Instructor: Professor Loyce M. Adams Office: Guggenheim 415K Tel: 5435077 Fax: 6851440 Email: lma3 AT uw DOT edu Office hours: MWF 4:005:00 or by appt. 

TA: Teaching Assistant: Joy Zhou Office: Gugg 406 Tel: Fax: Email: yzhou AT amath DOT washington DOT edu Office hours: Tu 910am, Th 1:302:30 
Homework  Grades  Other Resources  2012 Web Page 
Catalyst Page  EDGE Video Page  Course description  Textbook  Syllabus  Objectives  Schedule 
Catalyst WEB Page for AMATH585
Your homework will be submitted via the Homework Dropbox on the class Catalyst Page. Your written homework should be typed via Latex or some typesetting program that can be converted to .pdf format. Computer programs done in Matlab may graded by running them to check the output is correct. They will also be checked for good programming and numerical analysis practices. An analysis of the code's results as requested in the assignment will be submitted via the .pdf file to the Homework Dropbox. A goal of this course is for you to learn to analyze your computer results. You should be able to access the Catalyst site with your UW netid.Click here for Homework Dropbox, Discussion Boards, and Catalyst WEB page
EDGE STREAMING VIDEO WEB Page for AMATH585
The course is recorded by EDGE. You may watch the lectures by going to the link below:Click here for EDGE Streaming Video of Lectures
Course Description
Numerical methods for steadystate differential equations. Twopoint boundary value problems and elliptic equations. Iterative methods for sparse linear systems: conjugategradients, preconditioners, and multigrid. (This course is offered every Winter quarter. This quarter it is an EDGE course.)Textbook
 Finite Difference Methods for Ordinary and
Partial Differential Equations
by R.J. LeVeque. (SIAM, 2007)
We will use Chapters 14 and the Appendices.
It is available through the University Libraries as an Ebook. On campus students Click here.
Offcampus students Click here.
For your information, to use the University of Washington Library service for other ebooks from offcampus, paste the link of the book into the University's Proxy on the website Click here.
Some copies will be available in the bookstore, but note that members of SIAM receive a 30% discount if you buy it online, and all UW students are eligible for free membership in SIAM, see
 Membership page
 Order book
 Textbook webpage (includes some mfiles and exercises)
 Some references on iterative methods:
 A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM, 1997.
 L.N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, 1997.
 Loyce's Conjugate Gradient Notes
 Loyce's Preconditioned Conjugate Gradient Notes
 Loyce's GMRES Notes
 Loyce's FFT Discrete Sine Transform Notes
Syllabus (and tentative schedule)
 Chapter 1. Finite difference approximations (2 lectures)
 Chapter 2. Twopoint boundary value problems for ODEs (3 weeks)
 Character of solution; boundary conditions.
 Finite difference method for linear problem u'' = f, BCs at x = 0,1.
 Accuracy, convergence, stability.
 Finite difference methods for nonlinear problems
 Boundary layers and nonuniform grids
 Chapter 3. Elliptic Equations (3 weeks)
 Laplace/Poisson equation  some physical examples
 Finite difference method; solution via Gaussian elimination.
 Fast Poisson solvers using FFT.
 Chapter 4. Iterative Methods for Sparse Linear Systems (2 weeks)
 Jacobi, GaussSeidel, SOR
 Conjugate gradient and preconditioning
 Methods for nonsymmetric systems
 Multigrid methods
Learning Objectives and Instructor Expectations
The course will be a combination of computation and theoretical analysis. The goal is to obtain an understanding of numerical methods and their implementation, as well as learning mathematical techniques for analyzing the stability and accuracy of these methods.
There will be homework assignments roughly biweekly that will involve MATLAB programming and written exercises. You may consult with your classmates about how to do the homework, but you should write your own code and express the answers to the written questions in your own words. Any sources you use should be referenced.
Schedule and Homework
Follow links in the table below to obtain a copy of the homework in Latex (.tex) and Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems.
Homework and Exams  Homework Due Date  Homework Problem Sets  Homework Solutions 
Homework 1, See Catalyst Page  
Homework 2, See Catalyst Page  
Homework 3  
Homework 4  
Homework 5  
Final Project  
FinalWork Alone 
Grading
Homework: 70%, final project: 20%, workalone final: 10%. There will 5 homework assignments.Other resources
<lma3@uw.edu> 