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Instructor: Professor Loyce M. Adams Office: Lewis 306 Tel: 543-5077 Fax: 685-1440 Email: lma3 AT uw DOT edu Office hours: MWF 4:00-5:00 or by appt. |
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TA: Teaching Assistant: Yian Ma Office: Lewis 129 Tel: Fax: Email: yianma at uw dot edu Office hours: Tuesday 12-2 |
| Homework | Grades | Other Resources | 2013 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.Registered students 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 steady-state differential equations. Two-point boundary value problems and elliptic equations. Iterative methods for sparse linear systems: conjugate-gradients, 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 1-4 and the Appendices.
It is available through the University Libraries as an Ebook. On campus students Click here.
Off-campus students Click here.
For your information, to use the University of Washington Library service for other ebooks from off-campus, 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 m-files 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. Two-point 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, Gauss-Seidel, 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 bi-weekly 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
The homework will be assigned on the Catalyst Web site.Grading
Homework: 70%, final project: 20%, work-alone final: 10%. There will 5 homework assignments.Other resources
| <lma3@uw.edu> |