Question

find the laplace transform of the function​

Answer 1

In mathematics , the Laplace transform is an integral transform named after its inventor Pierre-Simon Laplace (/lə

ˈplɑːs/ ). It takes a function of a real variable t (often time) to a function of a

complex variable s (complex frequency).

The Laplace transform is very similar to the Fourier transform . While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable. Laplace transforms are usually restricted to functions of t with t ≥ 0. A consequence of this restriction is that the Laplace transform of a function is a

holomorphic function of the variable s . Unlike the Fourier transform, the Laplace transform of a distribution is generally a

well-behaved function. Techniques of complex variables can also be used to directly study Laplace transforms. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in

probability theory .