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Fourier Analysis

Activity Overview

Students use the TI InterActive!™ software to explore the connection between a function and its Fourier series.

Before the Activity

  • Install the TI InterActive!™ on the computer
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 2 from the PDF file for the class

    • During the Activity

    Distribute the printed pages to the class:

    Follow the Activity procedures:

  • Understand that Fourier series is a sum of sines and cosines that approximate a function over an interval
  • Define a function and decide the interval
  • Define the Fourier coefficients
  • Note that the Fourier coefficients depend on the function
  • Decide on the degree of the sum
  • Compute the partial sum in the function's Fourier series
  • Plot the partial sum and the function in the same coordinate plane
  • Observe that the partial sum of the function's Fourier series closely resembles the function on the given interval

    • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary

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