2008-35.md

course	course_year	question_number	tags	title	year
Complex Methods	IB	35	IB 2008 Complex Methods	3.I.5C	2008

Using the contour integration formula for the inversion of Laplace transforms find the inverse Laplace transforms of the following functions: (a) $\frac{s}{s^{2}+a^{2}} \quad(a$ real and non-zero $)$, (b) $\frac{1}{\sqrt{s}}$.

[You may use the fact that $\int_{-\infty}^{\infty} e^{-b x^{2}} d x=\sqrt{\pi / b}$.]