Calculate Laplace transforms and inverse transforms with step-by-step solutions, convergence analysis, and common transform pairs
Use standard notation: t^2, e^(at), sin(at), cos(at), etc.
| f(t) | F(s) | Domain | Description |
|---|---|---|---|
| 1 | 1/s | s > 0 | Unit step function |
| t | 1/s² | s > 0 | Linear ramp |
| t^n | n!/s^(n+1) | s > 0, n > -1 | Power function |
| t² | 2/s³ | s > 0 | Quadratic function |
| t³ | 6/s⁴ | s > 0 | Cubic function |
| e^(at) | 1/(s-a) | s > a | Exponential function |
| te^(at) | 1/(s-a)² | s > a | Exponential with linear factor |
| t^n e^(at) | n!/(s-a)^(n+1) | s > a | Power times exponential |