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Unformatted text preview: ) d d where = + = Z t Z f ( ) g (  ) h ( t ) d d = Z t Z f ( ) g (  )] d h ( t ) d = Z t ( f * g )( ) h ( t ) d = ( f * g ) * h ( t ) . Theorem 1 (The convolution theorem) . Let f and g be piecewise continuous and have exponential order . If F ( s ) = L f ( s ) and G ( s ) = L g ( s ) , then (3) F ( s ) G ( s ) = L ( f * g )( s ) for s > . A proof can be found in [1, Theorem 2.39, pp. 9293]. References [1] Joel L. Schi. The Laplace Transform Theory and Applications . SpringerVerlag New York, Inc., 1999....
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This note was uploaded on 11/11/2011 for the course MATH 255.01 taught by Professor Kwa during the Winter '11 term at Ohio State.
 Winter '11
 Kwa
 Differential Equations, Equations

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