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Understanding Fourier Coefficients using PDE
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[QUOTE="RJLiberator, post: 5354694, member: 504241"] [h2]Homework Statement [/h2] In my PDE course we have a homework question stating the following: Let ϑ(x) = x in the interval [-pi, pi ]. Find its Fourier Coefficients. [h2]Homework Equations[/h2] From my notes on this type of question: a_o = 2c_o = 1/pi * integral from -pi to pi [f(x) dx] a_n = c_n + c_(-n) = 1/pi * integral from -pi to pi [f(x) cos(n*x) dx ] b_n = i(c_n - c_(-n)) = 1/pi * integral from -pi to pi [f(x) sin(n*x) dx] [h2]The Attempt at a Solution[/h2] Is it as simple as just a plug and chug based off my noes? a_o's integration with f(x) = x just is x^2/(2*pi) from -pi to pi so we have a_o = pi/2 - pi/2 = 0 a_n's integration is just equal to 0 as well. b_n is just -2(-1)^n/n So thus, the Fourier coefficients here are b_n = [(-2)(-1)^n]/n for n ≥ 1 Am I understanding the question properly? [/QUOTE]
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Understanding Fourier Coefficients using PDE
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