Mathematic Methods HW Solutions 58

Mathematic Methods HW Solutions 58 - Chapter 13 2.1 T= 2.2...

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Unformatted text preview: Chapter 13 2.1 T= 2.2 T= 2.3 2.4 2.7 T= ∞ nπx (−1)n+1 −nπy/10 e sin n 10 1 200 π 4 π 1 odd n ∞ n2 2 even n −2 ∞ 2 n=2+4k nπx 1 −nπy/20 sin e n 20 n e−ny sin nx −1 πx 1 −3πy/30 120 −πy/30 3πx 1 −5πy/30 5πx e sin −e sin + e sin ··· π2 30 9 30 25 30 ∞ n 4 sinh n(1 − y ) sin nx T= π 2 (n2 − 1) sinh n even n ∞ bn nπx nπ 4nπ sinh 30 (40 − y ) sin 30 sinh 3 1 nπ 100 200 1 − cos = where bn = (1, 3, 4, 3, 1, 0, and repeat) nπ 3 nπ T= 2.9 T= 2.10 T = 2.11 T = T= + 200 π ∞ ∞ 1 odd n −2 ∞ 2 n=2+4k nπ nπx 1 sinh (10 − y) sin n sinh nπ 20 20 2 400 nπ nπx sinh (10 − y ) sin ; T (5, 5) ∼ 25◦ = nπ sinh nπ 10 10 1 odd n ∞ 400 nπ nπx nπ nπy sinh (10 − y ) sin + sinh (10 − x) sinh nπ sinh nπ 10 10 10 10 1 odd n ∞ 1 odd n ∞ 1 odd n 2.13 ∞ T= 2.8 2.12 20 π T (x, y ) = 400 nπ nπx sinh (30 − y ) sin nπ sinh 3nπ 10 10 nπ nπy 400 sinh (10 − x) sin nπ sinh(nπ/3) 30 30 20 π + 40 π ∞ 1 ∞ 1 (−1)n+1 nπ nπx sinh (20 − y) sin n sinh 2nπ 10 10 nπ (−1)n+1 nπy sinh (10 − x) sin n sinh nπ 20 20 2 58 ...
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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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