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# Peer Review

by Ken Levasseur

## Ratings

### Overall Rating:

Content Quality:
Effectiveness:
Ease of Use:
 Reviewed: May 20, 2004 by Mathematics Overview: This site is a member of a large collection of WebMathematica scripts written by the author. The applet allows the user to compute and plot the Taylor polynomial of a user defined function. A user has an option of choosing the center of expansion as well as the degree of the Taylor polynomial. Learning Goals: To illustrate the concept of approximating a function with Taylor Polynomials Target Student Population: Calculus students. Prerequisite Knowledge or Skills: Differential Calculus Type of Material: Simulation Recommended Uses: Classroom demonstration or student experimentation Technical Requirements: It requires a "Java-enabled" browser.

### Content Quality

Rating:
 Strengths: Taylor polynomials and approximations are topics that require special attention due to their importance and complexity. This applet provides an excellent tool to build a student?s understanding of Taylor polynomials of elementary functions.The user can input (using Mathematica syntax) many elementary functions, specify the center of expansion, choose the degree of the Taylor polynomial (up to six), and the width of the plotting window. The applet accurately graphs both function and approximating polynomial, displays all Taylor polynomials up to the sixth degree, and graphs the error of approximation. Concerns: The applet does not generate an error message if the user accidentally (or intentionally) chooses the center of expansion to be a point where the function is not defined.

### Potential Effectiveness as a Teaching Tool

Rating:
 Strengths: This applet gives users an excellent opportunity to explore how well Taylor polynomials of different degrees approximate common functions. Instructors can use the graphical and algebraic components of this applet for demonstration purposes as well as part of take-home assignments or projects. Because the user has the flexibility to choose the functions, it is easy to choose several meaningful examples. Concerns: None

### Ease of Use for Both Students and Faculty

Rating:
 Strengths: The applet has one button and one input window and is very easy to use. It uses Mathematica function syntax This is slightly different from most graphing calculators but is clearly explained on a separate linked page. The average user can begin using the applet immediately. Concerns: A simple way to print polynomials and plots separately might be useful.
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