This module is a part of the Saint Louis University collection of Calculus applets. The site contains an applet that is designed to show how the graph of a function in two variables can be constructed from the cross sections, which are each graphs of one variable.
Type of Material:
Classroom demonstration as well as visualization of functions in any setting (homework, projects, labs, etc.).
Identify Major Learning Goals:
This site provides students with a tool for visualization of 3-D graphs of functions of two variables.
Target Student Population:
Students in multivariable calculus/analysis.
Prerequisite Knowledge or Skills:
Basic course of multivariable Calculus.
This site contains a Java applet that gives quick, accurate plots of functions of two variables. Beside the graph of the surface itself, this applet generates three additional plots that represent a two dimensional view of the domain of the function, and two graphic windows showing respectively x- and y-cross sections of the surface.
A user has control over the function input, range, type of a graph, view angle, and many other useful features.
The click and drag mouse feature allows a user to rotate the plot in simulated 3D coordinate space in any direction.
All these features are well-integrated to produce an excellent learning/teaching tool.
Potential Effectiveness as a Teaching Tool
This site contains an applet that not only provides a 3-D graph of functions of two variables but also shows two different cross-sections as x- and y-slice of the graph. This feature can be particularly useful when discussing basic quadratic surfaces in multivariable Calculus.
An extensive input flexibility and the ability to change the view in the graphing window are excellent features that can apply the applet to a particular homework assignment and/or take-home student project.
The included applet worksheets are also handy for making out-of-class assignments and for enabling the site as a student resource.
The site could use an introduction section targeting potential Calculus students who plan to use this tool.
Ease of Use for Both Students and Faculty
The applet has multiple window structure that is convenient for demonstration purposes. A drag-and-rotate feature of the graphic window is a great plus.
The interface, while somewhat intuitive, still takes some time to pick up.
Changing the values of parameters in the control window requires hitting return every time the user needs to change input. An update or refresh plot button would be very helpful in the control window.
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