Engineering Board Exam Reviewer · Fourier Series · medium

Find the constant term a0/2 of the Fourier series of f(x)=x2 on (-π,π).

  1. 9.87
  2. 3.29
  3. 6.58
  4. 1.64

Answer

B. 3.29

Solution

a0/2 is the average value: 1/2π -ππx2,dx=1/2π·2π3/3=π2/3 3.29.

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  1. The square wave f(x)=-1 on (-π,0) and f(x)=1 on (0,π) has Fourier coefficients bn. Find b3.
  2. Find b3 in the Fourier series of f(x)=x on (-π,π).
  3. Which Fourier coefficients vanish for the odd function f(x)=x on (-π,π)?
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  5. The half-range sine series of f(x)=x on (0,2) is bn π x/2. Find b2.
  6. The square wave f(x)=-1 on (-π,0) and f(x)=1 on (0,π) has a jump at x=0. To what value does its Fourier series converge at x=0?
  7. Find a1 in the Fourier series of f(x)=|x| on (-π,π).

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