Education Technology

# Activities

• ##### Subject Area

• Math: Precalculus: Series

9-12

60 Minutes

• ##### Software

TI InterActive!™

## 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:

• 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