2302f11-mid3-formulae

# 2302f11-mid3-formulae - ay + by + cy = f ( t ) has solution...

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Formulas of possible use sin 2 x = 2 sin x cos x L { t n } = n ! s n +1 cos 2 x =c o s 2 x - sin 2 x L { e at } = 1 s - a sin 2 x = 1 - cos 2 x 2 L { sin bt } = b s 2 + b 2 cos 2 x = 1+cos2 x 2 L { cos bt } = s s 2 + b 2 sin( x + y ) = sin x cos y +cos x sin y L { e at f ( t ) } = F ( s - a ) , where F ( s )= L { f } . cos( x + y )=c o s x cos y - sin x sin y L { tf ( t ) } = - d ds L { f } ± tan udu = - ln | cos u | L { f ± ( y ) } = s L { f }- f (0) ± cot udu = ln | sin u | L { u ( t - a ) f ( t ) } = e - as L { f ( t + a ) } ± sec udu = ln | sec u +tan u | L { f , period T } = L { f T } 1 - e - sT ± csc udu = ln | csc u - cot u | , L { δ ( t - a ) } = e
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Unformatted text preview: ay + by + cy = f ( t ) has solution y ( t ) = C ( t ) y 1 ( t ) + D ( t ) y 2 ( t ) where C = -fy 2 a ( y 1 y 2-y 2 y 1 ) dt D = fy 1 a ( y 1 y 2-y 2 y 1 ) dt 4...
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## This note was uploaded on 12/10/2011 for the course MAP 2302 taught by Professor Tuncer during the Fall '08 term at University of Florida.

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