Unformatted text preview: n = 7, A 7 = 2 sinh 7 π ² 1 sin 2 7 πx dx = 1 sinh7 π . Thus u 1 ( x, y ) = 1 sinh7 π sin 7 πx sinh[7 π (1y )] . In a similar way, appealing to the formulas in the text, we ±nd u 2 ( x, y ) = 1 sinh π sin πx sinh( πy ) u 3 ( x, y ) = 1 sinh 3 π sinh[3 π (1x )] sin(3 πy ) u 4 ( x, y ) = 1 sinh 6 π sinh6 πx sin(6 πy ); u ( x, y ) = u 1 ( x, y ) + u 2 ( x, y ) + u 3 ( x, y ) + u 4 ( x, y ) = 1 sinh 7 π sin7 πx sinh[7 π (1y )] + 1 sinh π sin( πx ) sinh( πy ) + 1 sinh 3 π sinh[3 π (1x )] sin(3 πy ) + 1 sinh6 π sinh(6 πx ) sin(6 πy )...
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 Fall '11
 StuartChalk
 Sin, Berlin UBahn, U4, U7, sinh π

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