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9.)f(x) = [0, sin x, -T

9.)f(x) = [0, sin x, -T

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Problems 1-16, find the Fourier series of the function f on the given interval. Give the number to which the Fourier series converges at a point of discontinuity of f. (9.) f(x) = So, sin x, -T<x<0 0≤x≤T
Transcribed Image Text:In Problems 1-16, find the Fourier series of the function f on the given interval. Give the number to which the Fourier series converges at a point of discontinuity of f. (9.) f(x) = So, sin x, -T<x<0 0≤x≤T
9. ao an 2 = = = = [ ^_^1(x) dx = = = [² sin z dx = ² S x ㅠ ㅠ 0 ㅠ ㅠ bn = 12.2 Fourier Series b₁ a1 = = = •πT = [ f(x) cos nx π -T 1+ (−1)n π(1-n²) •π 22/17 SO 0 2π 0 f(x) ㅠ 1 dx TE sin 2x dx = 0 = - 21/17 100 (1 − cos 2x) dx = 2π ㅠ π [*_*f(x) sin nx dx = So π -π = for n = 2, 3, 4, . . . + sin x + •πT 1 S ∞ ㅠ •πT = 24/7 * (cos(1 − n)a − cos(1 + n)a) da=0_ for n = 2,3,4,... 2π 0 n=2 * sin x cos nx dx = S™ (sin 1 2 sin x sin nx dx 1+ (-1)" π(1 — n²) 2π Cos nx 641 sin(1 + n)r + sin(1 − n)x) dx
Transcribed Image Text:9. ao an 2 = = = = [ ^_^1(x) dx = = = [² sin z dx = ² S x ㅠ ㅠ 0 ㅠ ㅠ bn = 12.2 Fourier Series b₁ a1 = = = •πT = [ f(x) cos nx π -T 1+ (−1)n π(1-n²) •π 22/17 SO 0 2π 0 f(x) ㅠ 1 dx TE sin 2x dx = 0 = - 21/17 100 (1 − cos 2x) dx = 2π ㅠ π [*_*f(x) sin nx dx = So π -π = for n = 2, 3, 4, . . . + sin x + •πT 1 S ∞ ㅠ •πT = 24/7 * (cos(1 − n)a − cos(1 + n)a) da=0_ for n = 2,3,4,... 2π 0 n=2 * sin x cos nx dx = S™ (sin 1 2 sin x sin nx dx 1+ (-1)" π(1 — n²) 2π Cos nx 641 sin(1 + n)r + sin(1 − n)x) dx
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