This applet allows the user to plot the graph and create contour plots of functions of two variables that can be written in the form z = f (x,y).
Type of Material:
It requires a "Java-enabled" browser.
Identify Major Learning Goals:
Surface Plotter is designed to help students visualize surfaces and understand the behavior of functions of two variables geometrically.
Target Student Population:
This applet would be very useful in a Multivariable Calculus course.
Prerequisite Knowledge or Skills:
The user should have been introduced to functions of several variables.
Evaluation and Observation
This applet allows users to easily sketch the graphs and contour plots of functions of two variables. It allows the instructor to expand the list of functions that can be easily investigated in a typical multivariable calculus course. Using the different color and shade modes such as wireframe, color spectrum, and grayscale one is able to highlight particular interesting characteristics of the functions being studied.
The site could use an introduction section targeting potential Calculus students who plan to use this tool. A couple of textbook examples would be a plus.
Potential Effectiveness as a Teaching Tool
This tool will not only allow students to look at graphs and contour plots of functions of two variables, but will also allow them to visually explore such concepts as limits, relative maximums and minimums, saddle points, directional derivatives, and gradients. It also allows students to check their calculations visually. The bounding box is easily rotated using the mouse to allow users to view the plotted surface from many perspectives. Furthermore, users may graph two functions simultaneously and investigate surface intersections. Finally, it is much easier to use than more comprehensive packages like Maple, MATLAB, and Mathematica. Surface Plotter offers many of the same options as these other packages such as: Show Bounding Box, Show X-Y Mesh, Show Face Grids, Scale Bounding Box, Show X-Y ticks, Show Z ticks, Wireframe Mode, Hidden Surface Elimination, Color Spectrum Mode, Gray Scale Mode, and Dual Shades Mode.
Ease of Use for Both Students and Faculty
This is a very straightforward applet to use. The help pages are superb and are set up similar to many Windows applications. The bounding box settings are in plain view and are easily changed by a click of the mouse or by using the keyboard. The function syntax is similar to most graphing calculators and is clearly explained in the help pages. The user is allowed to modify the number of divisions used in the calculations and in the display of the graph. Users may also specify the number of contour lines used in a contour plot.
The applet starts automatically when the user opens the site. As a result the use of the browser navigation "Back" button produces multiple applet windows.