Math 694 Numerical Linear Algebra

CRN 50330

Spring 2009, UAF

Instructor: Ed Bueler
Office: Chapman 301C.  Office hours online.
Phone: 474-7693, eMail: ffelb@uaf.edu 		Class Time:  MWF 2:15 - 3:15pm,   Chapman 107
Text: Trefethen & Bau, Numerical Linear Algebra
Web Site: www.dms.uaf.edu/~bueler

Course Content and Goals: This course will describe how actual matrices and vectors can be handled in a stable, fast, and accurate manner, a key technology for scientific computation.  It will place these topics in the correct framework, emphasizing the geometry of the action of matrices.  Many of the ideas relate to famous matrix decompositions, theorems, and algorithms: spectral theorem/Schur decomposition, singular value decomposition (SVD), the QR method for eigenvalues, and Krylov subspace methods.  Applications of these ideas include solving large linear systems, systems of ordinary differential equations, statistical methods, inverse methods in geophysics, and Markov processes.  Good numerical linear algebra is perhaps in greatest need when working with discretized partial differential equations.

Examples in class will often use Matlab|Octave|pylab.  I will help students choose and learn how to use one of these tools, all of which are well-suited to numerical linear algebra.  Student competence with one of these tools, for the purpose of scientific computing though not necessarily general programming, is a goal of the course.

Assigned Work and Grade:  Weekly (nearly so ...) homework will include paper computations, proofs, and Matlab|Octave|pylab computations.

There will be a one hour in-class midterm exam, emphasizing definitions and basic manipulations.  There will be a take home final.

Exams/Homework
In class Midterm Exam
Take home Final Exam
Homework		 Percent of Grade
15%
30%
55%		 Dates
Wednesday March 25.
Due in my box 5:00 p.m., Thursday, May 7.
nearly weekly

Based on your raw homework and exam scores, I guarantee grades according to the following schedule: 90 - 100 % = A, 79 - 89 % = B, 68 - 78 % = C, 57 - 67 % = D, 0 - 56 % = F .  I reserve the right to increase your grade above this schedule based on the actual difficulty of the work and on average class performance.

Topic list: Policies:   The Dept of Mathematics and Statistics has reasonable policies on incompletes, late withdrawals, early final examinations, etc.  See www.dms.uaf.edu/dms/Policies.html .  You are covered by the UAF Student Code of Conduct.  I will work with the Office of Disabilities Services (203 WHIT, 474-7043) to provide reasonable accommodation to student with disabilities.

Prerequisites:    Undergraduate linear algebra and mathematical maturity.  Concretely, MATH 314 Linear Algebra or equivalent. Recommended: MATH 421 Applied Analysis OR MATH 401 Introduction to Real Analysis OR equivalent post-calculus course in analysis.