Chapter 7.1, Problem 39P

(a)

Program Plan Intro

Program Description: Purpose of the problem is to graph the staircase function $f\left(t\right)=n\text{if}n-1\le t<n,n=1,2,3,\dots$ .

(b)

Program Plan Intro

Program Description: Purpose of the problem is to show that staircase function can be described as $f\left(t\right)={\displaystyle \sum _{n=0}^{\infty }u\left(t-n\right)}$ .

(c)

Program Plan Intro

Program Description: Purpose of the problem is to show that Laplace transform of staircase function is $L\left\{f\left(t\right)\right\}=\frac{1}{s\left(1-e^{-s}\right)}$ .