Math 102. Applied Linear Algebra

Math 102. Applied Linear Algebra - Winter 08 - Hans Lindblad

Meetings Texts Exams Review Practice Exams Syllabus Schedule Lecture summary Homeworks

ANNOUNCEMENTS:

Meetings

Lecture: MWF 10.00-10.50, in Peterson 103 Lecture schedule and notes available below.
Section: Tuesdays. Homework due in box on 6th floor AP&M by 5pm, solutions below.
Office Hours: Instructor: Hans Lindblad: M 3.30-4.30 in AP&M 7220: lindblad@math.ucsd.edu
TA: Allison Cuttler: Tu 9.30-10.30, F 4-5 in AP&M 6446. acuttler@math.ucsd.edu

It is important that you have a look at the material before the lectures since it will help you to follow the lectures, Why? see the schedule where you also find lecture notes. Please ask questions in lectures, since if you don't quite understand something others may not understand either, and the explanations will help everyone understand better and keep the lectures at a pace you can follow. The best way to learn math is by doing examples so try to do all the homework problems and more similar problems. Let us know if you have any complaints and suggestions for improvements.

Texts

Strang, Linear Algebra and its Applications,

Strang's page at MIT with practice exams and videos of his lectures. A good advanced text is Axler, Linear Algebra Done Right and also Friedberg, Insel, Spence, Linear Algebra. Another book I like is Bretscher, Linear Algebra with Applications. A free linear algebra book

Exams

1st Midterm will be given on 1/30 during class time in Peter 103
2nd Midterm will be given on 2/27 during class time in Peter 103
Final Examination will be given on Friday 3/21, 8-11 in Peter 103

Bring identification to exams. No calculators, books or notes are allowed in exams. No make-up exams. The exams cover material in homeworks due before the exams, and corresponding lectures and reading. Further information about the exams will be given in lectures, reviews or on the web, but not on an individual basis. Questions about the grading should be brought up directly with your TA.

Review-going over questions from the practice exams. Review questions.

Review for 1st Midterm on 1/29, 6.30-8.00 pm in Peter 103
Review for 2nd Midterm on 2/26, 6.30-8.00 pm in Peter 103
Review for Final on Friday 3/14, in class

Practice Exams and Solutions to some of the exams. More practice exams

mid1s07s, mid1s07ps, mid1f06, mid2s07s, mid2s07ps, mid2f06, fins07s, fins05, finw06,

Syllabus

This is a second course in linear algebra focusing on computational aspects and applications, yet presenting the geometric concepts. We start with a rapid review of the basic methods to solve systems of linear equations and the associated geometric subspaces and concepts. The applications will cover graphs and networks, least square problems, fast fourier transform, difference and differential equations and numerical solutions of these. The course will go further than a first course in factorizing matrices. Diagonalization produce factorizations of most square matrices but in general we have triangularization and the Jordan normal form. Gaussian elimination and Gram-Schmidt orthogonalization produce factorizations but a more useful one is the Singular Value Decomposition, which in particular can be used to construct a Pseudoinverse when there is no inverse to solve least square problems.

Schedule and summary of lectures (tentative).

If you click on the day you might find a summary of the lecture, without the important pictures.
It is important that you have a look at the material before it is covered in the lectures. Why?

wk	date	Monday	Wednesday	Friday
1	1/7	1.1-1.3	1.4-1.5	1.6-1.7
2	1/14	2.1	2.2	2.3
3	1/21	Holiday	2.4-2.5	2.6
4	1/28	3.1	Exam	3.2-3.3
5	1/4	3.3	3.4	3.5
6	2/11	4.1-4.2	4.3-4.4	5.1
7	2/18	Holiday	5.2	5.3
8	2/25	5.4	Exam	5.4-5.5
9	3/3	5.6	5.6, Appendix B	6.1-6.2
10	3/10	6.3	Application 6.3*	review

(*) will deal with Image Compression. In the future I will do 3.2 and 3.3 in one lecture together. I the future I should also do the unique LDU and the symmetric LDL^T factorizations in section 1.5-1.6.

Homework Assignments (tentative)

Solutions to homeworks might be available for download below after they are due. All homeworks should be handed in, but we do not have resources to grade all problems. We will grade 3-4 problems on most homework sets but a couple might be returned ungraded. No late homeworks. The lowest homework score will be discarded. Homework due in box on 6th floor AP&M by 5pm.

HW #1 Due 1/8
1.2:3,10, 1.3:3,18,31, 1.4:6,10,32,

HW #2 Due 1/15
1.5:1,4,15, 1.6:4,6,22,35,50, 1.7:3,6,9, 2.1:3,7,8,25,26,

HW #3 Due 1/22
2.2:5,8,11,24,25,53,70, 2.3:2,9,12,13,20,21,26,30,

HW #4 Due 1/29
2.4:2,5,6,8,27,29,32,37, 2.5:6,7,8, 2.6:6,7,8,9,16,18,22,33,

HW #5 Due 2/5
3.1:2,6,7,11,14,16,19,22,32,37,44,51, 3.2:14,17,19,21, 3.3:4,6,12,14,17,22,26,27,

HW #6 Due 2/12
3.4:13,15,16,21,23,24,30, 3.5:11,14, 4.2:2,7,10,12,14,18,25,28,31,

HW #7 Due 2/19
4.3:3,5,28,34,36,43, 4.4:5,6,10,14,16,18,23,31,37,

HW #8 Due 2/26
5.1:4,5,7,14,25,27, 5.2:4,5,7,8,15,21,29,30,34,40, 5.3:2,8,10,12,15,25,28, 5.4:1,2,3,5,8,9,

HW #9 Due 3/4
5.5:16,17,18,36,38,39,41,42,44,46, 5.6:3,8,11,13,17,25,30,31,41,42,44,

HW #10 Due 3/11
6.1:4, 6.2:2,4,8,23,27,29,30,34,43, 6.3:2,3,5,10,15,19, App B:1,5,6,

Grades

The grade is based on a total score calculated from 10% homeworks 20% each midterm and 50% final.
Midterm I:Mean/Median 38, Grades: A's 45-56, B's 35-44, C's 20-34. Midterm II:Mean/Median 22.5/23.5, Grades: A's 30-40, B's 20-29, C's 10-19. Final:Mean/Median 51/49, Grades: A's 60-80, B's 40-59, C's 20-39. Course Grades: A's >75%, B's >50%, C's >25%.