The Laplace Transformation
The Laplace Transformation : In recent years , in the solution of differential equations much use has been made of what are known as "Operational Methods". Such methods have wide applications in science and engineering and represent a large field for advanced study . This method consists of a procedure of solving differential equations where the boundary or initial conditions are automatically satisfied in the course of the solution . The Laplace transformation is but one of many possible operational methods of solving linear differential equations . Definition : Given a function f(t) of a real variable t>0 , if we multiply it by e⁻ᵖᵗ and with respect to t between the limits 0 and ∞, the result is a function of p, say f̅(p). This function f̅(p) is called the Laplace Transformation of f(t) , also written as L{f(t)}. Thus ∞ L{f(t)} ≡ f̅(p) = ∫ e⁻ᵖᵗf(t) dt , 0