Fixed section heading

Removed use of hashes to denote section so PDF is generated
correctly.
This commit is contained in:
Roger Labbe 2014-12-20 14:36:06 -08:00
parent c865b57a74
commit af5f7af5b8

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@ -1,7 +1,7 @@
{
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"signature": "sha256:1049b9f0fbcda4862cb5dc5365b05cd5652e351863df7664b681da3fc3591c59"
},
"nbformat": 3,
"nbformat_minor": 0,
@ -646,12 +646,18 @@
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Forming First Order Equations from Higher Order Equations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Forming First Order Equations from Higher Order Equations\n",
"\n",
"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",
"\n",
"Given the system $\\ddot{x} - 6\\dot{x} + 9x = t$ find the first order equations.\n",