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**Unformatted text preview: **s = 0 sinh at | a s 2 − a 2 , Re s > a, single poles at s = ± a cosh at | s s 2 − a 2 , Re s > a, single poles at s = ± a and single zero at s = 0 More Properties : e ∓ βt f ( t ) | F ( s ± β ) , F ( s ) := L s { f ( t ) } f ( t − t d ) , t d > | e − st d F ( s ) , F ( s ) := L s { f ( t ) } Z t f ( τ ) dτ | 1 s F ( s ) , F ( s ) := L s { f ( t ) } t f ( t ) | − d ds F ( s ) , F ( s ) := L s { f ( t ) } t n f ( t ) , n ≥ | (for you to ﬁll in) d dt f ( t ) | sF ( s ) − f (0) , F ( s ) := L s { f ( t ) } d 2 dt 2 f ( t ) | s 2 F ( s ) − sf (0) − ˙ f (0) , d n dt n f ( t ) | s n F ( s ) − s n − 1 f (0) − s n − 2 ˙ f (0) · · · − f n − 1 (0) , n ≥ 1...

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- Spring '08
- Levan
- Laplace, Complex number, Complex Plane