QUESTION 2 [25]
The Laplace Transform and the Inverse Laplace Transform
1.1 Find the Laplace Transform of the following,
$k$
(t) = erfc$\frac{k}{2\sqrt{t}}$ (10)
Where the error function, erf t, and the complementary error function, erfc t, are defined by
$\frac{2}{\sqrt{\pi}} \int_0^t e^{-u^2} du$, erfc t = $\frac{2}{\sqrt{\pi}} \int_t^\infty e^{-u^2} du$,
1.2 Use the partial fraction expansion method to express and simplify $f_3(s)$ (15)
$F_3(s) = \frac{s+3}{s^3 + 5s^2 + 12s + 8}$
