AMATH 352: Applied Linear Algebra and Numerical Analysis

SLN 10211, MWF 12:30-1:20, Savery Hall 264
(Prerequisites: MATH 126 or MATH 136: recommended: CSE 142)

Instructor:

 Professor Anne Greenbaum
Guggenheim 418B
tel: 206-543-1175
fax: 206-685-1440
greenbau@amath.washington.edu
office hours: MW 3:30-4:30, Th 10-11

Homework Grades 2008 Web Page
Course description Textbook Syllabus Objectives Schedule

Course Description

The course covers the basic concepts of linear algebra and computational techniques for solving matrix problems. We will discuss vectors, vector spaces, linear transformations, matrix-vector manipulations, solving linear systems, and eigenvalue problems. The emphasis will be on practical aspects of linear algebra and numerical methods for solving some of the myriad types of applications that give rise to linear algebra problems.

Textbook

Greenbaum and Chartier, Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms. Available online:
Part 1
Part 2
Part 3
Part 4
Entire Textbook (Only above parts will be covered.)

Notes from R. LeVeque. Available online: Notes

Syllabus

(1) Matrix algebra and Gaussian elimination, MATLAB:
Vectors and vector spaces; matrices and systems of linear equations; basics of using MATLAB -- matrix computations, functions, loops and conditionals, printing and plotting.
(2) Direct Computational Methods for Linear Systems and Least Squares Problems:
Gaussian elimination, LU factorization, pivoting, operation counts, implementation considerations for high performance. The normal equations, QR decomposition, fitting polynomials to data.
(3) Conditioning of Problems, Stability of Algorithms:
Conditioning of problems, the condition number of a matrix, stability of algorithms, backward stability of methods for solving linear systems.
(4) Eigenvalues and eigenvectors:
The matrix of a linear transformation, similar matrices, eigenvalues and eigenvectors.
(5) Numerical Methods for Eigenvalue Problems and Iterative Methods for Solving Linear Systems:
The power method, inverse iteration, the QR algorithm, Google's Pagerank. Simple iteration methods for linear systems, the conjugate gradient algorithm, iterative methods for nonsymmetric systems.

Learning objectives and instructor expectations

Students should learn or review the basics of linear algebra and how to solve linear algebra problems with MATLAB. Emphasis will be on understanding results -- not just getting answers, but knowing something about the algorithms used to produce those answers, their computational efficiency, and the level of accuracy that can be expected.

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available.

Homework and Exams Homework Due Date Homework Problem Sets Homework Solutions
First day of classes Wednesday, September 30
Homework#1 due Friday, Oct. 9 Homework #1 (.ps, .pdf) HW #1 Solutions (.ps, .pdf)
Homework#2 due Friday, Oct. 16 Homework #2 (.ps, .pdf) HW #2 Solutions (textfile, problem3.eps, problem6.eps, rotate_triangle.m, rotate_triangle.eps, rotate_shrink_square.m, rotate_shrink_square.eps, rotate_shrink_translate_square.m, rotate_shrink_translate_square.eps)
Homework#3 due Friday, Oct. 23 Homework #3 (.ps, .pdf) HW #3 Solutions (.ps, .pdf)
Homework#4 due Friday, Oct. 30 Homework #4 (.ps, .pdf) HW #4 Solutions (.ps, .pdf)
Practice Problems for Midterm Practice Problems (.ps, .pdf) Solutions to Practice Problems (.ps, .pdf)
Midterm Wednesday, November 4 Midterm Midterm Solutions (.ps, .pdf)
Homework#5 due Friday, Nov. 20 Homework #5 (.ps, .pdf)
Veteran's Day Wednesday, November 11 No class
Homework#6 due Wednesday, Dec. 2 Homework #6 (.ps, .pdf)
Thanksgiving Thursday, November 26 No class
Thanksgiving Friday, November 27 No class
Last day of classes Friday, December 11

Class Summaries

class summaries

Grading

There will be weekly homework assignments (usually due on Fridays), with some MATLAB programming. NO late homework will be accepted without a doctor's excuse. (Exceptions were made on hw1 and hw2 due to starting up process; now need to turn in hw on time.) You may work together on homework assignments, but each person must write his/her own code and his/her own answers to written exercises. The homework will count 30-40% of your course grade. There will be a midterm (tentatively scheduled for Wed., Nov. 4), which will count for 20%, and a final, which will count for 40-50% of your course grade.

Using MATLAB

The Arts and Sciences Instructional Computing Lab is located in room B022 of the Communications Building. See ASLAB . The room contains 27 Windows XP systems with MATLAB. The lab also offers remote access for UW students via a terminal server. To see how to use MATLAB remotely, go to Instructions .

Schedules of MATLAB TA's can be found at MATLAB TA hours

MATLAB codes

Matlab code for Yoda: yoda.m .
Data for Yoda: yodapose_low.mat .

<greenbau@amath.washington.edu> Wed Sep 9 09:12:11 PDT 2009