Chapter 13 for Math 293: Surface Example

Start by looking at the function f(x,y)=cos(2x+y)+sin(x-2y)+3 We can get an image of this, for the values of x between 0 and 2.5 and the values of y between 0 and 2.5, via the http://www.flashandmath.com/mathlets/multicalc/contours/combo.html we site as in

Or we could get an image of the function using Microsoft Mathematics, as in

Furhermore, we could create a spreadsheet of values for the function. The linked pdf of such a sheet includes not only some selected points and the value of the function at those points in the first three columns, but also some of the associatede values of the partial derivatives and approximations derived from them. That particular spread sheet was used to make some 25 other images, a reduction of one of which is

Then printout of those 25 images were cut, folded, taped, and finally fit together to give thefollowing images: