Math 464A, Numerical Analysis, Fall, 2007

This is the Math 464A homepage. Consult it from time to time to find useful information for the course. I will include links to the syllabus and other course information.

Here is a copy of current course information.

  1. (12/09/07) I will leave your last graded homework outside my door.
  2. (12/09/07) Good problems on quadrature rules are section 6.2.2: 2, 4, 8, 9, 14.
  3. (12/05/07) Sample problems for the final exam.
  4. (11/11/07) Here's the information on Tuesday's talk: November 13, 2007 at 4pm, Mechanical Engineering Building 238. Douglas Arnold, University of Minnesota

    The Geometrical Basis of Numerical Stability. The accuracy of a numerical solution to a partial differential equation depends on the consistency and stability of the discretization method. While consistency is usually elementary to establish, stability of numerical methods can be subtle, and for some key PDE problems the development of stable methods is extremely challenging. After illustrating the situation through simple but surprising examples, we will describe a powerful new approach--the finite element exterior calculus--to the design and understanding of discretizations for a variety of elliptic PDE problems. This approach achieves stability by developing discretizations which are compatible with the geometrical and topological structures, such as de Rham cohomology and Hodge decompositions, which underlie well-posedness of the PDE problem being solved.

  5. (11/06/07) Remember, Monday, November 12 is a holiday.
  6. (10/23/07) Sample problems for the midterm.
  7. (10/19/07) Sorry about the mixed-up lecture. Here's what I should have said. If s is a fixed point of f and if |f'(s)|<1, then there is an interval I about s such that f maps I into I and |f'(x)| < L  <1 in I. In that case the fixed point is unique and fixed point iteration converges to s for any starting value in I. Moreover we have the estimate |xn-s|  < Ln|x1-x0|/(1-L ). I'll do this again in class Monday.
  8. (10/09/07) Sage talk Oct 9 at 5pm in Padelford C36 by Bobby Moretti: Title: "A Practical Introduction to SAGE" 
    
"I will introduce the computer math system known as SAGE (www.sagemath.org). I
will show science, math, and engineering students how to use SAGE in
their area of study. SAGE is an open source program that aims to
provide a viable free and open source alternative to Magma, Maple,
Mathematica and MATLAB. Started in 2005 by UW mathematics professor
William Stein, SAGE has grown into a highly functional general purpose
mathematics computing package. Best of all, there are several UW
undergraduates involved in SAGE development. You could be one too!"
  9. (10/08/07) Here is a matlab function to solve an upper triangular system Ux=y: 
    function x=upsolve(U,y)
%
% U = upper triangular matrix, Ux=y
% x=upsolve(U,y)
% 
n=length(y);
for i=n:-1:1;
 x(i)=y(i);
 for j=n:-1:i+1;
  x(i)=x(i)-U(i,j)*x(j);
 end;
x(i)=x(i)/U(i,i);
end;
  10. (10/02/07) I will carefully grade two problems on each assignment and assign 10 points to each of the graded problems. The rest will be read briefly and assigned a total of 10 points. So each assignment will total 30 points and that way all assignments will have equal weight.
  11. (9/26/07) If you are trying to access journal links from off campus via MYUW, Comcast, Qwest, etc., you must remember to authenticate yourself as UW affiliated.
  12. (9/26/07) The first midterm is Wednesday, October 31. I've corrected the syllabus.
  13. (9/25/07) A quote from Richard Hamming: "The purpose of numerical analysis is insight, not numbers."
  14. (9/25/07)SAGE website.
  15. (9/14/07)Course notes by Anne Greenbaum and Tim Chartier.
  16. (9/14/07) Syllabus
  17. (9/14/07) Numerical Recipes . This is a source book for numerical recipes. Many of them can be easily changed into Matlab functions.
  18. (9/14/07) If you want to write a matlab routine that takes a function as an argument, you include in the argument list a variable that represents the function name. When you call the function, you should supply the name of the function inside quote marks. For example: 
    function  y=newt(f,df,x,n)

% newton's method newt(f,df,x,n)
% x is the initial guess; n is the number of iterations
% files f.m and df.m contain the function and its derivatives
% the function and derivative names f and df must be supplied in
% quotes, i.e. a call would be of the form, newt('sin', 'cos', .2, 4).
    Your program will need to use feval to evaluate the functions.

morrow@math.washington.edu