The big project ``The Big Valley'' arrived 22 Oct 03

Here is a link to the project statement. Original draft statement.

The directions of the axes for the function in #4 f(x,y)=(2*x-y)^2+(1+y)^2 are given by <1,1/2+sqrt(5)/2> and <1,1/2-sqrt(5)/2>, which are uglier than I thought they would be. These are needed for #7 part 2.

Descenting the f(x,y) = x^2-x*y+y^2 valley

A short table of the approximations
 i,    x_i,      y_i,           z_i,
[0,      1,        0,            1],
[1,    2/7,     5/14,         3/28],
[2,   3/28,        0,        9/784],
[3,   3/98,   15/392,     27/21952],
[4,  9/784,        0,    81/614656],
[5, 9/2744, 45/10976, 243/17210368],

Here is a maple worksheet which shows how to make Maple do all the work for one step in the steepest descent of the function x^3-x*y+y^3 used in problems #5 and #7 on Test 2. There is no text version, web maple doesn't do justice to the pictures.

Here is a collection ti-89 commands which does similar calculations for steepest descent

Not a Mathematical link, but one to the 60's TV Show The Big Valley and another to a Barbara Stanwyck site