Problem 2 from homework: We have a cable of length \(L\) and suspend it from two given points. Find the graph \(y=f(x)\).
We obtain a curve \( \Bigl(x(s),f(x(s))\Bigr) \) with arc length \(s\in [0,L]\). The potential energy due to gravity is given by \(E=\int_{s=0}^L f(x(s))ds \). Among all possible curves of length \(L\) we will obtain the curve with minimal potential energy. This curve is called catenary. It is the graph of the function \( f(x) = a \cdot \cosh(x/a) \) (with the origin of the coordinate system suitably chosen).
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Additional Course Material (Required Reading)

Matlab programming

We will use Matlab to see how various algorithms work. We will use Matlab to see how various algorithms work.

How to hand in Matlab results for homeworks:

How to use the publish command in Matlab:
Use lines starting with %% for the main title and for each section title.
Lines starting with % right after a section title will be printed at the beginning of each section. Use this for your observations about the problem.