exercise4.tex

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\title{\coursename~Quiz 4: Due by \DueDate{\coursedate}{30}}
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\section*{Exercises}

\begin{enumerate}
\item Programming on paper (2 credits): \\
Write a program that outputs the Fibonacci sequence up to a number $N$. The Fibonacci sequence is given as
\begin{align*}
F(0) &= 0 \text{ and } F(1) = 1  \\
F(n) &= F(n-1) + F(n-2) \; \forall n > 1\text{.}
\end{align*} 

\item Definitions (2 credits): \\
Explain the following terms in your own words:
\begin{itemize}
\item Race condition and data race (1 credit)
\item Deadlock (1 credit)
\end{itemize}


\end{enumerate}

\section*{Programming exercise}

\begin{enumerate}

\item CMake: (2 credits)\\
Use any of your previous exercises and write a CMake file to compile this exercise.
\item Numerical integration (4 credits)\\
The trapezoidal rule can be used to approximate the definite integral 
\begin{align*}
\int\limits_a^b f(x) dx \approx \frac{h}{2} \sum\limits_{k=1}^N (f(x_{k-1}) + f(x_k))
\end{align*}
assuming a uniform grid in the interval $[a,b]$ with the grid size $h=\frac{b-a}{N}$.
\begin{enumerate}
\item Write a C++ program which approximates the integral for $f(x)=x^2$ on $[0,2]$ for any given $N$. (2 credits)
\item Use \lstinline|std::future| and \lstinline|std::async| compute the solution asynchronously. (2 credit)
\end{enumerate}
Validate both of your implementations against the solution 
\begin{align*}
\int\limits_0^2 x^2 = \left\vert \frac{x^3}{3}\right\vert_0^2 = \frac{2^3}{3} - \frac{0^2}{3} = \frac{8}{3}\text{.}
\end{align*}
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\end{enumerate}

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