Fourier Trigonometric Series for Symmetric Function: Homework Check

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SUMMARY

The discussion focuses on determining the first three terms of the Fourier trigonometric series for a symmetric function. Participants clarify that the terms refer to a0, a1, and a2, confirming the correct interpretation of the series terms. The symmetry of the function about the y-axis eliminates the need to calculate bn coefficients. The conversation highlights the importance of accurately defining the function before proceeding with Fourier series calculations.

PREREQUISITES
  • Understanding of Fourier series concepts
  • Familiarity with trigonometric functions
  • Knowledge of symmetry in mathematical functions
  • Basic proficiency in LaTeX for mathematical notation
NEXT STEPS
  • Study the derivation of Fourier series for symmetric functions
  • Learn about the significance of coefficients a0, a1, and a2 in Fourier series
  • Explore the implications of function symmetry on Fourier series calculations
  • Practice using LaTeX for presenting mathematical equations effectively
USEFUL FOR

Students studying mathematical analysis, particularly those focusing on Fourier series, as well as educators seeking to clarify concepts related to symmetric functions and their series representations.

roldy
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Homework Statement


Determine the first three terms in the Fourier trigonometric series for the function shown below.


Homework Equations


Look at attached jpeg. This tex tool is terrible. After making correction to the code, the preview still shows previous preview posts.


The Attempt at a Solution



See attached jpeg for solution and the other attachment for the function. Did I define the function correctly? I didn't solve for bn because this function is symmetric about the y-axis.

First three terms mean a0, a1, and a2 right?
Or is it n=1, 2, 3
 

Attachments

  • Fourier Series copy.jpg
    Fourier Series copy.jpg
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  • Untitled-1.jpg
    Untitled-1.jpg
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Would anyone check this for me please?
 

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