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MERLOT II


    

Peer Review


Taylor Polynomials

 

Ratings

Overall Rating:

4 stars
Content Quality: 4.5 stars
Effectiveness: 3.5 stars
Ease of Use: 5 stars
Reviewed: Jan 20, 2006 by Mathematics
Overview: This applet draws the graph of y = sin(x) along with its Maclaurin polynomial
(Taylor polynomial at c=0). The user can specify the degree of the approximating
polynomial and then increment it with a push of a button.
Learning Goals: To illustrate the concept of Taylor polynomial approximation.
Target Student Population: Students in Calculus II
Prerequisite Knowledge or Skills: College Algebra, Calculus I
Type of Material: Simulation
Recommended Uses: In-class demonstration
Technical Requirements: A Java-enabled browser.

Evaluation and Observation

Content Quality

Rating: 4.5 stars
Strengths: This applet does one thing and one thing only: it draws a graph of a Taylor
polynomial approximating y = sin(x) in the neighborhood of the point c = 0. A
user can change the degree of the polynomial either by manually typing it or by
clicking on the “Next” button. The latter method increments the degree by two
with each click and allows the user to observe the resulting quality of
approximation.
Concerns: The site could use an introductory paragraph explaining Taylor approximation and
perhaps giving a formula for a Maclaurin polynomial for y = sin(x) of degree n.

Potential Effectiveness as a Teaching Tool

Rating: 3.5 stars
Strengths: This applet is a great visual aid for a one-time in-class demonstration in a
Calculus course. Traditionally, Taylor approximation is one of the topics that
students find hard to absorb. This dynamic applet should help students grasp the
concept of Taylor approximation.
Concerns: The use of the applet is very limited. It would certainly widen the use if one
could have a way to change the input function (or at least choose from a list
of popular ones) and move the center of approximation.

Ease of Use for Both Students and Faculty

Rating: 5 stars
Strengths: The applet is extremely easy to use since it has only two control buttons and
one input box.
Concerns: none

Other Issues and Comments: