LAPLACE TRANSFORM

in mathematics, a particular integral transform. The Laplace transform f(p), also denoted by L{F(t)} or Lap F(t), is defined by the integral involving the exponential parameter p in the kernel K = e-pt. The linear Laplace operator L thus transforms each function F(t) of a certain set of functions into some function f(p). The inverse transform F(t) is written L-1{f(p)} or Lap-1f(p). The Laplace transform has many applications, such as in solution of linear differential equations with constant coefficients or the study of boundary value problems. These problems often arise in connection with calculations relating to physical systems. Notable early success in solving this type of problem was achieved by the 19th20th-century British physicist-engineer Oliver Heaviside, who developed a procedure called operational calculus. See also Fourier transform; integral transform.