Advanced Engineering Mathematics, 7th Edition

4.1 Definition of the Laplace Transform

INTRODUCTION

In elementary calculus you learned that differentiation and integration are transforms—this means, roughly speaking, that these operations transform a function into another function. For example, the function f(x) = x² is transformed, in turn, into a linear function, a family of cubic polynomial functions, and a constant by the operations of differentiation, indefinite integration, and definite integration:

Moreover, these two transforms possess the linearity property; this means the transform of a linear combination of functions is a linear combination of the transforms. For α and β constants, ...