Chapter 7.1, Problem 24P

Program Plan Intro

Program Description: Purpose of problem is to obtain the inverseLaplace transformation of given function $F\left(s\right)=s^{-\frac{3}{2}}$ .

Summary introduction:Program will use the inverse of Laplace transform as given below.

  $t^a=L^{-1}\left\{\frac{\Gamma \left(a+1\right)}{s^{a+1}}\right\}$

Here, the value of $a>-1$ and $s>0$ .

The linearity theorem of the Laplace transform for all $s$ such that the functions $f$ and $g$ both exists is defined as,

  $L\left\{af\left(t\right)+bg\left(t\right)\right\}=aL\left\{f\left(t\right)\right\}+bL\left\{g\left(t\right)\right\}$