The problem is from the domain of Signal Processing and requests to

 \paragraph{The Engineering Background of the Problem} comes out of the domain 

 determine the inverse ${\cal z}$-transform for a given term.

 Signal Processing, which takes a major part n the authors field of education. 

 Fig.\ref{fig-interactive}

 The given Problem requests to determine the inverse $z$-transform for a 

 also shows the beginning of the interactive construction of a solution

 given term.

 for the problem. This construction is done in the right window named

 \par

 ``Worksheet''.

 ``The $z$-Transform for discrete-time signals is the counterpart of the 

 Laplace transform for continuous-time signals, and they each have a similar 

 relationship to the corresponding Fourier transform. One motivation for 

 introducing this generalization is that the Fourier transform does not 

 converge for all sequences, and it is useful to have a generalization of the 

 Fourier transform that encompasses a broader class of signals. A second 

 advantage is that in analytic problems, the $z$-transform notation is often 

 more convenient than the Fourier transform notation.''

 ~\cite[p. 128]{oppenheim2010discrete}

 \par

 The $z$-transform can be defined as:

 \begin{equation}

 X(z)=\sum_{n=-\infty }^{\infty }x[n]z^{-n}

 \end{equation}

 Upper equation transforms a discrete time sequence $x[n]$ into the function 

 $X(z)$ where $z$ is a continuous complex variable. The inverse function (as it 

 is used in the given problem) is defined as:

 \begin{equation}

 x[n]=\frac{1}{2\pi j} \oint_{C} X(z)\cdot z^{n-1} dz

 \end{equation}

 The letter $C$ represents a contour within the range of converge of the $z$-

 transform. The unit circle can be a special case of this contour. Remember 

 that $j$ is the complex number in the field of engineering.

 As this transformation requires high effort to be solved, tables of 

 common transform pairs are used in education as well as in (TODO: real); such 

 tables can be found at~\cite{wiki:1} or~\cite[Table~3.1]{oppenheim2010discrete} as well.

 A completely solved and more detailed example can be found at

 ~\cite[p. 149f]{oppenheim2010discrete}. The upcoming implementation tries to 

 fit this example in the way it is toughed at the authors university.

 \paragraph{The educational aspect} can be explained by having a look at 

 Fig.\ref{fig-interactive} which shows the beginning of the interactive 

 construction of a solution for the problem. This construction is done in the 

 right window named ``Worksheet''.