ghdoru11
  • ghdoru11
Find the Fourier expansion for: f:R->R periodic T=2pi , f(x)=3x, x is between [-pi,pi]
Differential Equations
katieb
  • katieb
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beginnersmind
  • beginnersmind
Why was this question closed?
ghdoru11
  • ghdoru11
no one solve this and i have another question
beginnersmind
  • beginnersmind
Anyway you can just go back to the definition of fourier coefficients: \[a_n = \int_{-\pi}^{\pi} 3x*sin(nx)dx\] \[b_n = \int_{-\pi}^{\pi} 3x*cos(nx)dx\] then evaluate the integrals. Use the substitution t = nx and integration by parts with u being the linear term and v' the trigonometeric part.

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IrishBoy123
  • IrishBoy123
yeah, and it's odd so you ignore the cosine term
beginnersmind
  • beginnersmind
Right, that saves a lot of work :)
ghdoru11
  • ghdoru11
so just the first integral is neded?
beginnersmind
  • beginnersmind
Yes, \(b_n\) = 0 for every n.
ghdoru11
  • ghdoru11
thank you so much guys

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