Fixed section heading
Removed use of hashes to denote section so PDF is generated correctly.
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@ -1,7 +1,7 @@
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{
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"metadata": {
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"name": "",
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"signature": "sha256:dedbd7f55073b104a3b3626e73108b6a60611b932a173ce508666a264357c866"
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"signature": "sha256:1049b9f0fbcda4862cb5dc5365b05cd5652e351863df7664b681da3fc3591c59"
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},
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"nbformat": 3,
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"nbformat_minor": 0,
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@ -646,12 +646,18 @@
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],
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"prompt_number": 2
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},
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{
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"cell_type": "heading",
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"level": 3,
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"metadata": {},
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"source": [
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"Forming First Order Equations from Higher Order Equations"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Forming First Order Equations from Higher Order Equations\n",
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"\n",
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"In the sections above I spoke of *first order* differential equations; these are equations with only first derivatives. However, physical systems often require second or higher order equations. Any higher order system of equations can be converted to a first order set of equations by defining extra variables for the first order terms and then solving. Let's do an example. \n",
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"\n",
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"Given the system $\\ddot{x} - 6\\dot{x} + 9x = t$ find the first order equations.\n",
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