In this topic, you study the Table of Laplace Transforms.
Definition: Laplace transform of f(t) is
L[f(t)] = F(s) = \int\limits_0^\infty {f(t){e^{ – st}}dt}
Using above property, the Laplace transform of Basic Functions are
| L[f(t)] | F(s) |
| L[u(t)] | \frac{1}{s} |
| L[t] | \frac{1}{{{s^2}}} |
| L[{t^n}] | \frac{{n!}}{{{s^{n + 1}}}} |
| L[{e^{ – at}}] | \frac{1}{{s+a}} |
| L[e^{ at}] | \frac{1}{{s-a}} |
| L[\sin at] | \frac{{a}}{{{s^2} + a^2}} |
| L[\cos at] | \frac{{s}}{{{s^2} + a^2}} |
| L[\sinh at] | \frac{{a}}{{{s^2} – a^2}} |
| L[\cosh at] | \frac{{s}}{{{s^2} – a^2}} |
Note:- Defined for t ≥ 0, f(t) = 0, for t < 0.