Mathematic Methods HW Solutions 38

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

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.

Ask a homework question - tutors are online