##  [Laplace Transform](/laplace-transform) 

  ##  [Laplace Transform](https://natural.quantumdictionary.io/laplace-transform-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An integral transform that maps a time-domain function f(t) defined for t ≥ 0 to a complex-frequency function F(s) via F(s) = ∫_0^∞ e^{-s t} f(t) dt, with a region of convergence in the complex s-plane.

 

 

 

 

 





 

 



 ##  [Laplace Transform](https://puremath.quantumdictionary.io/laplace-transform-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An integral transform that maps a time-domain function f(t) (usually for t ≥ 0) to F(s) = ∫_0^∞ e^{-st} f(t) dt, producing a complex-frequency representation parametrized by s and widely used to solve linear ODEs and analyze system behavior.