Mikusiński operational calculus

Summary

The Mikusiński operational calculus, created by Jan Mikusiński, is an algebraic foundation of operational calculus that does not use integral transforms. Functions on $[0, \infty)$ are elements of the Mikusiński field of operators, in which differentiation is multiplication by an element $s$ up to initial values. Linear differential equations with constant coefficients become linear equations in this field, and the solution is read off by algebra. Unlike the Laplace transform approach, it needs no growth condition on the functions.