Difference between revisions of "Laplace Transform"
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|+ List of Common Laplace Transforms | |+ List of Common Laplace Transforms | ||
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− | ! <math> f(t) </math> !! <math> F(s) = \mathcal{L} | + | ! <math> f(t) </math> !! <math> F(s) = \mathcal{L}\{f\}(s) </math> |
|- | |- | ||
| <math> 1 </math> || <math> \frac{1}{s} </math> <math> s > 0 </math> | | <math> 1 </math> || <math> \frac{1}{s} </math> <math> s > 0 </math> |
Revision as of 16:42, 20 September 2021
In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that converts a function of a real variable t (often time) to a function of a complex variable s (complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms linear differential equations into algebraic equations and convolution into multiplication.
For suitable functions f, the Laplace transform is the integral
Resources
- Laplace Transforms, Paul's Online Notes