{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"%display latex"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"# Ableitungen"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 2,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"x = var('x')\n",
"f = x^2 * exp(2*x+3)\n",
"f"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 3,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f.diff(x)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 4,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f.diff(x).collect(exp(2*x+3))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 5,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f.diff(x, x).collect(exp(2*x+3))\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 6,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"f.diff(x).factor()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"df = f.diff(x)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"# Integration"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 8,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"ff = df.integral(x)\n",
"ff"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 9,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"ff.factor()"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"# Matrizen"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 10,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"M = Matrix([[1,2,3], [4,5,6], [7,8,9]])\n",
"M"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 11,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"M.kernel()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 12,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"M * vector([1,-2,1])"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": false
},
"source": [
"# Gewöhnliche Differentialgleichungen"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 13,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"phi = function('\\phi')\n",
"y = phi(x)\n",
"y"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 14,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"dgl = y.diff(x,x) + 4*y == 0\n",
"dgl"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 15,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"lsg = desolve(dgl, y)\n",
"lsg"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 16,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"lsg.variables()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 17,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"K1, K2, dummy = lsg.variables()\n",
"y1 = lsg.subs({K1: 1, K2: 0})\n",
"y2 = lsg.subs({K1: 0, K2: 1})\n",
"y1, y2"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 18,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"pl1 = plot(y1, -5, 5)\n",
"pl2 = plot(y2, -5, 5, color='red')\n",
"pl1 + pl2"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 19,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"dgl = y.diff(x) == sqrt(x*y)\n",
"dgl"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 20,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"lsg = desolve(dgl, y)\n",
"lsg"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 21,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"lsg2 = solve(lsg, y)[0]\n",
"lsg2"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 22,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"glg2 = (lsg2^2).expand().canonicalize_radical()\n",
"glg2"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 23,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"lsg3 = solve(glg2, y)\n",
"lsg3"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
""
]
},
"execution_count": 24,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"g = lsg3[0].rhs()\n",
"g.variables()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"C = g.variables()[0]"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
"pl1 = plot(g.subs({C:0}), 0, 2, thickness=2)\n",
"pl2 = plot(g.subs({C:-1}), 0, 2, color='red', thickness=2)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 27,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"pl1 + pl2"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 28,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"pl2a = plot(g.subs({C:-1}), 0, (3/2)^(2/3), color='red', thickness=2, linestyle=\"--\")\n",
"pl2b = plot(g.subs({C:-1}), (3/2)^(2/3), 2, color='red', thickness=2)\n",
"pl3 = plot(g.subs({C:1}), 0, 1.4, color='green', thickness=2)\n",
"pl1 + pl2a + pl2b + pl3"
]
},
{
"cell_type": "code",
"execution_count": 0,
"metadata": {
"collapsed": false
},
"outputs": [
],
"source": [
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath (stable)",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.14"
}
},
"nbformat": 4,
"nbformat_minor": 0
}