(see below for directions - read them while the applet loads!)
Directions:
Wait for the applet to load and for the graph of the function to appear
in the gray area above.
(If there is no gray area, check your browser settings to make sure that
Java is enabled, or try with another browser)
The applet combines several tools for viewing functions of two variables.
Use the Show menu to switch from one mode to another.
The applet initially starts in the Input mode, which lets you choose a
function to plot (you can either enter it manually, or select one from the
drop-down list; click on the Plot button to create the new plot). The applet starts directly with the function you will need
for Problem Set 3, so you don't need to do anything here, but you are
encouraged to experiment with some other functions as well (for extra
practice, especially if you feel that contour plots are slightly confusing).
The 3D plot can be rotated by clicking on it and dragging the mouse
(keeping the button pressed).
Now, switch to the Level curves mode (select it in the
Show menu). The left half of the display shows a contour plot
corresponding to the 3D plot in the right half. The slider control
in the lower-left corner moves a level curve highlighted in yellow on both
plots: experiment with it in order to perfect your understanding of the
contour plot and how it is related to the graph of the function.
Once you understand fairly well the contour plot, switch to the
Partial derivatives mode (select it in the Show menu).
The right half of the display still shows the graph of the function. The
lower-left corner shows a small contour plot, with a pink dot representing
the point where we measure the partial derivatives. To move the
point, simply click somewhere in the contour plot.
There are two small graphs above the contour plot: these represent
slices of the graph of the function through the given point
(intersecting the 3D graph with planes parallel to the xz- and
yz-planes: compare the small plots with the highlighted curves on the 3D plot). The partial
derivatives are, by
definition, the slopes of these graphs. Look at the bottom-right corner of
the display for the values of f_{x} and f_{y}
at the selected point.
The last mode (directional derivatives and gradient vector) will only
be used later in Unit 2, after these topics have been covered in lecture.