The Laplace transform is a very powerful mathematical tool applied in various areas of engineering and science. Its applications include analysis of electrical circuits in the area of physics could be to find out the harmonic vibration of a beam which is supported at its two ends, The Laplace transform can be applied to solve the switching transient phenomenon in the series or parallel RL, RC or RLC circuits, The modeling of a generator by applying the swing equation of a synchronous machine, Power systems are comprised of generation, transmission and distribution systems. If () is continuous for ≥ 0, the Laplace transform of is the function defined by
[infinity]
() = ∫ ()⁻ˢᵗ
0
and the domain of is the set consisting of all numbers for which the integral converges. Find the Laplace transform of () = ᵗ .