Mathematic Methods HW Solutions 38

# Mathematic Methods HW Solutions 38 - Chapter 7 38 ∞ 2 π...

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Unformatted text preview: Chapter 7 38 ∞ 2 π 2 (b) fs (x) = π 1 12.30 (a) fc (x) = π 1 (b) fs (x) = π sin 3α − 2 sin 2α cos αx dα α 0 ∞ 2 cos 2α − cos 3α − 1 sin αx dα α 0 ∞ 1 − cos 2α cos αx dα α2 0 ∞ 2α − sin 2α sin αx dα α2 0 12.29 (a) fc (x) = 13.2 f (x) = i 2π ∞ 1 2inπx e n −∞ n =0 13.4 (c) q (t) = CV 1 − 2(1 − e−1/2 ) 13.6 f (t) = ∞ −∞ (−1)n sin ωπ int e π (ω − n) π 4 13.7 f (x) = − 2 π 13.8 13.9 13.10 13.11 ∞ 1 odd n ∞ (1 + 4inπ )−1 e4inπt/(RC ) −∞ 1 cos nx n2 (a) 1/2 (b) 1 (b) −1/2, 0, 0, 1/2 (c) 13/6 (c) 0, −1/2, −2, −2 (d) −1, −1/2, −2, −1 Cosine series: a0 /2 = −3/4, 6 nπ nπ 4 −1 + sin an = 2 2 cos nπ 2 nπ 2 4 6 = 2 2 {−1, −2, −1, 0, and repeat} + {1, 0, −1, 0, and repeat} nπ nπ πx 3 4 6 2 cos fc (x) = − + − 2 + − 2 cos πx 4 π π 2 π 3πx 5πx 2 6 4 −4 cos cos − + + + ··· 2 2 9π π 2 25π 5π 2 Sine series: nπ 4 nπ 1 4 cos nπ − 6 cos + bn = 2 2 sin nπ 2 nπ 2 1 4 {−4, 10, −4, −2, and repeat} = 2 2 {1, 0, −1, 0, and repeat} + nπ nπ 4 πx 3πx 4 5 4 4 fs (x) = sin sin − + sin πx − + π2 π 2 π 9π 2 3π 2 1 5πx 4 4 5 − sin sin 2πx + − + sin 3πx · · · 2π 25π 2 5π 2 3π Exponential series of period 2: 3 fp (x) = − − 4 13.12 f = 90 13.13 (a) fs (x) = ∞ 1 ∞ −∞ odd n 5i 1 + n2 π 2 2nπ sin nx n 1 4 13.14 (a) f (x) = + 2 3π ∞ 1 einπx + (b) π 2 /6 cos nπx n2 (b) π 4 /90 i 2π ∞ −∞ even n=0 1 inπx e n ...
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## This note was uploaded on 02/29/2012 for the course MHF 2312 taught by Professor Dr.chet during the Fall '11 term at UNF.

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