
6.2 2, 5, 7 1
11. (due Nov. 17)
SOLUTIONS 6.2 4, 6
6.3 2M, 5, 6
6.4 1 (answer in book has a typo: cos(2t) should be cos(3t)),
2; Use matrix exponentiation for both problems
6.5 4, 5, 6, 7
12. (due Nov. 22)
SOLUTIONS 6.2 redo 4, 5, 6, 7 using matrix exponentiation (as in 6.5)
8.1 1, 4, 5, 6 16
8.2 3, 6

HOMEWORKS (M = use Matlab)
1. (due Sept. 1) SOLUTIONS	1.1	2 (as written in the book), 4, 8, 10
1.3	6, 10, 18
1.4	8, 14
2.2	1, 4, 5 (use any calculator)
2.3	2, 4, 6, 8, 9, 12, 14	22M, 23M
2. (due Sept. 8) SOLUTIONS	2.4	2 (rank of B!), 4
3.1	2, 4, 8	18M
3.2	4, 8, 12
3. (due Sept. 15) SOLUTIONS	2.4	8M, 10M
2.5	4M
3.1	14M, 16M
3.2	22M
3.3	2, 4, 6, 8, 10, 14	15
3.4	2, 3
4. (due Sept. 22) SOLUTIONS	3.5	2, 4, 10, 14M
3.6	1, 2, 4
3.7	2, 4, 7	1, 3, 12M
3.8	2, 4, 7, 8	10M, 12M [for the general Cramer's rule, see # 16 in sec. 8.1]
5. (due Sept. 29) SOLUTIONS	4.1	2, 4, 6, 8	11, 12, 18M
4.2	2, 4, 6, 10, 12, 18M	8, 16M, 19M
6. (due Oct. 6) SOLUTIONS	4.3	6(M), 8(M), 12(M), 14, 16
4.5	2, 4	1, 6, 9, 10
4.6	2M, 6, 8
7. (due Oct. 13) SOLUTIONS	4.7	2, 4	5, 7
4.8	2, 4, 6, 8, 10M
4.9	2, 4, 6M
8. (due Oct. 20) SOLUTIONS	4.4		1, 3, 5, 7
5.1	2, 4, 6, 8, 10, 12, 16 (use Thm. 5.1.4)
5.2	4, 8, 10, 12, 14, 20	11
9. (due Oct. 27) SOLUTIONS	5.3	8M	1, 4 (verify 8, from HW8), 7 (do by hand too)
5.4	2, 6, 8M, 10M
5.5	1, 2, 4
10. (due Nov. 10) SOLUTIONS	5.6	2, 6 (do not read sec. 5.6!)
6.1	12, 15, 16
6.2	2, 5, 7	1
11. (due Nov. 17) SOLUTIONS	6.2	4, 6
6.3	2M, 5, 6
6.4	1 (answer in book has a typo: cos(2t) should be cos(3t)), 2; Use matrix exponentiation for both problems
6.5	4, 5, 6, 7
12. (due Nov. 22) SOLUTIONS	6.2	redo 4, 5, 6, 7 using matrix exponentiation (as in 6.5)
8.1	1, 4, 5, 6	16
8.2	3, 6

Last modified:

HOMEWORKS (M = use Matlab)
HW #	Section	HAND IN	Solve only, do not hand in
1. (due Sept. 1) SOLUTIONS	1.1	2 (as written in the book), 4, 8, 10
	1.3	6, 10, 18
	1.4	8, 14
	2.2	1, 4, 5 (use any calculator)
	2.3	2, 4, 6, 8, 9, 12, 14	22M, 23M
2. (due Sept. 8) SOLUTIONS	2.4	2 (rank of B!), 4
	3.1	2, 4, 8	18M
	3.2	4, 8, 12
3. (due Sept. 15) SOLUTIONS	2.4	8M, 10M
	2.5	4M
	3.1	14M, 16M
	3.2	22M
	3.3	2, 4, 6, 8, 10, 14	15
	3.4	2, 3
4. (due Sept. 22) SOLUTIONS	3.5	2, 4, 10, 14M
	3.6	1, 2, 4
	3.7	2, 4, 7	1, 3, 12M
	3.8	2, 4, 7, 8	10M, 12M [for the general Cramer's rule, see # 16 in sec. 8.1]
5. (due Sept. 29) SOLUTIONS	4.1	2, 4, 6, 8	11, 12, 18M
5. (due Sept. 29) SOLUTIONS	4.2	2, 4, 6, 10, 12, 18M	8, 16M, 19M
6. (due Oct. 6) SOLUTIONS	4.3	6(M), 8(M), 12(M), 14, 16
	4.5	2, 4	1, 6, 9, 10
	4.6	2M, 6, 8
7. (due Oct. 13) SOLUTIONS	4.7	2, 4	5, 7
	4.8	2, 4, 6, 8, 10M
	4.9	2, 4, 6M
8. (due Oct. 20) SOLUTIONS	4.4		1, 3, 5, 7
	5.1	2, 4, 6, 8, 10, 12, 16 (use Thm. 5.1.4)
	5.2	4, 8, 10, 12, 14, 20	11
9. (due Oct. 27) SOLUTIONS	5.3	8M	1, 4 (verify 8, from HW8), 7 (do by hand too)
	5.4	2, 6, 8M, 10M
	5.5	1, 2, 4
10. (due Nov. 10) SOLUTIONS	5.6	2, 6 (do not read sec. 5.6!)
	6.1	12, 15, 16
	6.2	2, 5, 7	1
11. (due Nov. 17) SOLUTIONS	6.2	4, 6
	6.3	2M, 5, 6
	6.4	1 (answer in book has a typo: cos(2t) should be cos(3t)), 2; Use matrix exponentiation for both problems
	6.5	4, 5, 6, 7
12. (due Nov. 22) SOLUTIONS	6.2	redo 4, 5, 6, 7 using matrix exponentiation (as in 6.5)
	8.1	1, 4, 5, 6	16
	8.2	3, 6