Bisection.ipynb

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     "cell_type": "heading",
     "source": "Exercise for the course [Python for MATLAB users](http://sese.nu/python-for-matlab-users/), by Olivier Verdier",
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     "input": "%pylab\n%matplotlib inline\nfrom __future__ import division",
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     "source": "A  continuous functions $f$ which changes its sign in an interval $[a,b]$, i.e. $f(a)f(b)< 0$, has at least one root in this interval. Such a root can be found by the *bisection method*. \n\nThis method starts from the given interval. Then it investigates the sign changes in the subintervals $[a,\\frac{a+b}{2}]$ \nand $[\\frac{a+b}{2},b]$. If the sign changes in the first subinterval $ b$ is redefined to be \n$b:=\\frac{a+b}{2}$\notherwise $a$ is redefined in the same manner to \n$a:=\\frac{a+b}{2}$,\nand the process is repeated until the $b-a$ is less than a given tolerance.\n"
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     "cell_type": "code",
     "input": "def bisect(f, a, b):\n    return 0\n    # implement this!",
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    {
     "metadata": {},
     "cell_type": "markdown",
     "source": "Implement the function `bisect` above until the following does not complain:"
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     "input": "assert allclose(bisect(sin, 3., 4.), pi)",
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