Commit 7660f115 authored by Carsten Knoll's avatar Carsten Knoll

add two notebooks

parent 4a0d90bc
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"Das ist das Start-Notebook\n",
"\n",
"$$\n",
"\\alpha \\beta \\gamma = \\pi\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%load_ext ipydex.displaytools\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import sympy as sp\n",
"from sympy.interactive import printing\n",
"printing.init_printing()\n",
"from sympy import sin, cos, exp\n",
"import symbtools as st\n",
"from ipywidgets import interact, interactive, fixed, interact_manual"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Aufgabe: Visualisierung von Taylor-Polynomen verschiedener Ordnung\n",
"\n",
"\n",
"\n",
"<div style=\"font-size:150%;\">\n",
"\n",
"Geg:\n",
"\n",
"- $f(x) = \\sin(ax)$\n",
"\n",
"\n",
"Ges:\n",
"\n",
"- grafische Darstellung von $\\hat f_k(x; x_0) := \\sum_{i=0}^k\\frac{1}{k!}\\left.\\frac{d^k}{dx^k} f(x)\\right|_{x=x_0}$\n",
" \n",
"</div>"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f5f74b9a3c8>]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x, x0, a = sp.symbols(\"x, x0, a\")\n",
"\n",
"f1 = sin(a*x)# *f1\n",
"func1 = st.expr_to_func((a, x), f1)\n",
"\n",
"\n",
"xx_values = np.linspace(-10, 10, 300)\n",
"\n",
"a1 = 2\n",
"plt.plot(xx_values, func1(a1, xx_values))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# Vorabbrechnung der Taylor-Approximationen\n",
"\n",
"taylor_expressions = []\n",
"taylor_funcs = []\n",
"\n",
"Nmax = 12\n",
"\n",
"for i in range(Nmax + 1):\n",
" # taylor_expr = sp.series(f2, x, x0, n=i)\n",
" taylor_expr = st.multi_taylor(f1, (x,), (x0, ), order=i)\n",
" taylor_expressions.append(taylor_expr)\n",
" taylor_funcs.append(st.expr_to_func((a, x, x0), taylor_expr.removeO()))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\left( a, \\ x\\right)$"
],
"text/plain": [
"(a, x)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a, x"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "ad8018a2f7bd4493a252978dbeef150c",
"version_major": 2,
"version_minor": 0
},
"text/html": [
"<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
"<p>\n",
" If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
" that the widgets JavaScript is still loading. If this message persists, it\n",
" likely means that the widgets JavaScript library is either not installed or\n",
" not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
" Widgets Documentation</a> for setup instructions.\n",
"</p>\n",
"<p>\n",
" If you're reading this message in another frontend (for example, a static\n",
" rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
" it may mean that your frontend doesn't currently support widgets.\n",
"</p>\n"
],
"text/plain": [
"interactive(children=(IntSlider(value=6, description='n', max=12), FloatSlider(value=0.0, description='x01', max=5.0, min=-5.0, step=0.2), FloatSlider(value=0.5, description='a1', max=1.0, step=0.01), Output()), _dom_classes=('widget-interact',))"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"@interact(n=(0, Nmax, 1), x01=(-5, 5, 0.2), a1=(0.0, 1, 0.01))\n",
"def plot_func(n, x01, a1):\n",
" plt.figure(figsize=(12, 6))\n",
" plt.plot(xx_values, func1(a1, xx_values), \"b-\", lw=3)\n",
" plt.plot(xx_values, taylor_funcs[n](a1, xx_values, x01), \"r\")\n",
" plt.plot([x01], func1(a1, x01), \"ro\")\n",
" plt.axis([-10, 10, -1.3, 1.3])\n",
" # approx = taylor_expressions[n].subs(x0, x01) ##:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"<br><br><br><br><br><br><br><br><br><br><br><br><br>\n",
"\n",
"<br><br><br><br><br><br><br><br><br><br><br><br><br>\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"F := $\\displaystyle \\frac{3 x^{2}}{2}$"
],
"text/plain": [
"F := 2\n",
"3⋅x \n",
"────\n",
" 2 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"---\n"
]
},
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\frac{3}{2}$"
],
"text/plain": [
"3/2"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"F = sp.integrate(3*x, x ) ##:\n",
"\n",
"F.subs(x, 1) - F.subs(x, 0)\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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