Complimentary Microworld: Periodic Functions
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Author: Jim Swift

This 18 page book was designed to help you to explore Periodic Functions. There are three kinds of pages in this Microworld.

  • Descriptive material giving background information and/or instruction about the interaction on a following page. This includes Windows Help that you may pop up on each page.
  • Interactive pages that give you the opportunity to change the parameters in a periodic function, and observe how this changes the graph. In this way you will learn to read information about the graph from the function and information about the function from the graph.
  • Exercise pages where you can practice what you have learned on the interactive pages.

In this book you will have the opportunity to observe the behavior of periodic functions. You will also learn how to:

  • describe the motion of a point around a circle in terms of periodic functions.
  • learn the meanings of the terms amplitude, period, frequency and phase shift
  • determine the values of amplitude, period, frequency and phase shift by examining the parameters in periodic functions.
  • determine the equation of the graph of a periodic function.
  • construct mathematical models of applications of periodic functions

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    - James E. White, Ph.D. , Library Director,
    author of this website, Mathwright 2000, MindScapes,
    MathwrightWeb, and Mathwright32

 

Mathwright Visualization Studio free demonstration Microworld:

An Exploration of Periodic Functions

 

This Classic 18 page Microworld began life in 1993 as a WorkBook for IBM's Toolkit for Interactive Mathematics. We have translated it without change to our Microworld format so that you may view it either in your browser or offline. It is one of our new free Visualization Studio Microworlds in the Math Cafe, and readers are invited to check it out before joining the Library to get a glimpse of what is possible with Mathwright.

The aims of the Microworld are to help the novice learner visualize the "wrapping function" and its relation to the Sine and Cosine trigonometric functions. This is a venerable precalculus topic, and it is unfortunately often shrouded in a cloud of verbiage that can obscure the essential simple points.

Using the new page-by-page Windows Help Utility, the author guides the reader through a series of visual and dynamic animations (that the reader contols through her interactions) that illustrate the basic ideas in response to her own questions.

This "explanation" is supplemented on several pages with entertaining, game-like interactions in which the reader attempts to discover the formula that defines the graphs of periodic functions that the Microworld generates randomly. The overall effect is to encourage the reader to "play" as she learns each new idea, and in the process, to master the conventions and the notations that we wish to teach.

 

 

 

 

 

 

 

 

Requires the Java MathwrightWeb ActiveX Control to read in your Browser.
For proper viewing, be sure to use Version 2.10 or later, dated May 12, 2003


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For proper viewing, be sure to use Version 2.10 or later, dated May 12, 2003