Laplace Transform Calculator
Laplace transforms, named after the renowned French mathematician Pierre-Simon Laplace (1749-1827), are a powerful mathematical tool widely used in various fields of science and engineering. These integral transforms provide a method to convert complex differential equations into simpler algebraic equations, making them easier to solve and analyze.
The concept of Laplace transforms emerged from Laplace's work on probability theory and celestial mechanics in the late 18th and early 19th centuries. However, it wasn't until the 20th century that their full potential in solving differential equations and analyzing systems was realized. The advent of operational calculus, developed by Oliver Heaviside, brought Laplace transforms into the spotlight, particularly in the fields of physics and engineering.
Formally, the Laplace transform of a function f(t), defined for all real numbers t ≥ 0, is the function F(s) defined by:
