Chapter 4, Problem 4.15E

Interpretation Introduction

Interpretation:

The transfer function relating to the deviation of variables needs to be derived.

Concept introduction:

A Taylor series in mathematics is a description of a function as an infinite number of terms determined at a single point from the values of the function’s derivatives.

The Laplace transform of a time-domain function, $\text{f}\left(\text{t}\right)$ is represented by $\text{L}\left[\text{f}\left(\text{t}\right)\right]$ is defined as: $\text{L}\left[\text{f}\left(\text{t}\right)\right]\text{=f}\left(\text{s}\right)\text{=}{\int }_0^{\infty }\text{f}\left(\text{t}\right){\text{e}}^{\text{-st}}\text{dt}$.

An integral transform equation is named as Laplace transforms equation after the inventor Pierre-Simon Laplace. This transform equation has many applications in science and engineering field. This transformation is used to transfer a real variable $\left(t\right)$ into function of complex variable $\left(s\right)$.