This site contains an applet that allows the user to define a parameterized 2-dimensional curve and then create a three dimensional graph of this curve. Some additional properties of the curve can also be shown on the graph. This site is a member of the Saint Louis University Calculus collection.
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 parametric curves in 2- and 3-dimensional spaces.
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 plot of functions defined parametrically. A user has control over the function input, range, type of a graph, view angle, and many other useful features such as a plot of tangent and normal unit vector at a user-defined point on the graph.
The click and drag mouse feature allows a user to rotate the plot in simulated 3D coordinate space in any direction.
Potential Effectiveness as a Teaching Tool
Every multivariable calculus student (and instructor) faces the difficulty of graphing three-dimensional parametric curves. This site contains an applet that is a great tool for visualizing the graphs of parametric curves. An extensive input flexibility and the ability to change the view in the graphing window are excellent features that can produce a good starting point to discuss the nature of parametric curves in 2-D and 3-D. Another feature lets the user see tangent and normal unit vectors drawn at a user-chosen point on the graph and can be used during the study of tangential and normal components of acceleration.
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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