![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\" "\\"Open"){kind=icon}
![\"Download\"](\"https://img.shields.io/badge/Github-Download-blue.svg\" "\\"Download"){kind=icon}
"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[A.1 Python Library for CBE 30338](https://jckantor.github.io/CBE30338/A.01-Python-Library-for-CBE30338.html#A.1-Python-Library-for-CBE-30338)",
"section": "A.1 Python Library for CBE 30338"
}
},
"source": [
"# A.1 Python Library for CBE 30338"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[A.1.1 Some Python basics](https://jckantor.github.io/CBE30338/A.01-Python-Library-for-CBE30338.html#A.1.1-Some-Python-basics)",
"section": "A.1.1 Some Python basics"
}
},
"source": [
"## A.1.1 Some Python basics"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[A.1.1.1 Python functions](https://jckantor.github.io/CBE30338/A.01-Python-Library-for-CBE30338.html#A.1.1.1-Python-functions)",
"section": "A.1.1.1 Python functions"
}
},
"source": [
"### A.1.1.1 Python functions\n",
"\n",
"Here are essential things you need to know about Python functions:\n",
"\n",
"* Functions can be treated like Python objects\n",
"* Functions can be defined using either the `def` or `lambda` statements.\n",
"* `def` defines multiline functions that terminate and return values specified by the `return` statement.\n",
"* `lambda` defines single line functions that return a value.\n",
"\n",
"The following cells demonstrate these points in the process of computing a numerical solution to the system of differential equations describing the motion of a mass $m$ subject to a time-varying force $f(t)$\n",
"\n",
"\\begin{align}\n",
"\\frac{dx}{dt} & = v \\\\\n",
"\\frac{dv}{dt} & = \\frac{1}{m} f(t) \\\\\n",
"\\end{align}\n",
"\n",
"for various choices of $f(t)$. The cells show several different ways of coding $f(t)$, and the vector valued right hand sides of this system of differential equations, as Python functions. "
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 4,
"link": "[A.1.1.1.1 Functions are Python objects](https://jckantor.github.io/CBE30338/A.01-Python-Library-for-CBE30338.html#A.1.1.1.1-Functions-are-Python-objects)",
"section": "A.1.1.1.1 Functions are Python objects"
}
},
"source": [
"#### A.1.1.1.1 Functions are Python objects\n",
"\n",
"The first aspect of this simulation is to establish a specific function to describe the time-varying force $f(t)$. As an example, the following cell creates a plot of $\\cos(t)$ using the `numpy` library."
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"nbpages": {
"level": 4,
"link": "[A.1.1.1.1 Functions are Python objects](https://jckantor.github.io/CBE30338/A.01-Python-Library-for-CBE30338.html#A.1.1.1.1-Functions-are-Python-objects)",
"section": "A.1.1.1.1 Functions are Python objects"
}
},
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