Laplace transforms
The method of Laplace transforms is a system that relies on algebra (rather than calculus based methods) to solve linear differential equations. While it might seem to be a somewhat cumbersome method at times, it is a very powerful tool that enables us to readily deal with linear differential equations with discontinuous forcing functions.
Definition
Let 𝐹(𝑠) or 𝐿{𝑓(𝑡)}, is an integral transform given by the Laplace integral: 𝐿{𝑓(𝑡)}= 𝐹(𝑠)=∫𝑓(𝑡)𝑒−𝑠𝑡𝑑𝑡