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===== Guessing the Fourier Expansion of a Function: Instructor's Guide =====

==== Main Ideas ====
  - Fourier Series
  - Oscillatory Functions


==== Students' Task ====
//Estimated Time:15 minutes//

The students were assigned a function that was a superposition between two or more harmonic functions and asked to guess the harmonic terms of the series. Student used Mathematica/Maple to verify their guess against the plot of the original function. 


==== Prerequisite Knowledge ====

  * Superposition
  * Basic harmonic functions

==== Props/Equipment ====

  * [[:Props:start#maple|Computers with Mathematica or Maple]]  

==== Activity: Introduction ====
Students were first asked to build any unique superposition function using [[http://phet.colorado.edu/en/simulation/fourier|Fourier: Making Waves]]. This helped the students to grasp and apply the idea of superposition.  
Students then were asked to use a Mathematica/Maple worksheet to find the components of a function that is a superposition of several harmonic terms. 


==== Activity: Student Conversations ====
  * Students have fun building their own unique superposition function using [[http://phet.colorado.edu/en/simulation/fourier|Fourier: Making Waves]]. This is a good way to start students think about the superposition principle.
  * Most students have prior knowledge of superposition and successfully decompose the superposition function without too much trouble. 
  * Some students simply "guess-and-check" their answers.
    * One effective way to guide students is to ask them what they see as the dominant component in the oscillatory nature of the function.   

==== Activity: Wrap-up ====
The wrap-up discussion focuses on the application of the superposition principle. The discussion should emphasize that this method of "guess-and-check" is helpful as a learning tool but not practical. This is a good way to introduce Fourier Series. 

==== Extensions ====