AMATH 352
SLN 10205, MWF 12:30-1:20, Loew Hall 113
(Prerequisites: MATH 126 or MATH 136: recommended: CSE 142)

Applied Linear Algebra and Numerical Analysis


Instructor:

 Nicholas Cain
Guggenheim 407
Tel: (206) 685-9395
Fax: (206) 685-1440
nicain (at) amath.washington.edu
Office hours: M, 5:00-6:00 and Th, 2:30-3:30

Teaching Assistant:

 Lisa Bishop
Guggenheim 407
Tel: (206) 685-9395
Fax: (206) 685-1440
lbishop (at) amath.washington.edu
Office hours: M, 2:00-3:00 and Tu, 10:30-11:30

AS Lab Assistant:

 Edwin Ding
Guggenheim 407
Tel: (206) 685-9395
Fax: (206) 685-1440
ding (at) amath.washington.edu
Office hours: M, 4:00-6:00 and Tu, 11:30-3:30
Homework Grades Course Notes
Course Description Course Feedback Form Textbook Syllabus Objectives Schedule Supplements

Course Description

Development and application of numerical methods and algorithms to problems in the applied sciences and engineering. Applied linear algebra and introduction to numerical methods. Emphasis on use of conceptual methods in engineering, mathematics, and science.

Course Feedback

To send feedback or questions to the instructor, either anonymously or with sender information included, and without having to open your email, you can use the folloing link:

Textbook

There is no required textbook for this course, as topics will be developed according to lecture notes originally authored by Dr. Randy Levesque. These will be made available periodically as the quarter progresses, and it is strongly suggested that students read through the relevent sections before they are presented in class. Some additional readings that may be of interest include:

Course Notes

The lecture notes can be found here; refer to the course handout for remote login information.

Syllabus

Below is an at-a-glance overview of topics covered this winter, of course subject to change as the quarter progresses. The syllabus from the first day of class is also available, however the most up-to-date information will undoubtably be on the course homepage. Also, a copy of the homework guidelines handed out on the first day are available.
(1) Review of Applied Linear Algebra: Basis, range, dimension, rank, vector norms, matrix norms. Special matrices: symmetric, orthogonal, lower and upper triangular, tridiagonal.

(2) Direct Methods for Solving Dense Systems of Linear Equations: Solution of triangular systems, multiple right hand sides. Tridiagonal systems.

(3) Solution of a Single Nonlinear Equation: Bisection method. Newton's method. Regula Falsi. Convergence to a root.

(4) Interpolation: Polynomial interpolation by Lagrange polynomials. Cubic splines. Divided differences.

(5) Numerical Quadrature: Trapezoid and Simpson quadrature. Recursive quadrature.

(9) Ordinary Differential Equations - Initial Value Problems: Taylor Series. Euler's method. Accuracy and stability. Trapezoid method.

Learning Objectives and Instructor Expectations

The main goal of the course is to introduce approximate numerical methods for solving mathematical equations that cannot be solved exactly by analytical techniques. Such problems arise constantly in science, engineering, finance, computer graphics, and elsewhere. We will study several basic numerical algorithms, how to implement them, and how to analyze their behavior mathematically.

We will also study basic concepts in linear algebra, including matrix-vector manipulations, solving linear systems, least squares problems, and a bit about eigenvalue problems. The emphasis will be on practical aspects of linear algebra and numerical methods for solving these problems. Math 308 (Linear Algebra) is not a prerequisite for this class. This class and that one should complement one another and can be taken in either order.

You should also become adept at using the MATLAB language for numerical problem solving. MATLAB has many built-in functions for solving particular problems and you will learn how to use these. You should also gain an understanding of how they work, why they sometimes don't work, and how to use them intellegently.

Computing

You may use the computers in the College of Arts and Sciences Instructional Computing Lab (AS LAB, previously known as MSCC), located in Communications B022. See the AS Lab webpage for hours of operation and other information. Most other computer labs on campus do not have Matlab.

You can buy the student edition of Matlab at the bookstore for Windows, Mac, or Linux.

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. For additional information regarding viewing and printing the homework and solution sets, click here.

Homework and Exams Homework Due Date Homework Problem Sets Homework Solutions
First day of classes Monday, January 7
Homework#1 due Wednesday, 1/16 Homework #1 HW 1 Solutions
Martin Luther King Day Monday, January 21 No class
Homework#2 due Wednesday, January 23 Homework #2 HW 2 Solutions
Homework#3 due Wednesday, January 30 Homework #3
Homework#4 due Wednesday, February 6 Homework #4
Homework#5 due Wednesday, February 13 Homework #5
President's Day Monday, February 18 No class
MIDTERM Wednesday, February 20 Midterm Review Midterm Solutions
Homework#6 due Wednesday, March 5 Homework #6
Homework#7 due Friday, March 14 Homework #7
Last day of classes Friday, March 14
Final Exam Thursday, March 20 Review Review Solutions

Grading

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

Supplements

Here you can find supplemental papers and links for relevant examples seen in class.

Tutorials

No on-line tutorials have been assigned for AMATH 352.

<nicain@amath.washington.edu> Mon Nov 19 17:25:12 PST 2007