Chapter 7.3, Problem 1P

Program Plan Intro

Program Description: Purpose of problem is to obtain the Laplace transformation of the functions $f\left(t\right)=t^4{e}^{\pi t}$ by using translation theorem.

Summary introduction: The translation theorem is defined as if $F\left(s\right)=L\left\{f\left(t\right)\right\}$ exists for $s>c$ , then $L\left\{e^{at}f\left(t\right)\right\}$ exists for $s>a+c$ and $L\left\{f\left(t\right)\right\}=F\left(s\right)\Rightarrow L\left\{e^{at}f\left(t\right)\right\}=F\left(s-a\right)$ .