Table of Laplace Transforms
Definition of Laplace Transforms
Let f(t) be a function of the real variable t, such that t ≥ 0. The Laplace transform F(s) of f is given by the integral
s is a complex variable. f(t) is called the original and F(s) is called the image function.
Table of Laplace Transforms
| f(t) | F(s) |
| 1 | 1 / s |
| t | 1 / s 2 |
| t n | n! / s n+1 , (n = 1,2,3...) |
| t 1/2 | Pi 1/2 / 2s 3/2 |
| t -1/2 | (Pi / s) 1/2 |
| e -a t | 1 / (s + a) |
| t e -a t | 1 / (s + a) 2 |
| sin a t | a / (s 2 + a 2) |
| t sin a t | 2 a s / (s 2 + a 2) 2 |
| e -at sin b t | b / ( (s + a) 2 + b 2 ) |
| cos a t | s / (s 2 + a 2) |
| t cos a t | (s 2 - a 2) / (s 2 + a 2) 2 |
| e -at cos b t | (s + a) / ( (s + a) 2 + b 2 ) |
| sinh a t | a / (s 2 - a 2) |
| cosh a t | s / (s 2 - a 2) |
| 1 - cos a t | a 2 / ( s (s 2 + a 2) ) |
| (2 / t)( t - cos a t) | ln [ (s 2 + a 2) / s 2 ] |
| (2 / t)( t - cosh a t) | ln [ (s 2 - a 2) / s 2 ] |
| (1 / t)( sin a t) | arctan(a / s) |
More references on integrals in calculus
Laplace Transform with Examples and Solutions
Find Area Under Curve
table of integrals
properties of integrals
