AMATH 584
SLN 10220, MWF 2:30-3:20, Loew Hall 216

Applied Linear Algebra and Introductory Numerical Analysis


Instructor:

 David George
Guggenheim 415 D
tel: TBA
fax: 1-206-685-1440
dgeorge@amath.washington.edu
office hours: Wed., Fri. 3:30-4:30, or by appt.

Teaching Assistant:

 Meng Huo Chen
Guggenheim 407
mchen01@amath.washington.edu
office hours: Tues. Thurs. 10:00-11:00, Gug. 415 L (conference room)

Schedule Homework Grades Edge Home Page Lecture Videos Announcements

Course Description and Syllabus

This course covers numerical methods for linear algebra (solving linear systems of equations, linear least squares problems, matrix factorizations, eigenvalue problems) and an introduction to numerical methods for differential equations (finite difference methods for initial value ODEs). The emphasis of the course is on numerical linear algebra with only a brief introduction to numerical methods for differential equations. AMATH 585 in the winter and 586 in the spring are a continuation of AMATH 584, and cover numerical methods for differential equations in more detail. A more detailed summary of topics is below. (Topics are not necessarily covered in this order.)

Textbook

Numerical Linear Algebra, Trefethen and Bau, SIAM, 1997.

Some optional additional references are below.

Schedule

Below is an approximate topic and reading schedule. You should also consult the lecture and the homework assignments to gauge your reading. Approximately the first 2/3 of the course will follow most of the first five chapters of Trefethen and Bau. The final part of the course will be based on other references with lecture notes or reading material provided at this site as needed.

Week

Dates

Reading

Topics

Supplemental Material

1 Sep. 26,28 Trefethen/Bau: Lectures 1-2 Matrix-Vector Multiplication, Orthogonal Vectors and Matrices. ---
2 Oct. 1,3,5 Trefethen/Bau: Lectures 3-5 Norms, Singular Value Decomposition ---
3 Oct. 8,10,12 Trefethen/Bau: Lectures 6,7,9 Projectors, QR factorization, Gram-Schmidt. Read MATLAB lecture on your own. ---
4 Oct. 15, 17, 19 Trefethen/Bau: Lectures 8,10,11 More QR: Gram-Schmidt, Householder triangularization. Least Squares Problems ---
5 Oct. 22, 24, 26 Trefethen/Bau: Lectures 12-15 Conditioning and Stablility ---
6 Oct. 29, 31, Nov. 2 Trefethen/Bau: Lectures 15-17, 20 Conditioning and Stability cont., Gaussian Elimination. ---
7 Nov. 5,7,9 Trefethen/Bau: Lectures 20-23 MIDTERM. Solving Systems Gaussian Elimination. Midterm Review Topics (.pdf)
8 Nov. 14, 16 Trefethen/Bau: Lectures 23-24 VETERANS DAY. Gaussian Elimination, Cholesky Factorization, Eigenvalues ---
9 Nov. 19, 21 Trefethen/Bau: Lectures 25-27 Eigenvalues. THANKSGIVING. ---
10 Nov. 26, 28, 30 Trefethen/Bau: Lectures 28. Supplementary Notes Eigenvalues. Nonlinear iteration, Intro to ODEs ---
11 Dec. 3, 5, 7 Lecture Notes (.pdf) Intro to ODEs. Review Topics (.pdf)

Homework

Homework assignments will typically be assigned weekly, usually on Friday and collected the following Friday anytime before class or at the start of class time. Late homework will not be accepted since solutions will be posted after class. Homework accounts for 50% of your final grade. Below you will find links to the homework assignments and solution sets in .pdf form.

Homework/Exam

Due Date

Solution Set

Homework #1 (.pdf) Monday, October 8th. Solution Set # 1 (.pdf)
Homework #2 (.pdf) Monday, October 15th. Solution Set # 2 (.pdf)
Homework #3 (.pdf) Monday, October 22nd. Solution Set # 3 (.pdf)
Homework #4 (.pdf) Friday, Nov. 2nd. Solution Set # 4 (.pdf)
Midterm (.pdf) Friday, Nov. 9th Solution Set (.pdf)
Homework #5 (.pdf) Wednesday, Nov. 14th Solution Set # 5 (.pdf)
Homework #6 (.pdf) Wednesday, Nov. 28th Solution Set # 6 (.pdf)
Homework #7 (.pdf) Friday, Dec. 7th Solution Set # 7 (.pdf)
Final Tuesday, DECEMBER 11, 230-420P Solution Set

Grading

Your final course grade will be a weighted average of grades on your homework, midterm and final exam:

You may view your homework and exam grades on-line.

Prerequisites

Coursework

Undergraduate ODEs (AMATH 351, MATH 307, or equivalent). Undergraduate Linear Algebra (MATH 308 or equivalent).

Computer Usage

Familiarity with some programming and Matlab is useful but not strictly required if you are willing to learn quickly. Basic Matlab usage will not be covered in lecture, but you can ask me or the t.a. for help at office hours or use various outside resources. You will also need access to a computer with Matlab. Using the Math Sciences Computing Center (MSCC) (basement of the Communications Building) is one option for non-applied mathematics graduate students. Ask the MSCC about Matlab help and tutorials if you need them. They also have a Matlab "help-desk" during certain hours. For off-campus students, purchasing the student version of Matlab is another option.

Below are some online Matlab tutorials. You can probably also find many others.

Tutorials

No on-line tutorials have been assigned for AMATH 584.

Website url

Official Class (this) website: http://www.amath.washington.edu/courses/584-autumn-2007

Edge Website: http://www.engr.washington.edu/edge/amath584/index.html

<dgeorge@amath.washington.edu> Thu Sep 13 16:34:50 PDT 2007