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Merge pull request #22 from FireDynamics/release-v0.6.1
Release v0.6.1
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book/content/modelling/02_fluids/02_cfd.ipynb

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"The [big O notation](https://en.wikipedia.org/wiki/Big_O_notation) $\\mf \\mathcal{O}$ indicates the asymptotical behaviour of a function. In the approximation of derivatives, shown in this section, it indicates the functional reduction of the approximation error for $\\mf h \\rightarrow 0$.\n",
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"```\n",
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"\n",
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"In practice, the expansion is aborted at a given order $\\mf \\mathcal{O}(h^n)$, where $\\mf n$ indicates the numer of Taylor terms considered, i.e. \n",
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"In practice, the expansion is aborted at a given order $\\mf \\mathcal{O}(h^n)$, where $\\mf n$ indicates the number of Taylor terms considered, i.e. \n",
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"\n",
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"$$\n",
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"\\mf f(x_0 + h) =\\sum_{i=0}^{n-1}\\left(\\frac{1}{i!}\\left.\\frac{d^if}{dx^i}\\right|_{x_0}\\cdot h^i\\right) + \\mathcal{O}(h^n)\\quad .\n",
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"id": "00c757e5",
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"metadata": {},
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"source": [
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"The following figures illustrate the accoring Taylor approximations for up to $\\mf n=3$.\n",
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"The following figures illustrate the according Taylor approximations for up to $\\mf n=3$.\n",
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"\n",
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"```{tabbed} f(x)\n",
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"<img src=\"./figs/taylor_fnk.svg\" width=\"90%\">\n",
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"\\end{align}\n",
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"$$\n",
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"\n",
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"Subracting the first equation from the second\n",
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"Subtracting the first equation from the second\n",
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"\n",
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"$$\n",
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"\\mf f(x_0+h) - f(x_0-h) = 2f'(x_0)\\cdot h + \\mathcal{O}(h^3)\n",

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