Advanced Engineering Mathematics, 7th Edition

4.4 Additional Operational Properties

INTRODUCTION

In this section we develop several more operational properties of the Laplace transform. Specifically, we shall see how to find the transform of a function f(t) that is multiplied by a monomial tⁿ, the transform of a special type of integral, and the transform of a periodic function. The last two transform properties allow us to solve some equations that we have not encountered up to this point: Volterra integral equations, integrodifferential equations, and ordinary differential equations in which the input function is a periodic piecewise-defined function.

4.4.1 Derivatives of Transforms

Multiplying a Function by tⁿ

The Laplace transform of the product of a function f(t) with t can ...