Laplace Sine Transform

  • #1
[itex]L[sin(at)]=\frac{a}{s^{2}+a^{2}}, Re>0[/itex]

[itex]L[e^{kt}]=\frac{1}{s-k}, s>k[/itex]
[itex]L[e^{-kt}]=\frac{1}{s+k}, s<-k[/itex]

[itex]L[sin(at)]=\frac{1}{2i}L[e^{iat}-e^{-iat}][/itex]
[itex]=\frac{1}{2i}L[e^{iat}]-L[e^{-iat}][/itex]
Using the above relations
[itex]=\frac{1}{2i}[\frac{1}{s-ia}-\frac{1}{s+ia}], s>ia, s<-ia[/itex]

The problem is that I don't understand, how s>ia and s<-ia could imply that Real part of s>0?
 

Answers and Replies

  • #2
lurflurf
Homework Helper
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Complex numbers are not ordered,
s>ia and s<-ia
does not make sense.
Real part of s>0
Is needed to assure the existence of the integral.
 

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