\begin{definition}[Definition:Inverse Laplace Transform/Definition 2]
Let $\map f s: S \to \R$ be a complex function, where $S \subset \R$.
{{mistake|How can it be a complex function when both its domain and codomain are wholly real?}}
The '''inverse Laplace transform''' of $f$, denoted $\map F t: \R \to S$, is defined as:
:$\map F t = \dfrac 1 {2 \pi i} \PV_{c \mathop - i \, \infty}^{c \mathop + i \, \infty} e^{s t} \map f s \rd s = \frac 1 {2 \pi i} \lim_{T \mathop \to \infty} \int_{c \mathop - i \, T}^{c \mathop + i \, T} e^{s t} \map f s \rd s$
where:
:$\PV$ is the Cauchy principal value of the integral
:$c$ is any real constant such that all the singular points of $\map f s$ lie to the left of the line $\map \Re s = c$ in the complex $s$ plane.
{{explain|Establish the fact that $\map \Re s {{=}} c$ specifies a line, and define what that line is}}
\end{definition}