Mathematic Methods HW Solutions 34

Mathematic Methods HW Solutions 34 - Chapter 7 34 8.20 f...

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 34 8.20 f (x) = 2 + 3 ∞ an cos 1 2nπx + 3 ∞ 1 0 , n = 3 k an = −9 , otherwise 8 n2 π 2 9.1 9.2 9.3 9.5 9.7 (a) cos nx + i sin nx x (a) 1 ln |1 − x2 | + 1 ln | 1−x | 2 2 1+ (a) (−x4 − 1) + (x5 + x3 ) ∞ 1 4 sin nx f (x) = π1n an = f (x) 9.8 odd n 2 sin nπ , a0 /2 = 1/2 nπ 2 2 = 1 + π (cos πx − 1 cos 3πx 2 2 3 2 ∞ n+1 (−1) n f (x) = 1 9.9 f (x) = 1 1 +2 12 π π 2 9.10 f (x) = − 4 π 9.11 f (x) = 1 ∞ odd n + 1 5 cos 5πx · · · ) 2 (−1)n cos 2nπx n2 1 cos 2nx n2 1 + 2 ∞ 1 (−1)n cos nx n2 + 1 1 sin nπx n 1 4 9.15 fc (x) = − 2 2π ∞ 1 odd n cos nπx n2 2 fs (x) = π ∞ 1 (−1)n+1 sin nπx n sin nx fc = fp = (1 − cos 2x)/2 n(4 − n2 ) o dd n=1 4 1 1 9.17 fc (x) = (cos πx − cos 3πx + cos 5πx · · · ) π 3 5 ∞ 1 4 fs (x) = fp (x) = sin 2nπx π1n 9.16 fs = 8 π 1 ∞ 1 odd n ∞ 2 9.12 f (x) = − π (b) x sinh x + x cosh x (b) (cos x + x sin x) + (sin x + x cos x) (b) (1 + cosh x) + sinh x ∞ 1 4 nπx 9.6 f (x) = sin π1n l sin 2nx ∞ 2 sinh π π 2nπx bn sin , where 3 − 1 , n = 3 k √ nπ 1 33 bn = − − , n = 3k + 1 nπ 8n2 π 2 √ 1 33 − + 2 2 , n = 3k + 2 nπ 8n π odd n 9.18 Even function: a0 /2 = 1/3, 2 nπ √ 3 nπ {1, 1, 0, −1, −1, 0, and repeat} 1 fc (x) = 1 + π3 (cos πx + 1 cos 2πx − 1 cos 4πx − 1 cos 5πx + 7 cos 7πx 3 3 2 3 4 3 5 3 3 2 1 Odd function: bn = nπ (1 − cos nπ ) = nπ {1, 3, 4, 3, 1, 0, and repeat} 3 1 4 fs (x) = π (sin πx + 3 sin 2πx + 3 sin 3πx 3 2 3 3 3 + 4 sin 4πx + 1 sin 5πx + 1 sin 7πx · · · ) 3 5 3 7 3 an = sin nπ = 3 √ ···) ...
View Full Document

Ask a homework question - tutors are online