Section65

Section65 - 1 Laplace Transform of Dirac Delta function δ...

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Unformatted text preview: 1 Laplace Transform of Dirac Delta function δ (1 of 2) • The Laplace Transform of δ is defined by and thus { } { } , ) ( lim ) ( > − = − → t t t d L t t L τ τ δ { } ( ) ( ) [ ] ) cosh( lim ) sinh( lim 2 lim 2 1 lim 2 lim 2 1 lim ) ( lim ) ( st st st s s st t s t s t t st t t st st e s s s e s s e e e s e e e s s e dt e dt t t d e t t L − → − → − − − → − − + − → + − − → + − − → ∞ − → = = = − = + − = − = = − = − ∫ ∫ τ τ τ τ τ τ τ δ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ + < < − = − otherwise , , 2 1 ) ( τ τ τ τ t t t t t d ), ( lim ) ( > − = − → t t t d t t τ τ δ Laplace Transform of δ (2 of 2) • Thus the Laplace Transform of δ is • For Laplace Transform of δ at t = 0, take limit as follows: • For example, when t = 10, we have L { δ ( t-10)} = e- 10 s ....
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This note was uploaded on 04/09/2012 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue.

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Section65 - 1 Laplace Transform of Dirac Delta function δ...

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