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GRAPHING APPLETS FOR CALCULUS--BASINS OF ATTRACTION

 

Ratings

Overall Rating:

5 stars
Content Quality: 5 stars
Effectiveness: 5 stars
Ease of Use: 4 stars
Reviewed: Apr 09, 2003 by Mathematics
Overview: This applet allows students to experiment with basins of attraction for Newton's Method. The applet also indicates how many steps Newton's method takes to converge (to six digit of accuracy) for a given initial point.


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Learning Goals: To give students a visual example of the convergence properties of Newton's method.
Target Student Population: Students in a differential calculus class or a numerical methods class.
Prerequisite Knowledge or Skills: Students must understand both how to find derivatives as well as the graphical interpretation of the derivative.
Type of Material: Simulation
Recommended Uses: This applet could serve as a classroom demonstration tool or as a basis for student experimentation.
Technical Requirements: It requires a "Java-enabled" browser.

Evaluation and Observation

Content Quality

Rating: 5 stars
Strengths: This applet allows the user to specify a specific function and modify window settings. There is a badge above the graph that displays cursor location so that the user may explore where specific starting values convergence. The user can change window settings with a click and a drag or use the zoom feature to easily change the scale of a given simulation. This applet also includes a well prepared project that guides students through an exploration using the applet.
Concerns: The Web page containing the applet could use a title.

Potential Effectiveness as a Teaching Tool

Rating: 5 stars
Strengths: These applets allow users to explore many of the concepts from the study of Calculus both graphically and numerically. Because the user has the freedom to choose different beginning inputs, it is easy to choose very meaningful examples.
Concerns: None.

Ease of Use for Both Students and Faculty

Rating: 4 stars
Strengths: The buttons found on these applets are clearly marked. They allow the user to enter functions, view graph range controls, and view accurate cursor location information. The function syntax is similar to most graphing calculators, and is clearly explained on a separate page. There are also 11 commonly used functions available, including sine, cosine, tangent, arcsine, arctangent, exp, and absolute value. The use of this applet is fairly intuitive. The average user can begin using it immediately with a brief introduction. Although the applet is copyrighted, it is available for free academic, non-profit use. The class files and most of the source code are also made available for download as well as an introduction to writing your own applets using these resources.
Concerns: None
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