This procedure gives rise to an operator that is linear and returns unique results.
It is thought that Euler and Lagrange both explored rudimentary forms of this procedure. The techniques leading to the development of this procedure were explored in detail by Oliver Heaviside over a century after its namesake first conceived it. This procedure can be performed unilaterally and bilaterally but it can be reversed using a formula named for Bromwich. One way of arriving at its results is computing a generalized product through a convolution integral. This procedure gives rise to an operator that is linear and returns unique results. The transfer function obtained by this procedure can be identified as the impulse response of the system. One prominent application of this technique is solving differential equations with constant coefficients by turning differential equations into algebraic polynomial equations. For ten points, identify this transform named for a French mathematician whose unilateral is formally defined as the integral from zero to infinity of e to the negative s t times f of t with respect to t.
It is thought that Euler and Lagrange both explored rudimentary forms of this procedure.
Laplace Transform