Technology Notes

Level Curves (Contour Plot)

On Derive:

Ex. Suppose we want the level curves of the function f(x,y) = x^2+x*y-y^2.

1. Define the function: f(x,y) := x^2+x*y-y^2
2. make a vector of the level curves for f(x) = -5, -3, -1, 1, 3, 5: vector(f(x,y)=k,k,-5,5,2) This creates a vector of functions: [x^2+xy-y^2=-5,x^2+xy-y^2=-3,… x^2+xy-y^2=5] (6 functions)
3. To plot it, highlight the vector of functions and click on Plot2D

Note: The default is to graph each level curve in color. Some of the colors do not come out very well on the black and white printer. There is a way to turn the colors off – ask a lab assistant to help you with this.

On TI-89:

In 3D graphing mode, define an equation and graph it as you would any 3D equation, with the following exception. Display the GRAPH FORMATS dialog box (from Graph Screen, under Tools, Select 9). Then set: Style = CONTOUR LEVELS

- The viewing angle is set initially so that you are viewing the contours by looking down the z axis. You can change the viewing angle as necessary.

- The graph is shown in expanded view. To switch between expanded and normal view, press p.

- The Labels format is set to OFF automatically.

How Are Z Values Determined?

You can set the ncontour Window variable ( under [WINDOW]) to specify the

number of contours that will be evenly distributed along the displayed range of z values, where:

increment =(zmax – zmin)/(ncontour+1)

ncontour + 1

The z values for the contours are:

zmin + increment

zmin + 2(increment)

zmin + 3(increment)

…

zmin + ncontour(increment)

So for the example given in the Derive section, we would want 6 curves graphed

At z=-5,-3,-1,1,3,5. So our increment is 2. Since the curves at zmin and zmax are not graphed, we want zmin to be -7 and zmax to be 7, and of course the number of contours,

ncontour, to be 6.