Appendix 1
Table for the Laplace Transform
| Case no. | f(t) |  |
| 1 | 1 | 1/s |
| 2 | t | 1/s2 |
| 3 | tn–1 | (n – 1)!/sn (n = 1,2,3,….) |
| 4 | t–1/2 |  |
| 5 | t1/2 |  |
| 6 | tk–1 |  = Gamma function |
| 7 | eat | 1/(s – a) |
| 8 | teat | 1/(s–a)2 |
| 9 | tn– 1eat |  |
| 10 | tk– 1eat |  = Gamma function |
| 11 | eat–ebt |  |
| 12 | aeat–bebt |  |
| 13 | Dirac function: δ0(t) | 1 |
| 14 | δa(t) | e– as |
| 15 | Unit step function: ua(t) | e– as/s |
| 16 | ln t |  |
| 17 | sin(ωt) |  |
| 18 | cos(ωt) |  |
| 19 | sinh(at) | a/(s2–a2) |
| 20 | cosh(at) | s/(s2–a2) |
| 21 | eatsin(ωt) |  |
| 22 | eatcos(ωt) |  |
| 23 | tsin(ωt) |  |
| 24 | ωt – sin(ωt) |  |
| 25 | J0(at) |  |
| 26 |  |
e– k/s/s |
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