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laplace transform

# laplace transform - 14 e ct f t F s − c Sec 6.3 15 f ct 1...

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304 Chapter 6. The Laplace Transform TABLE 6.2.1 Elementary Laplace Transforms f ( t ) = L 1 { F ( s ) } F ( s ) = L { f ( t ) } Notes 1. 1 1 s , s > 0 Sec. 6.1; Ex. 4 2. e at 1 s a , s > a Sec. 6.1; Ex. 5 3. t n ; n = positive integer n ! s n + 1 , s > 0 Sec. 6.1; Prob. 27 4. t p , p > 1 ±( p + 1 ) s p + 1 , s > 0 Sec. 6.1; Prob. 27 5. sin at a s 2 + a 2 , s > 0 Sec. 6.1; Ex. 6 6. cos at s s 2 + a 2 , s > 0 Sec. 6.1; Prob. 6 7. sinh at a s 2 a 2 , s > | a | Sec. 6.1; Prob. 8 8. cosh at s s 2 a 2 , s > | a | Sec. 6.1; Prob. 7 9. e at sin bt b ( s a ) 2 + b 2 , s > a Sec. 6.1; Prob. 13 10. e at cos bt s a ( s a ) 2 + b 2 , s > a Sec. 6.1; Prob. 14 11. t n e at , n = positive integer n ! ( s a ) n + 1 , s > a Sec. 6.1; Prob. 18 12. u c ( t ) e cs s , s > 0 Sec. 6.3 13. u c ( t ) f ( t c ) e cs F ( s ) Sec. 6.3
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Unformatted text preview: 14. e ct f ( t ) F ( s − c ) Sec. 6.3 15. f ( ct ) 1 c F ± s c ² , c > Sec. 6.3; Prob. 19 16. ³ t f ( t − τ) g (τ) d τ F ( s ) G ( s ) Sec. 6.6 17. δ( t − c ) e − cs Sec. 6.5 18. f ( n ) ( t ) s n F ( s ) − s n − 1 f ( ) − ··· − f ( n − 1 ) ( ) Sec. 6.2 19. ( − t ) n f ( t ) F ( n ) ( s ) Sec. 6.2; Prob. 28...
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