This demo shows contour maps and level sets on the left and the graph of the function \(f(x,y)\) on the right. Use the drop-down menu to pick a function from the list. A function might contain parameters. Use the slider bars on the right to change parameters. (You can study a family of functions this way.)
A level set \(f(x,y) = k\) is given by a colored curve. Color represents a height in \(z\)-value if the graph of \(f(x,y)\) is plotted in \(xyz\)-coordinates. You can color the contour map and the graph by checking 'colored by height.' To show many level sets at once, check 'show level sets.'
Even though level sets live on \(xy\)-plane, we can think of them as intersections of the graph of \(f(x,y)\) and the plane \(z = k\). To show the plane, check 'show slice plane.'
You can change settings such as domain and range of the function, and the number of level curves by open up the setting menu. For each slider bar, if you click on the plus sign on the right, there will be more settings to play with. For example, you can let a parameter run from \(a\) to \(b\) giving you an animation.
Because Mathematica doesn't allow it, you cannot input you own function. Let me know if there's a function (or a family of function) you want me to put in.
With the current technology, in order to use this demo, you need a CDF Player Plugin for your web browser. You can download it for free from Wolfram.
By Nics Theerakarn.
This work is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA)