├── tutorial11
    └── leaves.jpg
├── tutorial5.ipynb
├── tutorial2.ipynb
├── all.ipynb
├── tutorial4.ipynb
├── tutorial9.ipynb
├── newton_raphson_approximation.ipynb
└── tutorial8.ipynb


/tutorial11/leaves.jpg:
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https://raw.githubusercontent.com/ruwanego/cm2607/HEAD/tutorial11/leaves.jpg


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/tutorial5.ipynb:
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  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 103,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "# Assumptions"
 12 |    ]
 13 |   },
 14 |   {
 15 |    "cell_type": "code",
 16 |    "execution_count": 104,
 17 |    "outputs": [],
 18 |    "source": [
 19 |     "import sympy as sym"
 20 |    ],
 21 |    "metadata": {
 22 |     "collapsed": false
 23 |    }
 24 |   },
 25 |   {
 26 |    "cell_type": "code",
 27 |    "execution_count": 105,
 28 |    "outputs": [
 29 |     {
 30 |      "data": {
 31 |       "text/plain": "{'integer': True,\n 'hermitian': True,\n 'complex': True,\n 'real': True,\n 'noninteger': False,\n 'rational': True,\n 'infinite': False,\n 'irrational': False,\n 'finite': True,\n 'algebraic': True,\n 'imaginary': False,\n 'extended_real': True,\n 'commutative': True,\n 'transcendental': False,\n 'positive': True,\n 'negative': False,\n 'extended_nonpositive': False,\n 'extended_negative': False,\n 'nonzero': True,\n 'nonpositive': False,\n 'extended_nonnegative': True,\n 'nonnegative': True,\n 'zero': False,\n 'extended_positive': True,\n 'extended_nonzero': True}"
 32 |      },
 33 |      "execution_count": 105,
 34 |      "metadata": {},
 35 |      "output_type": "execute_result"
 36 |     }
 37 |    ],
 38 |    "source": [
 39 |     "x = sym.symbols(\"x\")\n",
 40 |     "# n = sym.Symbol('n')\n",
 41 |     "n = sym.Symbol('n', integer=True, positive=True)\n",
 42 |     "n.assumptions0"
 43 |    ],
 44 |    "metadata": {
 45 |     "collapsed": false
 46 |    }
 47 |   },
 48 |   {
 49 |    "cell_type": "code",
 50 |    "execution_count": 106,
 51 |    "outputs": [
 52 |     {
 53 |      "data": {
 54 |       "text/plain": "sin(n*x)",
 55 |       "text/latex": "$\\displaystyle \\sin{\\left(n x \\right)}$"
 56 |      },
 57 |      "execution_count": 106,
 58 |      "metadata": {},
 59 |      "output_type": "execute_result"
 60 |     }
 61 |    ],
 62 |    "source": [
 63 |     "eq = sym.sin(n * x)\n",
 64 |     "eq"
 65 |    ],
 66 |    "metadata": {
 67 |     "collapsed": false
 68 |    }
 69 |   },
 70 |   {
 71 |    "cell_type": "code",
 72 |    "execution_count": 107,
 73 |    "outputs": [
 74 |     {
 75 |      "data": {
 76 |       "text/plain": "0",
 77 |       "text/latex": "$\\displaystyle 0$"
 78 |      },
 79 |      "execution_count": 107,
 80 |      "metadata": {},
 81 |      "output_type": "execute_result"
 82 |     }
 83 |    ],
 84 |    "source": [
 85 |     "eq1 = eq.integrate((x, 0, 2 * sym.pi))\n",
 86 |     "eq1"
 87 |    ],
 88 |    "metadata": {
 89 |     "collapsed": false
 90 |    }
 91 |   },
 92 |   {
 93 |    "cell_type": "markdown",
 94 |    "source": [
 95 |     "# Functions"
 96 |    ],
 97 |    "metadata": {
 98 |     "collapsed": false
 99 |    }
100 |   },
101 |   {
102 |    "cell_type": "code",
103 |    "execution_count": 108,
104 |    "outputs": [
105 |     {
106 |      "data": {
107 |       "text/plain": "f"
108 |      },
109 |      "execution_count": 108,
110 |      "metadata": {},
111 |      "output_type": "execute_result"
112 |     }
113 |    ],
114 |    "source": [
115 |     "f = sym.Function('f')\n",
116 |     "f\n",
117 |     "# g = sym.Symbol('g', cls='Function')"
118 |    ],
119 |    "metadata": {
120 |     "collapsed": false
121 |    }
122 |   },
123 |   {
124 |    "cell_type": "code",
125 |    "execution_count": 109,
126 |    "outputs": [
127 |     {
128 |      "data": {
129 |       "text/plain": "Derivative(f(x), x)",
130 |       "text/latex": "$\\displaystyle \\frac{d}{d x} f{\\left(x \\right)}$"
131 |      },
132 |      "execution_count": 109,
133 |      "metadata": {},
134 |      "output_type": "execute_result"
135 |     }
136 |    ],
137 |    "source": [
138 |     "f_ = sym.diff(f(x), x)\n",
139 |     "f_"
140 |    ],
141 |    "metadata": {
142 |     "collapsed": false
143 |    }
144 |   },
145 |   {
146 |    "cell_type": "markdown",
147 |    "source": [
148 |     "# f(x) = sin(x) => f`(x) - sin(x) = 0"
149 |    ],
150 |    "metadata": {
151 |     "collapsed": false
152 |    }
153 |   },
154 |   {
155 |    "cell_type": "code",
156 |    "execution_count": 110,
157 |    "outputs": [
158 |     {
159 |      "data": {
160 |       "text/plain": "-sin(x) + Derivative(f(x), x)",
161 |       "text/latex": "$\\displaystyle - \\sin{\\left(x \\right)} + \\frac{d}{d x} f{\\left(x \\right)}$"
162 |      },
163 |      "execution_count": 110,
164 |      "metadata": {},
165 |      "output_type": "execute_result"
166 |     }
167 |    ],
168 |    "source": [
169 |     "f2 = f_ - sym.sin(x)\n",
170 |     "f2"
171 |    ],
172 |    "metadata": {
173 |     "collapsed": false
174 |    }
175 |   },
176 |   {
177 |    "cell_type": "code",
178 |    "execution_count": 111,
179 |    "outputs": [
180 |     {
181 |      "data": {
182 |       "text/plain": "Eq(f(x), C1 - cos(x))",
183 |       "text/latex": "$\\displaystyle f{\\left(x \\right)} = C_{1} - \\cos{\\left(x \\right)}$"
184 |      },
185 |      "execution_count": 111,
186 |      "metadata": {},
187 |      "output_type": "execute_result"
188 |     }
189 |    ],
190 |    "source": [
191 |     "f3 = sym.dsolve(f2, f(x))\n",
192 |     "f3"
193 |    ],
194 |    "metadata": {
195 |     "collapsed": false
196 |    }
197 |   },
198 |   {
199 |    "cell_type": "code",
200 |    "execution_count": 112,
201 |    "outputs": [
202 |     {
203 |      "data": {
204 |       "text/plain": "f(x) - 2*Derivative(f(x), x) + Derivative(f(x), (x, 2))",
205 |       "text/latex": "$\\displaystyle f{\\left(x \\right)} - 2 \\frac{d}{d x} f{\\left(x \\right)} + \\frac{d^{2}}{d x^{2}} f{\\left(x \\right)}$"
206 |      },
207 |      "execution_count": 112,
208 |      "metadata": {},
209 |      "output_type": "execute_result"
210 |     }
211 |    ],
212 |    "source": [
213 |     "f4 = sym.Derivative(f(x), x, 2) - 2 * sym.Derivative(f(x), x) + f(x)\n",
214 |     "f4"
215 |    ],
216 |    "metadata": {
217 |     "collapsed": false
218 |    }
219 |   },
220 |   {
221 |    "cell_type": "markdown",
222 |    "source": [
223 |     "# Solve ordinary differential equation eq for function f(x)"
224 |    ],
225 |    "metadata": {
226 |     "collapsed": false
227 |    }
228 |   },
229 |   {
230 |    "cell_type": "code",
231 |    "execution_count": 113,
232 |    "outputs": [
233 |     {
234 |      "data": {
235 |       "text/plain": "Eq(f(x), (C1 + C2*x)*exp(x))",
236 |       "text/latex": "$\\displaystyle f{\\left(x \\right)} = \\left(C_{1} + C_{2} x\\right) e^{x}$"
237 |      },
238 |      "execution_count": 113,
239 |      "metadata": {},
240 |      "output_type": "execute_result"
241 |     }
242 |    ],
243 |    "source": [
244 |     "sym.dsolve(f4, f(x))"
245 |    ],
246 |    "metadata": {
247 |     "collapsed": false
248 |    }
249 |   },
250 |   {
251 |    "cell_type": "code",
252 |    "execution_count": null,
253 |    "outputs": [],
254 |    "source": [],
255 |    "metadata": {
256 |     "collapsed": false
257 |    }
258 |   }
259 |  ],
260 |  "metadata": {
261 |   "kernelspec": {
262 |    "display_name": "Python 3",
263 |    "language": "python",
264 |    "name": "python3"
265 |   },
266 |   "language_info": {
267 |    "codemirror_mode": {
268 |     "name": "ipython",
269 |     "version": 2
270 |    },
271 |    "file_extension": ".py",
272 |    "mimetype": "text/x-python",
273 |    "name": "python",
274 |    "nbconvert_exporter": "python",
275 |    "pygments_lexer": "ipython2",
276 |    "version": "2.7.6"
277 |   }
278 |  },
279 |  "nbformat": 4,
280 |  "nbformat_minor": 0
281 | }
282 | 


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/tutorial2.ipynb:
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  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "# when using the package it is always better to import under an alias.\n",
 12 |     "# there are functions with the same name when using with numpy and can cause\n",
 13 |     "# conflicts and confusion.\n",
 14 |     "import sympy as sym"
 15 |    ]
 16 |   },
 17 |   {
 18 |    "cell_type": "code",
 19 |    "execution_count": 2,
 20 |    "outputs": [],
 21 |    "source": [
 22 |     "# defines x as a symbol.\n",
 23 |     "x = sym.symbols('x')"
 24 |    ],
 25 |    "metadata": {
 26 |     "collapsed": false
 27 |    }
 28 |   },
 29 |   {
 30 |    "cell_type": "code",
 31 |    "execution_count": 3,
 32 |    "outputs": [
 33 |     {
 34 |      "data": {
 35 |       "text/plain": "2*x + 5",
 36 |       "text/latex": "$\\displaystyle 2 x + 5$"
 37 |      },
 38 |      "execution_count": 3,
 39 |      "metadata": {},
 40 |      "output_type": "execute_result"
 41 |     }
 42 |    ],
 43 |    "source": [
 44 |     "# defines an equation in x, the symbol we defined before.\n",
 45 |     "eq = 2 * x + 5\n",
 46 |     "eq"
 47 |    ],
 48 |    "metadata": {
 49 |     "collapsed": false
 50 |    }
 51 |   },
 52 |   {
 53 |    "cell_type": "code",
 54 |    "execution_count": 4,
 55 |    "outputs": [
 56 |     {
 57 |      "data": {
 58 |       "text/plain": "7",
 59 |       "text/latex": "$\\displaystyle 7$"
 60 |      },
 61 |      "execution_count": 4,
 62 |      "metadata": {},
 63 |      "output_type": "execute_result"
 64 |     }
 65 |    ],
 66 |    "source": [
 67 |     "# substitutes x = 1 in equation defined earlier.\n",
 68 |     "eq.subs(x, 1)"
 69 |    ],
 70 |    "metadata": {
 71 |     "collapsed": false
 72 |    }
 73 |   },
 74 |   {
 75 |    "cell_type": "code",
 76 |    "execution_count": 5,
 77 |    "outputs": [
 78 |     {
 79 |      "data": {
 80 |       "text/plain": "9",
 81 |       "text/latex": "$\\displaystyle 9$"
 82 |      },
 83 |      "execution_count": 5,
 84 |      "metadata": {},
 85 |      "output_type": "execute_result"
 86 |     }
 87 |    ],
 88 |    "source": [
 89 |     "# substitutes x = 2 in equation defined earlier.\n",
 90 |     "eq.subs(x, 2)"
 91 |    ],
 92 |    "metadata": {
 93 |     "collapsed": false
 94 |    }
 95 |   },
 96 |   {
 97 |    "cell_type": "code",
 98 |    "execution_count": 6,
 99 |    "outputs": [
100 |     {
101 |      "data": {
102 |       "text/plain": "2*x + 3*y + 4*z",
103 |       "text/latex": "$\\displaystyle 2 x + 3 y + 4 z$"
104 |      },
105 |      "execution_count": 6,
106 |      "metadata": {},
107 |      "output_type": "execute_result"
108 |     }
109 |    ],
110 |    "source": [
111 |     "# define multiple symbols\n",
112 |     "x, y, z = sym.symbols('x,y,z')\n",
113 |     "eq1 = 2 * x + 3 * y + 4 * z\n",
114 |     "eq1"
115 |    ],
116 |    "metadata": {
117 |     "collapsed": false
118 |    }
119 |   },
120 |   {
121 |    "cell_type": "code",
122 |    "execution_count": 7,
123 |    "outputs": [
124 |     {
125 |      "data": {
126 |       "text/plain": "2*x + 4*z + 3",
127 |       "text/latex": "$\\displaystyle 2 x + 4 z + 3$"
128 |      },
129 |      "execution_count": 7,
130 |      "metadata": {},
131 |      "output_type": "execute_result"
132 |     }
133 |    ],
134 |    "source": [
135 |     "eq2 = eq1.subs(y, 1)\n",
136 |     "eq2"
137 |    ],
138 |    "metadata": {
139 |     "collapsed": false
140 |    }
141 |   },
142 |   {
143 |    "cell_type": "code",
144 |    "execution_count": 8,
145 |    "outputs": [
146 |     {
147 |      "data": {
148 |       "text/plain": "9",
149 |       "text/latex": "$\\displaystyle 9$"
150 |      },
151 |      "execution_count": 8,
152 |      "metadata": {},
153 |      "output_type": "execute_result"
154 |     }
155 |    ],
156 |    "source": [
157 |     "# It is also possible to substitute multiple variables at once:\n",
158 |     "# substitute x = y = z = 1\n",
159 |     "# pay attention to the format for multiple substitution\n",
160 |     "eq1.subs([(x, 1), (y, 1), (z, 1)])"
161 |    ],
162 |    "metadata": {
163 |     "collapsed": false
164 |    }
165 |   },
166 |   {
167 |    "cell_type": "code",
168 |    "execution_count": 36,
169 |    "outputs": [
170 |     {
171 |      "data": {
172 |       "text/plain": "4*z + 5",
173 |       "text/latex": "$\\displaystyle 4 z + 5$"
174 |      },
175 |      "execution_count": 36,
176 |      "metadata": {},
177 |      "output_type": "execute_result"
178 |     }
179 |    ],
180 |    "source": [
181 |     "# You do not have to substitute all the variables\n",
182 |     "eqZ = eq1.subs([(x, 1), (y, 1)])\n",
183 |     "eqZ"
184 |    ],
185 |    "metadata": {
186 |     "collapsed": false
187 |    }
188 |   },
189 |   {
190 |    "cell_type": "code",
191 |    "execution_count": 35,
192 |    "outputs": [
193 |     {
194 |      "data": {
195 |       "text/plain": "[-5/4]"
196 |      },
197 |      "execution_count": 35,
198 |      "metadata": {},
199 |      "output_type": "execute_result"
200 |     }
201 |    ],
202 |    "source": [
203 |     "# You can solve for the remaining variable\n",
204 |     "sym.solve(eqZ, z)"
205 |    ],
206 |    "metadata": {
207 |     "collapsed": false
208 |    }
209 |   },
210 |   {
211 |    "cell_type": "code",
212 |    "execution_count": 17,
213 |    "outputs": [
214 |     {
215 |      "data": {
216 |       "text/plain": "[-5/2]"
217 |      },
218 |      "execution_count": 17,
219 |      "metadata": {},
220 |      "output_type": "execute_result"
221 |     }
222 |    ],
223 |    "source": [
224 |     "# solve the first equation (2x + 5 = 0) for x\n",
225 |     "sym.solve(eq, x)"
226 |    ],
227 |    "metadata": {
228 |     "collapsed": false
229 |    }
230 |   },
231 |   {
232 |    "cell_type": "code",
233 |    "execution_count": 16,
234 |    "outputs": [
235 |     {
236 |      "data": {
237 |       "text/plain": "[-3/2]"
238 |      },
239 |      "execution_count": 16,
240 |      "metadata": {},
241 |      "output_type": "execute_result"
242 |     }
243 |    ],
244 |    "source": [
245 |     "# solve (2x + 5 = 2) for x\n",
246 |     "# 2x + 5 - 2 = 0\n",
247 |     "sym.solve(eq - 2, x)\n"
248 |    ],
249 |    "metadata": {
250 |     "collapsed": false
251 |    }
252 |   },
253 |   {
254 |    "cell_type": "code",
255 |    "execution_count": 19,
256 |    "outputs": [
257 |     {
258 |      "data": {
259 |       "text/plain": "{x: 2, y: 3}"
260 |      },
261 |      "execution_count": 19,
262 |      "metadata": {},
263 |      "output_type": "execute_result"
264 |     }
265 |    ],
266 |    "source": [
267 |     "# define simultaneous equations\n",
268 |     "# 2x + 3y = 13 => 2x + 3y - 13 = 0\n",
269 |     "# 3x - 5y = -9 => 3x - 5y + 9 = 0\n",
270 |     "eq_a = 2 * x + 3 * y - 13\n",
271 |     "eq_b = 3 * x - 5 * y + 9\n",
272 |     "# solve\n",
273 |     "sym.solve([eq_a, eq_b], (x, y))"
274 |    ],
275 |    "metadata": {
276 |     "collapsed": false
277 |    }
278 |   },
279 |   {
280 |    "cell_type": "code",
281 |    "execution_count": 20,
282 |    "outputs": [
283 |     {
284 |      "data": {
285 |       "text/plain": "3*x**2 - 5*x - 2",
286 |       "text/latex": "$\\displaystyle 3 x^{2} - 5 x - 2$"
287 |      },
288 |      "execution_count": 20,
289 |      "metadata": {},
290 |      "output_type": "execute_result"
291 |     }
292 |    ],
293 |    "source": [
294 |     "# Differentiation:\n",
295 |     "eq_c = 3 * x ** 2 - 5 * x - 2\n",
296 |     "eq_c"
297 |    ],
298 |    "metadata": {
299 |     "collapsed": false
300 |    }
301 |   },
302 |   {
303 |    "cell_type": "code",
304 |    "execution_count": 23,
305 |    "outputs": [
306 |     {
307 |      "data": {
308 |       "text/plain": "6*x - 5",
309 |       "text/latex": "$\\displaystyle 6 x - 5$"
310 |      },
311 |      "execution_count": 23,
312 |      "metadata": {},
313 |      "output_type": "execute_result"
314 |     }
315 |    ],
316 |    "source": [
317 |     "# differentiate with respect to x\n",
318 |     "eq_diff = sym.diff(eq_c, x)\n",
319 |     "eq_diff"
320 |    ],
321 |    "metadata": {
322 |     "collapsed": false
323 |    }
324 |   },
325 |   {
326 |    "cell_type": "code",
327 |    "execution_count": 25,
328 |    "outputs": [
329 |     {
330 |      "data": {
331 |       "text/plain": "0",
332 |       "text/latex": "$\\displaystyle 0$"
333 |      },
334 |      "execution_count": 25,
335 |      "metadata": {},
336 |      "output_type": "execute_result"
337 |     }
338 |    ],
339 |    "source": [
340 |     "# This differentiates the equation with respect to x.\n",
341 |     "# It is also possible to apply higher order differentiation. It can be done in one of two ways:\n",
342 |     "# 2nd order differentiation\n",
343 |     "eq_diff_2ndOrder = sym.diff(eq, x, x)\n",
344 |     "eq_diff_2ndOrder"
345 |    ],
346 |    "metadata": {
347 |     "collapsed": false
348 |    }
349 |   },
350 |   {
351 |    "cell_type": "code",
352 |    "execution_count": 28,
353 |    "outputs": [
354 |     {
355 |      "data": {
356 |       "text/plain": "0",
357 |       "text/latex": "$\\displaystyle 0$"
358 |      },
359 |      "execution_count": 28,
360 |      "metadata": {},
361 |      "output_type": "execute_result"
362 |     }
363 |    ],
364 |    "source": [
365 |     "# does the same thing, but more convenient for higher orders\n",
366 |     "eq_diff_2ndOrder = sym.diff(eq, x, 2)\n",
367 |     "eq_diff_2ndOrder"
368 |    ],
369 |    "metadata": {
370 |     "collapsed": false
371 |    }
372 |   }
373 |  ],
374 |  "metadata": {
375 |   "kernelspec": {
376 |    "display_name": "Python 3",
377 |    "language": "python",
378 |    "name": "python3"
379 |   },
380 |   "language_info": {
381 |    "codemirror_mode": {
382 |     "name": "ipython",
383 |     "version": 2
384 |    },
385 |    "file_extension": ".py",
386 |    "mimetype": "text/x-python",
387 |    "name": "python",
388 |    "nbconvert_exporter": "python",
389 |    "pygments_lexer": "ipython2",
390 |    "version": "2.7.6"
391 |   }
392 |  },
393 |  "nbformat": 4,
394 |  "nbformat_minor": 0
395 | }
396 | 


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/all.ipynb:
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  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [
 10 |     {
 11 |      "data": {
 12 |       "text/plain": "<Figure size 640x480 with 1 Axes>",
 13 |       "image/png": 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\n"
 14 |      },
 15 |      "metadata": {},
 16 |      "output_type": "display_data"
 17 |     }
 18 |    ],
 19 |    "source": [
 20 |     "import matplotlib.pyplot as plt\n",
 21 |     "import numpy as np\n",
 22 |     "import sympy as sym\n",
 23 |     "\n",
 24 |     "# Define symbols\n",
 25 |     "x = sym.symbols('x')\n",
 26 |     "n = sym.symbols('n', integer=True, positive=True)\n",
 27 |     "\n",
 28 |     "# Initialize array to store Fourier series coefficients\n",
 29 |     "ms = np.empty(100, dtype=object)\n",
 30 |     "\n",
 31 |     "# Generate x values\n",
 32 |     "xrange = np.linspace(3 * np.pi, -3 * np.pi, 1000)\n",
 33 |     "\n",
 34 |     "# Initialize array to store function values for each iteration\n",
 35 |     "y = np.zeros([101, 1000])\n",
 36 |     "\n",
 37 |     "# Define the function equation\n",
 38 |     "eq = x ** 2\n",
 39 |     "\n",
 40 |     "# Calculate a0 coefficient\n",
 41 |     "a0 = (1 / (2 * sym.pi)) * eq.integrate((x, 0, sym.pi))\n",
 42 |     "\n",
 43 |     "# Store a0 in the array\n",
 44 |     "ms[0] = a0\n",
 45 |     "\n",
 46 |     "# Convert a0 to a numpy function and evaluate on xrange\n",
 47 |     "f = sym.lambdify(x, ms[0], 'numpy')\n",
 48 |     "y[0, :] = f(xrange)\n",
 49 |     "\n",
 50 |     "# Calculate Fourier series coefficients\n",
 51 |     "for m in range(1, 100):\n",
 52 |     "    an = (1 / sym.pi) * sym.integrate((eq * sym.cos(n * x)), (x, 0, sym.pi)).subs(n, m)\n",
 53 |     "    bn = (1 / sym.pi) * sym.integrate((eq * sym.sin(n * x)), (x, 0, sym.pi)).subs(n, m)\n",
 54 |     "    ms[m] = ms[m - 1] + an * sym.cos(m * x) + bn * sym.sin(m * x)\n",
 55 |     "\n",
 56 |     "    # Convert ms[m] to a numpy function and evaluate on xrange\n",
 57 |     "    f = sym.lambdify(x, ms[m], 'numpy')\n",
 58 |     "    y[m, :] = f(xrange)\n",
 59 |     "\n",
 60 |     "# Piecewise plotting\n",
 61 |     "for m in range(1000):\n",
 62 |     "    if 0 < xrange[m] < np.pi:\n",
 63 |     "        y[100, m] = xrange[m] ** 2\n",
 64 |     "    elif 2 * np.pi < xrange[m] <= 3 * np.pi:\n",
 65 |     "        y[100, m] = (xrange[m] - 2 * np.pi) ** 2\n",
 66 |     "    elif -2 * np.pi < xrange[m] <= np.pi:\n",
 67 |     "        y[100, m] = (xrange[m] + 2 * np.pi) ** 2\n",
 68 |     "\n",
 69 |     "# Plotting\n",
 70 |     "plt.plot(xrange, y[4, :])\n",
 71 |     "plt.plot(xrange, y[9, :])\n",
 72 |     "plt.plot(xrange, y[99, :])\n",
 73 |     "plt.plot(xrange, y[100, :])\n",
 74 |     "\n",
 75 |     "# Add legend\n",
 76 |     "plt.legend([\"5\", \"10\", \"100\", \"func\"])\n",
 77 |     "plt.show()\n"
 78 |    ]
 79 |   },
 80 |   {
 81 |    "cell_type": "code",
 82 |    "execution_count": null,
 83 |    "outputs": [],
 84 |    "source": [],
 85 |    "metadata": {
 86 |     "collapsed": false
 87 |    }
 88 |   }
 89 |  ],
 90 |  "metadata": {
 91 |   "kernelspec": {
 92 |    "display_name": "Python 3",
 93 |    "language": "python",
 94 |    "name": "python3"
 95 |   },
 96 |   "language_info": {
 97 |    "codemirror_mode": {
 98 |     "name": "ipython",
 99 |     "version": 2
100 |    },
101 |    "file_extension": ".py",
102 |    "mimetype": "text/x-python",
103 |    "name": "python",
104 |    "nbconvert_exporter": "python",
105 |    "pygments_lexer": "ipython2",
106 |    "version": "2.7.6"
107 |   }
108 |  },
109 |  "nbformat": 4,
110 |  "nbformat_minor": 0
111 | }
112 | 


--------------------------------------------------------------------------------
/tutorial4.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 89,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "import numpy as np\n",
 12 |     "import sympy as sym\n",
 13 |     "import matplotlib.pyplot as plt\n",
 14 |     "\n",
 15 |     "x = sym.symbols('x')"
 16 |    ]
 17 |   },
 18 |   {
 19 |    "cell_type": "code",
 20 |    "execution_count": 90,
 21 |    "outputs": [
 22 |     {
 23 |      "data": {
 24 |       "text/plain": "2*x**4 + 5/(x + 1)**2 + 3/x**3",
 25 |       "text/latex": "$\\displaystyle 2 x^{4} + \\frac{5}{\\left(x + 1\\right)^{2}} + \\frac{3}{x^{3}}$"
 26 |      },
 27 |      "execution_count": 90,
 28 |      "metadata": {},
 29 |      "output_type": "execute_result"
 30 |     }
 31 |    ],
 32 |    "source": [
 33 |     "eq = 2 * (x ** 4) + 3 / (x ** 3) + 5 / ((x + 1) ** 2)\n",
 34 |     "eq"
 35 |    ],
 36 |    "metadata": {
 37 |     "collapsed": false
 38 |    }
 39 |   },
 40 |   {
 41 |    "cell_type": "code",
 42 |    "execution_count": 91,
 43 |    "outputs": [
 44 |     {
 45 |      "data": {
 46 |       "text/plain": "x**2/2",
 47 |       "text/latex": "$\\displaystyle \\frac{x^{2}}{2}$"
 48 |      },
 49 |      "execution_count": 91,
 50 |      "metadata": {},
 51 |      "output_type": "execute_result"
 52 |     }
 53 |    ],
 54 |    "source": [
 55 |     "sym.integrate(x)"
 56 |    ],
 57 |    "metadata": {
 58 |     "collapsed": false
 59 |    }
 60 |   },
 61 |   {
 62 |    "cell_type": "code",
 63 |    "execution_count": 92,
 64 |    "outputs": [
 65 |     {
 66 |      "data": {
 67 |       "text/plain": "2*x**5/5 + (-10*x**2 - 3*x - 3)/(2*x**3 + 2*x**2)",
 68 |       "text/latex": "$\\displaystyle \\frac{2 x^{5}}{5} + \\frac{- 10 x^{2} - 3 x - 3}{2 x^{3} + 2 x^{2}}$"
 69 |      },
 70 |      "execution_count": 92,
 71 |      "metadata": {},
 72 |      "output_type": "execute_result"
 73 |     }
 74 |    ],
 75 |    "source": [
 76 |     "eq_int = sym.integrate(eq, x)\n",
 77 |     "eq_int"
 78 |    ],
 79 |    "metadata": {
 80 |     "collapsed": false
 81 |    }
 82 |   },
 83 |   {
 84 |    "cell_type": "code",
 85 |    "execution_count": 93,
 86 |    "outputs": [
 87 |     {
 88 |      "data": {
 89 |       "text/plain": "1723/120",
 90 |       "text/latex": "$\\displaystyle \\frac{1723}{120}$"
 91 |      },
 92 |      "execution_count": 93,
 93 |      "metadata": {},
 94 |      "output_type": "execute_result"
 95 |     }
 96 |    ],
 97 |    "source": [
 98 |     "eq_int.subs(x, 2) - eq_int.subs(x, 1)"
 99 |    ],
100 |    "metadata": {
101 |     "collapsed": false
102 |    }
103 |   },
104 |   {
105 |    "cell_type": "code",
106 |    "execution_count": 94,
107 |    "outputs": [
108 |     {
109 |      "data": {
110 |       "text/plain": "1723/120",
111 |       "text/latex": "$\\displaystyle \\frac{1723}{120}$"
112 |      },
113 |      "execution_count": 94,
114 |      "metadata": {},
115 |      "output_type": "execute_result"
116 |     }
117 |    ],
118 |    "source": [
119 |     "eq.integrate((x, 1, 2))"
120 |    ],
121 |    "metadata": {
122 |     "collapsed": false
123 |    }
124 |   },
125 |   {
126 |    "cell_type": "code",
127 |    "execution_count": 95,
128 |    "outputs": [
129 |     {
130 |      "data": {
131 |       "text/plain": "1723/120",
132 |       "text/latex": "$\\displaystyle \\frac{1723}{120}$"
133 |      },
134 |      "execution_count": 95,
135 |      "metadata": {},
136 |      "output_type": "execute_result"
137 |     }
138 |    ],
139 |    "source": [
140 |     "sym.integrate(eq, (x, 1, 2))"
141 |    ],
142 |    "metadata": {
143 |     "collapsed": false
144 |    }
145 |   },
146 |   {
147 |    "cell_type": "code",
148 |    "execution_count": 96,
149 |    "outputs": [
150 |     {
151 |      "data": {
152 |       "text/plain": "exp(x)*sin(2*x)",
153 |       "text/latex": "$\\displaystyle e^{x} \\sin{\\left(2 x \\right)}$"
154 |      },
155 |      "execution_count": 96,
156 |      "metadata": {},
157 |      "output_type": "execute_result"
158 |     }
159 |    ],
160 |    "source": [
161 |     "eq_1 = sym.exp(x) * sym.sin(2 * x)\n",
162 |     "eq_1"
163 |    ],
164 |    "metadata": {
165 |     "collapsed": false
166 |    }
167 |   },
168 |   {
169 |    "cell_type": "code",
170 |    "execution_count": 97,
171 |    "outputs": [
172 |     {
173 |      "data": {
174 |       "text/plain": "exp(2)*sin(4)/5 - E*sin(2)/5 + 2*E*cos(2)/5 - 2*exp(2)*cos(4)/5",
175 |       "text/latex": "$\\displaystyle \\frac{e^{2} \\sin{\\left(4 \\right)}}{5} - \\frac{e \\sin{\\left(2 \\right)}}{5} + \\frac{2 e \\cos{\\left(2 \\right)}}{5} - \\frac{2 e^{2} \\cos{\\left(4 \\right)}}{5}$"
176 |      },
177 |      "execution_count": 97,
178 |      "metadata": {},
179 |      "output_type": "execute_result"
180 |     }
181 |    ],
182 |    "source": [
183 |     "eq_1_1to2 = eq_1.integrate((x, 1, 2))\n",
184 |     "eq_1_1to2"
185 |    ],
186 |    "metadata": {
187 |     "collapsed": false
188 |    }
189 |   },
190 |   {
191 |    "cell_type": "code",
192 |    "execution_count": 98,
193 |    "outputs": [
194 |     {
195 |      "data": {
196 |       "text/plain": "E*(E*sin(4) - sin(2) + 2*cos(2) - 2*E*cos(4))/5",
197 |       "text/latex": "$\\displaystyle \\frac{e \\left(e \\sin{\\left(4 \\right)} - \\sin{\\left(2 \\right)} + 2 \\cos{\\left(2 \\right)} - 2 e \\cos{\\left(4 \\right)}\\right)}{5}$"
198 |      },
199 |      "execution_count": 98,
200 |      "metadata": {},
201 |      "output_type": "execute_result"
202 |     }
203 |    ],
204 |    "source": [
205 |     "eq_1_1to2.simplify()"
206 |    ],
207 |    "metadata": {
208 |     "collapsed": false
209 |    }
210 |   },
211 |   {
212 |    "cell_type": "markdown",
213 |    "source": [
214 |     "# Numerical Eval"
215 |    ],
216 |    "metadata": {
217 |     "collapsed": false
218 |    }
219 |   },
220 |   {
221 |    "cell_type": "code",
222 |    "execution_count": 99,
223 |    "outputs": [
224 |     {
225 |      "data": {
226 |       "text/plain": "-8.0637827656458"
227 |      },
228 |      "execution_count": 99,
229 |      "metadata": {},
230 |      "output_type": "execute_result"
231 |     }
232 |    ],
233 |    "source": [
234 |     "f = sym.lambdify(x, eq_1, 'numpy')\n",
235 |     "f(2) - f(1)"
236 |    ],
237 |    "metadata": {
238 |     "collapsed": false
239 |    }
240 |   },
241 |   {
242 |    "cell_type": "code",
243 |    "execution_count": 100,
244 |    "outputs": [
245 |     {
246 |      "data": {
247 |       "text/plain": "-8.0637827656458"
248 |      },
249 |      "execution_count": 100,
250 |      "metadata": {},
251 |      "output_type": "execute_result"
252 |     }
253 |    ],
254 |    "source": [
255 |     "f2 = sym.lambdify(x, eq_1_1to2, 'numpy')\n",
256 |     "f(2) - f(1)"
257 |    ],
258 |    "metadata": {
259 |     "collapsed": false
260 |    }
261 |   },
262 |   {
263 |    "cell_type": "code",
264 |    "execution_count": 101,
265 |    "outputs": [
266 |     {
267 |      "data": {
268 |       "text/plain": "exp(sin(x))",
269 |       "text/latex": "$\\displaystyle e^{\\sin{\\left(x \\right)}}$"
270 |      },
271 |      "execution_count": 101,
272 |      "metadata": {},
273 |      "output_type": "execute_result"
274 |     }
275 |    ],
276 |    "source": [
277 |     "eg1 = sym.exp(sym.sin(x))\n",
278 |     "eg1"
279 |    ],
280 |    "metadata": {
281 |     "collapsed": false
282 |    }
283 |   },
284 |   {
285 |    "cell_type": "code",
286 |    "execution_count": 102,
287 |    "outputs": [
288 |     {
289 |      "data": {
290 |       "text/plain": "Integral(exp(sin(x)), x)",
291 |       "text/latex": "$\\displaystyle \\int e^{\\sin{\\left(x \\right)}}\\, dx$"
292 |      },
293 |      "execution_count": 102,
294 |      "metadata": {},
295 |      "output_type": "execute_result"
296 |     }
297 |    ],
298 |    "source": [
299 |     "eg1.integrate(x)"
300 |    ],
301 |    "metadata": {
302 |     "collapsed": false
303 |    }
304 |   },
305 |   {
306 |    "cell_type": "code",
307 |    "execution_count": 103,
308 |    "outputs": [
309 |     {
310 |      "data": {
311 |       "text/plain": "Integral(exp(sin(x)), (x, 1, 2))",
312 |       "text/latex": "$\\displaystyle \\int\\limits_{1}^{2} e^{\\sin{\\left(x \\right)}}\\, dx$"
313 |      },
314 |      "execution_count": 103,
315 |      "metadata": {},
316 |      "output_type": "execute_result"
317 |     }
318 |    ],
319 |    "source": [
320 |     "eg1.integrate((x,1,2))"
321 |    ],
322 |    "metadata": {
323 |     "collapsed": false
324 |    }
325 |   },
326 |   {
327 |    "cell_type": "code",
328 |    "execution_count": 104,
329 |    "outputs": [
330 |     {
331 |      "data": {
332 |       "text/plain": "Integral(exp(sin(x)), x)",
333 |       "text/latex": "$\\displaystyle \\int e^{\\sin{\\left(x \\right)}}\\, dx$"
334 |      },
335 |      "execution_count": 104,
336 |      "metadata": {},
337 |      "output_type": "execute_result"
338 |     }
339 |    ],
340 |    "source": [
341 |     "sym.Integral(eg1,x)"
342 |    ],
343 |    "metadata": {
344 |     "collapsed": false
345 |    }
346 |   },
347 |   {
348 |    "cell_type": "markdown",
349 |    "source": [
350 |     "# Plotting"
351 |    ],
352 |    "metadata": {
353 |     "collapsed": false
354 |    }
355 |   },
356 |   {
357 |    "cell_type": "code",
358 |    "execution_count": 105,
359 |    "outputs": [
360 |     {
361 |      "data": {
362 |       "text/plain": "sin(x**2 + 3*x) - cos(3*x)",
363 |       "text/latex": "$\\displaystyle \\sin{\\left(x^{2} + 3 x \\right)} - \\cos{\\left(3 x \\right)}$"
364 |      },
365 |      "execution_count": 105,
366 |      "metadata": {},
367 |      "output_type": "execute_result"
368 |     }
369 |    ],
370 |    "source": [
371 |     "eqn2 = sym.sin(x ** 2 + 3 * x) - sym.cos(3 * x)\n",
372 |     "eqn2"
373 |    ],
374 |    "metadata": {
375 |     "collapsed": false
376 |    }
377 |   },
378 |   {
379 |    "cell_type": "code",
380 |    "execution_count": 106,
381 |    "outputs": [
382 |     {
383 |      "data": {
384 |       "text/plain": "sqrt(2)*sqrt(pi)*(-sin(9/4)*fresnelc(sqrt(2)*(2*x + 3)/(2*sqrt(pi))) + cos(9/4)*fresnels(sqrt(2)*(2*x + 3)/(2*sqrt(pi))))/2 - sin(3*x)/3",
385 |       "text/latex": "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{\\pi} \\left(- \\sin{\\left(\\frac{9}{4} \\right)} C\\left(\\frac{\\sqrt{2} \\cdot \\left(2 x + 3\\right)}{2 \\sqrt{\\pi}}\\right) + \\cos{\\left(\\frac{9}{4} \\right)} S\\left(\\frac{\\sqrt{2} \\cdot \\left(2 x + 3\\right)}{2 \\sqrt{\\pi}}\\right)\\right)}{2} - \\frac{\\sin{\\left(3 x \\right)}}{3}$"
386 |      },
387 |      "execution_count": 106,
388 |      "metadata": {},
389 |      "output_type": "execute_result"
390 |     }
391 |    ],
392 |    "source": [
393 |     "eqn2I = eqn2.integrate(x)\n",
394 |     "eqn2I"
395 |    ],
396 |    "metadata": {
397 |     "collapsed": false
398 |    }
399 |   },
400 |   {
401 |    "cell_type": "code",
402 |    "execution_count": 107,
403 |    "outputs": [],
404 |    "source": [
405 |     "eqn2I_lmb = sym.lambdify(x, eqn2I)"
406 |    ],
407 |    "metadata": {
408 |     "collapsed": false
409 |    }
410 |   },
411 |   {
412 |    "cell_type": "code",
413 |    "execution_count": 111,
414 |    "outputs": [
415 |     {
416 |      "data": {
417 |       "text/plain": "array([-3.14159265, -3.11001886, -3.07844506, -3.04687127, -3.01529747,\n       -2.98372368, -2.95214988, -2.92057608, -2.88900229, -2.85742849,\n       -2.8258547 , -2.7942809 , -2.76270711, -2.73113331, -2.69955952,\n       -2.66798572, -2.63641193, -2.60483813, -2.57326433, -2.54169054,\n       -2.51011674, -2.47854295, -2.44696915, -2.41539536, -2.38382156,\n       -2.35224777, -2.32067397, -2.28910017, -2.25752638, -2.22595258,\n       -2.19437879, -2.16280499, -2.1312312 , -2.0996574 , -2.06808361,\n       -2.03650981, -2.00493602, -1.97336222, -1.94178842, -1.91021463,\n       -1.87864083, -1.84706704, -1.81549324, -1.78391945, -1.75234565,\n       -1.72077186, -1.68919806, -1.65762426, -1.62605047, -1.59447667,\n       -1.56290288, -1.53132908, -1.49975529, -1.46818149, -1.4366077 ,\n       -1.4050339 , -1.3734601 , -1.34188631, -1.31031251, -1.27873872,\n       -1.24716492, -1.21559113, -1.18401733, -1.15244354, -1.12086974,\n       -1.08929595, -1.05772215, -1.02614835, -0.99457456, -0.96300076,\n       -0.93142697, -0.89985317, -0.86827938, -0.83670558, -0.80513179,\n       -0.77355799, -0.74198419, -0.7104104 , -0.6788366 , -0.64726281,\n       -0.61568901, -0.58411522, -0.55254142, -0.52096763, -0.48939383,\n       -0.45782003, -0.42624624, -0.39467244, -0.36309865, -0.33152485,\n       -0.29995106, -0.26837726, -0.23680347, -0.20522967, -0.17365588,\n       -0.14208208, -0.11050828, -0.07893449, -0.04736069, -0.0157869 ,\n        0.0157869 ,  0.04736069,  0.07893449,  0.11050828,  0.14208208,\n        0.17365588,  0.20522967,  0.23680347,  0.26837726,  0.29995106,\n        0.33152485,  0.36309865,  0.39467244,  0.42624624,  0.45782003,\n        0.48939383,  0.52096763,  0.55254142,  0.58411522,  0.61568901,\n        0.64726281,  0.6788366 ,  0.7104104 ,  0.74198419,  0.77355799,\n        0.80513179,  0.83670558,  0.86827938,  0.89985317,  0.93142697,\n        0.96300076,  0.99457456,  1.02614835,  1.05772215,  1.08929595,\n        1.12086974,  1.15244354,  1.18401733,  1.21559113,  1.24716492,\n        1.27873872,  1.31031251,  1.34188631,  1.3734601 ,  1.4050339 ,\n        1.4366077 ,  1.46818149,  1.49975529,  1.53132908,  1.56290288,\n        1.59447667,  1.62605047,  1.65762426,  1.68919806,  1.72077186,\n        1.75234565,  1.78391945,  1.81549324,  1.84706704,  1.87864083,\n        1.91021463,  1.94178842,  1.97336222,  2.00493602,  2.03650981,\n        2.06808361,  2.0996574 ,  2.1312312 ,  2.16280499,  2.19437879,\n        2.22595258,  2.25752638,  2.28910017,  2.32067397,  2.35224777,\n        2.38382156,  2.41539536,  2.44696915,  2.47854295,  2.51011674,\n        2.54169054,  2.57326433,  2.60483813,  2.63641193,  2.66798572,\n        2.69955952,  2.73113331,  2.76270711,  2.7942809 ,  2.8258547 ,\n        2.85742849,  2.88900229,  2.92057608,  2.95214988,  2.98372368,\n        3.01529747,  3.04687127,  3.07844506,  3.11001886,  3.14159265])"
418 |      },
419 |      "execution_count": 111,
420 |      "metadata": {},
421 |      "output_type": "execute_result"
422 |     }
423 |    ],
424 |    "source": [
425 |     "x_vals = np.linspace(-np.pi, np.pi, 200)\n",
426 |     "x_vals"
427 |    ],
428 |    "metadata": {
429 |     "collapsed": false
430 |    }
431 |   },
432 |   {
433 |    "cell_type": "code",
434 |    "execution_count": 112,
435 |    "outputs": [],
436 |    "source": [
437 |     "y_vals = eqn2I_lmb(x_vals)"
438 |    ],
439 |    "metadata": {
440 |     "collapsed": false
441 |    }
442 |   },
443 |   {
444 |    "cell_type": "code",
445 |    "execution_count": 114,
446 |    "outputs": [
447 |     {
448 |      "data": {
449 |       "text/plain": "<Figure size 640x480 with 1 Axes>",
450 |       "image/png": 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\n"
451 |      },
452 |      "metadata": {},
453 |      "output_type": "display_data"
454 |     }
455 |    ],
456 |    "source": [
457 |     "plt.plot(y_vals,x_vals)\n",
458 |     "plt.show()"
459 |    ],
460 |    "metadata": {
461 |     "collapsed": false
462 |    }
463 |   },
464 |   {
465 |    "cell_type": "code",
466 |    "execution_count": 110,
467 |    "outputs": [],
468 |    "source": [],
469 |    "metadata": {
470 |     "collapsed": false
471 |    }
472 |   }
473 |  ],
474 |  "metadata": {
475 |   "kernelspec": {
476 |    "display_name": "Python 3",
477 |    "language": "python",
478 |    "name": "python3"
479 |   },
480 |   "language_info": {
481 |    "codemirror_mode": {
482 |     "name": "ipython",
483 |     "version": 2
484 |    },
485 |    "file_extension": ".py",
486 |    "mimetype": "text/x-python",
487 |    "name": "python",
488 |    "nbconvert_exporter": "python",
489 |    "pygments_lexer": "ipython2",
490 |    "version": "2.7.6"
491 |   }
492 |  },
493 |  "nbformat": 4,
494 |  "nbformat_minor": 0
495 | }
496 | 


--------------------------------------------------------------------------------
/tutorial9.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 11,
  6 |    "metadata": {
  7 |     "collapsed": true
  8 |    },
  9 |    "outputs": [],
 10 |    "source": [
 11 |     "import matplotlib.pyplot as plt\n",
 12 |     "import numpy as np\n",
 13 |     "import sympy as sym"
 14 |    ]
 15 |   },
 16 |   {
 17 |    "cell_type": "code",
 18 |    "execution_count": 12,
 19 |    "outputs": [],
 20 |    "source": [
 21 |     "x = sym.symbols('x')\n",
 22 |     "n = sym.symbols('n', integer=True, positive=True)\n",
 23 |     "\n",
 24 |     "ms = np.empty(100, dtype=object)\n",
 25 |     "xrange = np.linspace(3 * np.pi, -3 * np.pi, 1000)\n",
 26 |     "y = np.zeros([101, 1000])"
 27 |    ],
 28 |    "metadata": {
 29 |     "collapsed": false
 30 |    }
 31 |   },
 32 |   {
 33 |    "cell_type": "code",
 34 |    "execution_count": 13,
 35 |    "outputs": [
 36 |     {
 37 |      "data": {
 38 |       "text/plain": "x**2",
 39 |       "text/latex": "$\\displaystyle x^{2}$"
 40 |      },
 41 |      "execution_count": 13,
 42 |      "metadata": {},
 43 |      "output_type": "execute_result"
 44 |     }
 45 |    ],
 46 |    "source": [
 47 |     "eq = x ** 2\n",
 48 |     "eq"
 49 |    ],
 50 |    "metadata": {
 51 |     "collapsed": false
 52 |    }
 53 |   },
 54 |   {
 55 |    "cell_type": "code",
 56 |    "execution_count": 14,
 57 |    "outputs": [
 58 |     {
 59 |      "data": {
 60 |       "text/plain": "pi**2/6",
 61 |       "text/latex": "$\\displaystyle \\frac{\\pi^{2}}{6}$"
 62 |      },
 63 |      "execution_count": 14,
 64 |      "metadata": {},
 65 |      "output_type": "execute_result"
 66 |     }
 67 |    ],
 68 |    "source": [
 69 |     "a0 = (1 / (2 * sym.pi)) * eq.integrate((x, 0, sym.pi))\n",
 70 |     "a0"
 71 |    ],
 72 |    "metadata": {
 73 |     "collapsed": false
 74 |    }
 75 |   },
 76 |   {
 77 |    "cell_type": "code",
 78 |    "execution_count": 15,
 79 |    "outputs": [
 80 |     {
 81 |      "data": {
 82 |       "text/plain": "2*(-1)**n/n**2",
 83 |       "text/latex": "$\\displaystyle \\frac{2 \\left(-1\\right)^{n}}{n^{2}}$"
 84 |      },
 85 |      "execution_count": 15,
 86 |      "metadata": {},
 87 |      "output_type": "execute_result"
 88 |     }
 89 |    ],
 90 |    "source": [
 91 |     "an = (1 / sym.pi) * sym.integrate((eq * sym.cos(n * x)), (x, 0, sym.pi))\n",
 92 |     "an"
 93 |    ],
 94 |    "metadata": {
 95 |     "collapsed": false
 96 |    }
 97 |   },
 98 |   {
 99 |    "cell_type": "code",
100 |    "execution_count": 16,
101 |    "outputs": [
102 |     {
103 |      "data": {
104 |       "text/plain": "(-(-1)**n*pi**2/n + 2*(-1)**n/n**3 - 2/n**3)/pi",
105 |       "text/latex": "$\\displaystyle \\frac{- \\frac{\\left(-1\\right)^{n} \\pi^{2}}{n} + \\frac{2 \\left(-1\\right)^{n}}{n^{3}} - \\frac{2}{n^{3}}}{\\pi}$"
106 |      },
107 |      "execution_count": 16,
108 |      "metadata": {},
109 |      "output_type": "execute_result"
110 |     }
111 |    ],
112 |    "source": [
113 |     "bn = (1 / sym.pi) * sym.integrate((eq * sym.sin(n * x)), (x, 0, sym.pi))\n",
114 |     "bn"
115 |    ],
116 |    "metadata": {
117 |     "collapsed": false
118 |    }
119 |   },
120 |   {
121 |    "cell_type": "code",
122 |    "execution_count": 17,
123 |    "outputs": [],
124 |    "source": [
125 |     "ms[0] = a0\n",
126 |     "\n",
127 |     "f = sym.lambdify(x, ms[0], 'numpy')\n",
128 |     "y[0, :] = f(xrange)"
129 |    ],
130 |    "metadata": {
131 |     "collapsed": false
132 |    }
133 |   },
134 |   {
135 |    "cell_type": "markdown",
136 |    "source": [
137 |     "# Calc. fourier series coefficients"
138 |    ],
139 |    "metadata": {
140 |     "collapsed": false
141 |    }
142 |   },
143 |   {
144 |    "cell_type": "code",
145 |    "execution_count": 18,
146 |    "outputs": [],
147 |    "source": [
148 |     "for m in range(1, 100):\n",
149 |     "    ms[m] = ms[m - 1] + an.subs(n, m) * sym.cos(m * x) + bn.subs(n, m) * sym.sin(m * x)\n",
150 |     "    f = sym.lambdify(x, ms[m], 'numpy')\n",
151 |     "    y[m, :] = f(xrange)"
152 |    ],
153 |    "metadata": {
154 |     "collapsed": false
155 |    }
156 |   },
157 |   {
158 |    "cell_type": "code",
159 |    "execution_count": 19,
160 |    "outputs": [
161 |     {
162 |      "data": {
163 |       "text/plain": "(-4 + pi**2)*sin(x)/pi - pi*sin(2*x)/2 + (-4/27 + pi**2/3)*sin(3*x)/pi - pi*sin(4*x)/4 + (-4/125 + pi**2/5)*sin(5*x)/pi - pi*sin(6*x)/6 + (-4/343 + pi**2/7)*sin(7*x)/pi - pi*sin(8*x)/8 + (-4/729 + pi**2/9)*sin(9*x)/pi - pi*sin(10*x)/10 - 2*cos(x) + cos(2*x)/2 - 2*cos(3*x)/9 + cos(4*x)/8 - 2*cos(5*x)/25 + cos(6*x)/18 - 2*cos(7*x)/49 + cos(8*x)/32 - 2*cos(9*x)/81 + cos(10*x)/50 + pi**2/6",
164 |       "text/latex": "$\\displaystyle \\frac{\\left(-4 + \\pi^{2}\\right) \\sin{\\left(x \\right)}}{\\pi} - \\frac{\\pi \\sin{\\left(2 x \\right)}}{2} + \\frac{\\left(- \\frac{4}{27} + \\frac{\\pi^{2}}{3}\\right) \\sin{\\left(3 x \\right)}}{\\pi} - \\frac{\\pi \\sin{\\left(4 x \\right)}}{4} + \\frac{\\left(- \\frac{4}{125} + \\frac{\\pi^{2}}{5}\\right) \\sin{\\left(5 x \\right)}}{\\pi} - \\frac{\\pi \\sin{\\left(6 x \\right)}}{6} + \\frac{\\left(- \\frac{4}{343} + \\frac{\\pi^{2}}{7}\\right) \\sin{\\left(7 x \\right)}}{\\pi} - \\frac{\\pi \\sin{\\left(8 x \\right)}}{8} + \\frac{\\left(- \\frac{4}{729} + \\frac{\\pi^{2}}{9}\\right) \\sin{\\left(9 x \\right)}}{\\pi} - \\frac{\\pi \\sin{\\left(10 x \\right)}}{10} - 2 \\cos{\\left(x \\right)} + \\frac{\\cos{\\left(2 x \\right)}}{2} - \\frac{2 \\cos{\\left(3 x \\right)}}{9} + \\frac{\\cos{\\left(4 x \\right)}}{8} - \\frac{2 \\cos{\\left(5 x \\right)}}{25} + \\frac{\\cos{\\left(6 x \\right)}}{18} - \\frac{2 \\cos{\\left(7 x \\right)}}{49} + \\frac{\\cos{\\left(8 x \\right)}}{32} - \\frac{2 \\cos{\\left(9 x \\right)}}{81} + \\frac{\\cos{\\left(10 x \\right)}}{50} + \\frac{\\pi^{2}}{6}$"
165 |      },
166 |      "execution_count": 19,
167 |      "metadata": {},
168 |      "output_type": "execute_result"
169 |     }
170 |    ],
171 |    "source": [
172 |     "ms[10]"
173 |    ],
174 |    "metadata": {
175 |     "collapsed": false
176 |    }
177 |   },
178 |   {
179 |    "cell_type": "code",
180 |    "execution_count": 20,
181 |    "outputs": [
182 |     {
183 |      "data": {
184 |       "text/plain": "(-4 + pi**2)*sin(x)/pi - 2*cos(x) + pi**2/6",
185 |       "text/latex": "$\\displaystyle \\frac{\\left(-4 + \\pi^{2}\\right) \\sin{\\left(x \\right)}}{\\pi} - 2 \\cos{\\left(x \\right)} + \\frac{\\pi^{2}}{6}$"
186 |      },
187 |      "execution_count": 20,
188 |      "metadata": {},
189 |      "output_type": "execute_result"
190 |     }
191 |    ],
192 |    "source": [
193 |     "ms[1]"
194 |    ],
195 |    "metadata": {
196 |     "collapsed": false
197 |    }
198 |   },
199 |   {
200 |    "cell_type": "markdown",
201 |    "source": [
202 |     "# Piecewise plotting"
203 |    ],
204 |    "metadata": {
205 |     "collapsed": false
206 |    }
207 |   },
208 |   {
209 |    "cell_type": "code",
210 |    "execution_count": 21,
211 |    "outputs": [
212 |     {
213 |      "data": {
214 |       "text/plain": "<Figure size 640x480 with 1 Axes>",
215 |       "image/png": 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\n"
216 |      },
217 |      "metadata": {},
218 |      "output_type": "display_data"
219 |     }
220 |    ],
221 |    "source": [
222 |     "for m in range(0, 1000):\n",
223 |     "    if 0 < xrange[m] < np.pi:\n",
224 |     "        y[100, m] = xrange[m] ** 2\n",
225 |     "    elif 2 * np.pi < xrange[m] <= 3 * np.pi:\n",
226 |     "        y[100, m] = (xrange[m] - 2 * np.pi) ** 2\n",
227 |     "    elif -2 * np.pi < xrange[m] <= np.pi:\n",
228 |     "        y[100, m] = (xrange[m] + 2 * np.pi) ** 2\n",
229 |     "\n",
230 |     "plt.plot(xrange, y[4, :])\n",
231 |     "plt.plot(xrange, y[9, :])\n",
232 |     "plt.plot(xrange, y[99, :])\n",
233 |     "plt.plot(xrange, y[100, :])\n",
234 |     "\n",
235 |     "plt.legend([\"5\", \"10\", \"100\", \"func\"])\n",
236 |     "plt.show()"
237 |    ],
238 |    "metadata": {
239 |     "collapsed": false
240 |    }
241 |   },
242 |   {
243 |    "cell_type": "code",
244 |    "execution_count": 21,
245 |    "outputs": [],
246 |    "source": [],
247 |    "metadata": {
248 |     "collapsed": false
249 |    }
250 |   }
251 |  ],
252 |  "metadata": {
253 |   "kernelspec": {
254 |    "display_name": "Python 3",
255 |    "language": "python",
256 |    "name": "python3"
257 |   },
258 |   "language_info": {
259 |    "codemirror_mode": {
260 |     "name": "ipython",
261 |     "version": 2
262 |    },
263 |    "file_extension": ".py",
264 |    "mimetype": "text/x-python",
265 |    "name": "python",
266 |    "nbconvert_exporter": "python",
267 |    "pygments_lexer": "ipython2",
268 |    "version": "2.7.6"
269 |   }
270 |  },
271 |  "nbformat": 4,
272 |  "nbformat_minor": 0
273 | }
274 | 


--------------------------------------------------------------------------------
/newton_raphson_approximation.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |   "nbformat": 4,
  3 |   "nbformat_minor": 0,
  4 |   "metadata": {
  5 |     "colab": {
  6 |       "provenance": [],
  7 |       "authorship_tag": "ABX9TyMAiQYluC6Df0euxtWNPB/Q",
  8 |       "include_colab_link": true
  9 |     },
 10 |     "kernelspec": {
 11 |       "name": "python3",
 12 |       "display_name": "Python 3"
 13 |     },
 14 |     "language_info": {
 15 |       "name": "python"
 16 |     }
 17 |   },
 18 |   "cells": [
 19 |     {
 20 |       "cell_type": "markdown",
 21 |       "metadata": {
 22 |         "id": "view-in-github",
 23 |         "colab_type": "text"
 24 |       },
 25 |       "source": [
 26 |         "<a href=\"https://colab.research.google.com/github/ruwanego/cm2607/blob/main/newton_raphson_approximation.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
 27 |       ]
 28 |     },
 29 |     {
 30 |       "cell_type": "code",
 31 |       "execution_count": null,
 32 |       "metadata": {
 33 |         "colab": {
 34 |           "base_uri": "https://localhost:8080/",
 35 |           "height": 689
 36 |         },
 37 |         "id": "_V1HnNGgpmoZ",
 38 |         "outputId": "b8eaec88-dfb1-439b-d47c-4aeaaa920924"
 39 |       },
 40 |       "outputs": [
 41 |         {
 42 |           "output_type": "stream",
 43 |           "name": "stdout",
 44 |           "text": [
 45 |             "Iteration\t x_n\t\t x_(n+1)\t\t f(x_n)\t\t f'(x_n)\n",
 46 |             "1\t\t 1.500000\t 1.347826\t 0.875000\t 5.750000\n",
 47 |             "2\t\t 1.347826\t 1.325200\t 0.100682\t 4.449905\n",
 48 |             "3\t\t 1.325200\t 1.324718\t 0.002058\t 4.268468\n",
 49 |             "4\t\t 1.324718\t 1.324718\t 0.000001\t 4.264635\n",
 50 |             "5\t\t 1.324718\t 1.324718\t 0.000000\t 4.264633\n",
 51 |             "6\t\t 1.324718\t 1.324718\t 0.000000\t 4.264633\n"
 52 |           ]
 53 |         },
 54 |         {
 55 |           "output_type": "display_data",
 56 |           "data": {
 57 |             "text/plain": [
 58 |               "<Figure size 800x600 with 1 Axes>"
 59 |             ],
 60 |             "image/png": 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\n"
 61 |           },
 62 |           "metadata": {}
 63 |         }
 64 |       ],
 65 |       "source": [
 66 |         "# Import required libraries for plotting\n",
 67 |         "import matplotlib.pyplot as plt\n",
 68 |         "import numpy as np\n",
 69 |         "\n",
 70 |         "# Define the function and its derivative using lambda functions for simplicity\n",
 71 |         "# f represents the equation we want to find the root of (x^3 - x - 1 = 0)\n",
 72 |         "f = lambda x: x**3 - x - 1\n",
 73 |         "\n",
 74 |         "# def f(x):\n",
 75 |         "#   return x**3 - x - 1\n",
 76 |         "\n",
 77 |         "# f_prime is the derivative of f, used to adjust our guesses in the Newton-Raphson method\n",
 78 |         "f_prime = lambda x: 3 * x**2 - 1\n",
 79 |         "\n",
 80 |         "# def f_prime(x):\n",
 81 |         "#   return 3 * x**2 - 1\n",
 82 |         "\n",
 83 |         "# Starting point for our guess of the root, chosen as 1.5\n",
 84 |         "x0 = 1.5\n",
 85 |         "\n",
 86 |         "# Iteration parameters\n",
 87 |         "# tolerance defines how close we need to get to the actual root before stopping\n",
 88 |         "tolerance = 1e-20\n",
 89 |         "\n",
 90 |         "# max_iterations limits the number of times we'll try to find the root\n",
 91 |         "max_iterations = 15\n",
 92 |         "\n",
 93 |         "# List to store details of each iteration (for demonstration and later display)\n",
 94 |         "iterations = []\n",
 95 |         "\n",
 96 |         "# Newton-Raphson iteration loop\n",
 97 |         "for i in range(max_iterations):\n",
 98 |         "    # Calculate the next guess using the Newton-Raphson formula:\n",
 99 |         "    # x1 = x0 - f(x0) / f_prime(x0)\n",
100 |         "    x1 = x0 - f(x0) / f_prime(x0)\n",
101 |         "\n",
102 |         "    # Store the current iteration details: iteration number, current guess, next guess,\n",
103 |         "    # function value at the current guess, and derivative value at the current guess\n",
104 |         "    iterations.append((i + 1, x0, x1, f(x0), f_prime(x0)))\n",
105 |         "\n",
106 |         "    # Check if the change between our new guess and the old one is small enough (within tolerance)\n",
107 |         "    if abs(x1 - x0) < tolerance:\n",
108 |         "        # If so, we're close enough to the root, so break out of the loop\n",
109 |         "        break\n",
110 |         "\n",
111 |         "    # Update x0 to be the new guess for the next iteration\n",
112 |         "    x0 = x1\n",
113 |         "\n",
114 |         "# Display the results without using pandas, printing each iteration in a readable format\n",
115 |         "print(\"Iteration\\t x_n\\t\\t x_(n+1)\\t\\t f(x_n)\\t\\t f'(x_n)\")\n",
116 |         "for iteration in iterations:\n",
117 |         "    print(f\"{iteration[0]}\\t\\t {iteration[1]:.6f}\\t {iteration[2]:.6f}\\t {iteration[3]:.6f}\\t {iteration[4]:.6f}\")\n",
118 |         "\n",
119 |         "# Generate values for x to plot the function\n",
120 |         "x_values = np.linspace(-2, 2, 400)\n",
121 |         "y_values = f(x_values)\n",
122 |         "\n",
123 |         "# Create the plot\n",
124 |         "plt.figure(figsize=(8, 6))\n",
125 |         "\n",
126 |         "# Plot the function f(x)\n",
127 |         "plt.plot(x_values, y_values, label=r\"$f(x) = x^3 - x - 1$\", color=\"blue\")\n",
128 |         "\n",
129 |         "# Highlight the x-axis for reference\n",
130 |         "plt.axhline(0, color='black',linewidth=0.5)\n",
131 |         "\n",
132 |         "# Plot each Newton-Raphson iteration as a point\n",
133 |         "for iteration in iterations:\n",
134 |         "    x_n = iteration[1]\n",
135 |         "    plt.plot(x_n, f(x_n), 'ro')  # Red point for each guess\n",
136 |         "\n",
137 |         "# # Draw arrows to indicate the steps from one guess to the next\n",
138 |         "# for i in range(len(iterations) - 1):\n",
139 |         "#     x_n = iterations[i][1]\n",
140 |         "#     x_next = iterations[i][2]\n",
141 |         "#     plt.annotate('', xy=(x_next, 0), xytext=(x_n, f(x_n)),\n",
142 |         "#                  arrowprops=dict(arrowstyle='->', color='red'))\n",
143 |         "\n",
144 |         "# Add labels and a legend\n",
145 |         "plt.xlabel(\"x\")\n",
146 |         "plt.ylabel(\"f(x)\")\n",
147 |         "plt.title(\"Newton-Raphson Iterations for f(x) = x^3 - x - 1\")\n",
148 |         "plt.legend()\n",
149 |         "plt.grid(True)\n",
150 |         "\n",
151 |         "# Display the plot\n",
152 |         "plt.show()\n"
153 |       ]
154 |     }
155 |   ]
156 | }


--------------------------------------------------------------------------------
/tutorial8.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "code",
  5 |    "execution_count": 1,
  6 |    "outputs": [],
  7 |    "source": [
  8 |     "import matplotlib.pyplot as plt\n",
  9 |     "import numpy as np\n",
 10 |     "# Import necessary libraries\n",
 11 |     "import sympy as sym"
 12 |    ],
 13 |    "metadata": {
 14 |     "collapsed": false
 15 |    }
 16 |   },
 17 |   {
 18 |    "cell_type": "code",
 19 |    "execution_count": 2,
 20 |    "outputs": [],
 21 |    "source": [
 22 |     "# Step 1: Define the symbolic variable x\n",
 23 |     "x = sym.symbols('x')"
 24 |    ],
 25 |    "metadata": {
 26 |     "collapsed": false
 27 |    }
 28 |   },
 29 |   {
 30 |    "cell_type": "code",
 31 |    "execution_count": 3,
 32 |    "outputs": [
 33 |     {
 34 |      "data": {
 35 |       "text/plain": "x**2*sin(0.5*x)",
 36 |       "text/latex": "$\\displaystyle x^{2} \\sin{\\left(0.5 x \\right)}$"
 37 |      },
 38 |      "execution_count": 3,
 39 |      "metadata": {},
 40 |      "output_type": "execute_result"
 41 |     }
 42 |    ],
 43 |    "source": [
 44 |     "# Step 2: Define the function f(x) = x^2 * sin(0.5x)\n",
 45 |     "f = (x ** 2) * sym.sin(0.5 * x)\n",
 46 |     "f"
 47 |    ],
 48 |    "metadata": {
 49 |     "collapsed": false
 50 |    }
 51 |   },
 52 |   {
 53 |    "cell_type": "code",
 54 |    "execution_count": 5,
 55 |    "outputs": [
 56 |     {
 57 |      "data": {
 58 |       "text/plain": "array([None, None, None, None, None, None, None, None, None, None, None,\n       None, None, None, None, None, None, None, None, None], dtype=object)"
 59 |      },
 60 |      "execution_count": 5,
 61 |      "metadata": {},
 62 |      "output_type": "execute_result"
 63 |     }
 64 |    ],
 65 |    "source": [
 66 |     "# Step 3: Initialize an array to store Maclaurin series terms\n",
 67 |     "ms = np.empty(20, dtype=object)\n",
 68 |     "ms"
 69 |    ],
 70 |    "metadata": {
 71 |     "collapsed": false
 72 |    }
 73 |   },
 74 |   {
 75 |    "cell_type": "code",
 76 |    "execution_count": 6,
 77 |    "outputs": [
 78 |     {
 79 |      "data": {
 80 |       "text/plain": "array([-5.        , -4.97995992, -4.95991984, -4.93987976, -4.91983968,\n       -4.8997996 , -4.87975952, -4.85971944, -4.83967936, -4.81963928,\n       -4.7995992 , -4.77955912, -4.75951904, -4.73947896, -4.71943888,\n       -4.6993988 , -4.67935872, -4.65931864, -4.63927856, -4.61923848,\n       -4.5991984 , -4.57915832, -4.55911824, -4.53907816, -4.51903808,\n       -4.498998  , -4.47895792, -4.45891784, -4.43887776, -4.41883768,\n       -4.3987976 , -4.37875752, -4.35871743, -4.33867735, -4.31863727,\n       -4.29859719, -4.27855711, -4.25851703, -4.23847695, -4.21843687,\n       -4.19839679, -4.17835671, -4.15831663, -4.13827655, -4.11823647,\n       -4.09819639, -4.07815631, -4.05811623, -4.03807615, -4.01803607,\n       -3.99799599, -3.97795591, -3.95791583, -3.93787575, -3.91783567,\n       -3.89779559, -3.87775551, -3.85771543, -3.83767535, -3.81763527,\n       -3.79759519, -3.77755511, -3.75751503, -3.73747495, -3.71743487,\n       -3.69739479, 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4.51903808,  4.53907816,  4.55911824,  4.57915832,  4.5991984 ,\n        4.61923848,  4.63927856,  4.65931864,  4.67935872,  4.6993988 ,\n        4.71943888,  4.73947896,  4.75951904,  4.77955912,  4.7995992 ,\n        4.81963928,  4.83967936,  4.85971944,  4.87975952,  4.8997996 ,\n        4.91983968,  4.93987976,  4.95991984,  4.97995992,  5.        ])"
 81 |      },
 82 |      "execution_count": 6,
 83 |      "metadata": {},
 84 |      "output_type": "execute_result"
 85 |     }
 86 |    ],
 87 |    "source": [
 88 |     "# Step 4: Create an array of 500 points from -5 to 5 for plotting\n",
 89 |     "x_values = np.linspace(-5, 5, 500)\n",
 90 |     "x_values"
 91 |    ],
 92 |    "metadata": {
 93 |     "collapsed": false
 94 |    }
 95 |   },
 96 |   {
 97 |    "cell_type": "code",
 98 |    "execution_count": 8,
 99 |    "outputs": [
100 |     {
101 |      "data": {
102 |       "text/plain": "array([[0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       ...,\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.],\n       [0., 0., 0., ..., 0., 0., 0.]])"
103 |      },
104 |      "execution_count": 8,
105 |      "metadata": {},
106 |      "output_type": "execute_result"
107 |     }
108 |    ],
109 |    "source": [
110 |     "# Step 5: Create a 2D array to store function values and approximations for plotting\n",
111 |     "function_and_approximations = np.zeros([21, 500])\n",
112 |     "function_and_approximations"
113 |    ],
114 |    "metadata": {
115 |     "collapsed": false
116 |    }
117 |   },
118 |   {
119 |    "cell_type": "code",
120 |    "execution_count": 10,
121 |    "outputs": [],
122 |    "source": [
123 |     "# Step 6: Evaluate and store the function values at each point in x_values\n",
124 |     "function_evaluation = sym.lambdify(x, f, 'numpy')\n",
125 |     "function_evaluation\n",
126 |     "function_and_approximations[20, :] = function_evaluation(x_values)"
127 |    ],
128 |    "metadata": {
129 |     "collapsed": false
130 |    }
131 |   },
132 |   {
133 |    "cell_type": "code",
134 |    "execution_count": 11,
135 |    "outputs": [
136 |     {
137 |      "name": "stdout",
138 |      "output_type": "stream",
139 |      "text": [
140 |       "1 : 0\n",
141 |       "2 : 0\n",
142 |       "3 : 0\n",
143 |       "4 : 0.5*x**3\n",
144 |       "5 : 0\n",
145 |       "6 : -0.0208333333333333*x**5\n",
146 |       "7 : 0\n",
147 |       "8 : 0.000260416666666667*x**7\n",
148 |       "9 : 0\n",
149 |       "10 : -1.55009920634921e-6*x**9\n",
150 |       "11 : 0\n",
151 |       "12 : 5.38228891093474e-9*x**11\n",
152 |       "13 : 0\n",
153 |       "14 : -1.2232474797579e-11*x**13\n",
154 |       "15 : 0\n",
155 |       "16 : 1.96033249961201e-14*x**15\n",
156 |       "17 : 0\n",
157 |       "18 : -2.33372916620478e-17*x**17\n",
158 |       "19 : 0\n",
159 |       "20 : 2.14497166011469e-20*x**19\n"
160 |      ]
161 |     }
162 |    ],
163 |    "source": [
164 |     "# Step 7: Perform Taylor series expansion around x = 0\n",
165 |     "for degree in range(20):\n",
166 |     "    # Calculate the nth derivative of f(x) at x = 0\n",
167 |     "    ms[degree] = f.diff(x, degree).subs(x, 0) * (\n",
168 |     "            x ** degree) / (np.math.factorial(degree))\n",
169 |     "\n",
170 |     "    # Convert the symbolic expression to a NumPy function\n",
171 |     "    taylor_series_function = sym.lambdify(x, ms[degree], 'numpy')\n",
172 |     "\n",
173 |     "    # Evaluate and store the approximation at each point in x_values\n",
174 |     "    function_and_approximations[degree, :] = taylor_series_function(x_values)\n",
175 |     "\n",
176 |     "    # Print the Taylor series term for better understanding\n",
177 |     "    print(degree + 1, \":\", ms[degree])"
178 |    ],
179 |    "metadata": {
180 |     "collapsed": false
181 |    }
182 |   },
183 |   {
184 |    "cell_type": "code",
185 |    "execution_count": 12,
186 |    "outputs": [
187 |     {
188 |      "data": {
189 |       "text/plain": "<Figure size 640x480 with 1 Axes>",
190 |       "image/png": 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ewr95c7MjuY1qdTh7lVOUD1NM2tY6OgV8Ai96NY0aNWLr1q0AfP3112zbto309PTS65fNnDmTpUuX8uGHHzJgwABefvll+vXrx/333w/AuHHjWL58Obm5uWXWGxgYyPz58/Hx8QHgzTffxGq1Mn/+fCwWC1AyuhMWFsbq1avp3Lkzzz77LM8//3zpddUSExPZvn07r776Kn369Dll/jZt2vDWW2/RoEEDDh06xKRJk7jmmmv49ddfqVGjxkW/PyIile3of/7D4flvABA3ZTJB111rciL3ouLj4QzDKC0imzdvJjc396TCUFBQwO7duwH4/fffGThwYJn7r7rqKr766qsy8y6//PLS0nNi3bt27TrpZJKFhYXs3r2bjIwMkpOT6devHw8++GDp/cXFxYSGhp42f5cuXco8Z9u2balXrx6LFi0qPcGliEh1kffDD6RNmAhA5KOPEnr77SYncj8qPhfDO6Bk5MWs5y4HO3bsIDExEQCXy0VsbCyrV68+abmwsLDS708UpRNOdVLJwMCyo1Eul4tWrVrxzjvvnLRszZo1KSwsBEo2d7VpU/Z6Mzab7Zxey4nnvfzyy3VhWhGpdux79nDg8SeguJiQW28l8rFHzY7kllR8LobFUi6bm8zy1VdfsW3bNp588kkAWrZsSVpaGl5eXtStW/eUj2nYsCEbNmygd+/epfM2bdp01udq2bIlH3zwQelO038VGhpKfHw8e/bsoVevXhf2ggC73c6OHTu4/vrrL3gdIiKVrfjoUZIfehhXdjb+LVoQO2XySX9kSvnQzs0ewm63k5aWxsGDB/nxxx+ZMmUKXbt25bbbbuO+++4DoGPHjrRt25Zu3brx5ZdfsnfvXtatW8fTTz9dWm4GDRrEG2+8waJFi9i5cyeTJk1i69atZ/0F7dWrF5GRkXTt2pVvvvmGpKQk1qxZwxNPPMGBAweAknPyTJ06lRdffJE//viDbdu2sWDBAmbNmnXa9Q4dOpQ1a9aQlJTE+vXrufPOO8nOzj7tPkEiIlWNUVTEwcefoCg5Ge9atag1919Yj+9nKeVPIz4e4osvviA2NhYvLy/Cw8Np3rw5L730En369MFqLem/FouFZcuWMWbMGB544AEyMjKIiYnhhhtuIDo6GigpMHv27GHo0KEUFhZy991307dvXzZs2HDG5w8ICGDt2rWMGDGC7t27k5OTQ3x8PDfddFPpCFD//v0JCAhgxowZDB8+vHSz1eDBg0+73gMHDnDPPfeQmZlJzZo1ufrqq/nhhx+oU6dO+bxxIiIV7NCMGeRv3Ig1MJCEV+bhFRFhdiS3ZjHOdNVPD5SdnU1oaChZWVknbZIpLCwkKSmJxMRE/Pz8TEpY9XTq1ImYmBgWL15sdpRyoZ+ziFSWrE8+IWX4CABqzXmZ4I4dTU5UfZ3p8/vPNOIj5yU/P59XXnmFm2++GZvNxnvvvcfKlStZsWKF2dFERKqVwu3bSR07DoAajzys0lNJVHzkvJzYHDZp0iTsdjsNGzZkyZIldNQvrIjIOSs+epQDjw3CsNsJvPEGaj72mNmRPIaKj5wXf39/Vq5caXYMEZFqy3A6SXnqKYpSUvCuXZv46dOxnMdpO+Ti6KguERGRSpT5r3+Rt+57LP7+1JrzMrYznKRVyp+Kj4iISCXJ/e47Mue9AkDsxIn4Hb+Is1QeFR8REZFKUJSeTsqw4WAYhN19N6G332Z2JI+k4iMiIlLBDKeTlKHDcB45gm/DhkSPHmV2JI+l4iMiIlLBMv81l/wNG7AGBBD/wgtYdY4w06j4iIiIVKC8devInDcPgJiJE/G9JNHkRJ5NxUdERKSCFKWnc/DEfj133UXobbeaHcnjqfh4gL59+2KxWLBYLHh7exMdHU2nTp148803cblcZse7KGvXruX2228nLi4Oi8XC0qVLT1rGMAzGjx9PXFwc/v7+tGvXjl9//bXyw4qIRzFcLlJGjMB5+DC+DRoQPWa02ZEEFR+Pccstt5CamsrevXv5/PPPad++PU888QS33XYbxcXFFfrcDoejwtadl5dH8+bNmTNnzmmXmT59OrNmzWLOnDls3LiRmJgYOnXqRE5OToXlEhE5smAh+d//gMXfn/jZ2q+nqlDx8RC+vr7ExMQQHx9Py5YtGT16NB9//DGff/45CxcuLF0uKyuLAQMGEBUVRUhICB06dODnn38us65JkyYRFRVFcHAw/fv3Z+TIkbRo0aL0/r59+9KtWzemTp1KXFwcDY6fp+LgwYP06NGD8PBwatSoQdeuXdm7d2+ZdS9YsIDLLrsMPz8/GjVqxNy5c8/4urp06cKkSZPo3r37Ke83DIPZs2czZswYunfvTtOmTVm0aBH5+fm8++675/4Gioich8Lt20mfPRuA6FEj8b3kEnMDSSkVn4tgGAb5RfmmTIZhXHT+Dh060Lx5cz766KPS13PrrbeSlpbGsmXL2Lx5My1btuSmm27iyJEjALzzzjtMnjyZadOmsXnzZmrXrs284zvt/dmqVavYsWMHK1as4LPPPiM/P5/27dsTFBTE2rVr+fbbbwkKCuKWW24pHRF6/fXXGTNmDJMnT2bHjh1MmTKFsWPHsmjRogt+jUlJSaSlpdG5c+fSeb6+vtx4442sW7fugtcrInI6roICDg4dBkVFBHfqSNhdd5kdSf5E1+q6CAXFBbR5t40pz73+3vUEeAdc9HoaNWrE1q1bAfj666/Ztm0b6enp+Pr6AjBz5kyWLl3Khx9+yIABA3j55Zfp168f999/PwDjxo1j+fLl5ObmlllvYGAg8+fPx8fHB4A333wTq9XK/PnzsVgsQMnoTlhYGKtXr6Zz5848++yzPP/886WjN4mJiWzfvp1XX32VPn36XNDrS0tLAyA6OrrM/OjoaPbt23dB6xQROZND06bh2LMHr6goYiZOLP0/T6oGFR8PZxhG6S/l5s2byc3NpUaNGmWWKSgoYPfu3QD8/vvvDBw4sMz9V111FV999VWZeZdffnlp6Tmx7l27dhEcHFxmucLCQnbv3k1GRgbJycn069ePBx98sPT+4uJiQsvhOjZ//Y/nz69bRKS85KxaxbH3PwAg7rmpeIWHm5xI/krF5yL4e/mz/t71pj13edixYweJiSXnlHC5XMTGxrJ69eqTlgsLCyv9/lQl4q8CAwPL3Ha5XLRq1Yp33nnnpGVr1qxJYWEhULK5q02bsqNotou4anFMTAxQMvITGxtbOj89Pf2kUSARkYtRlJ5O6pinAYh44AECr7nG5ERyKio+F8FisZTL5iazfPXVV2zbto0nn3wSgJYtW5KWloaXlxd169Y95WMaNmzIhg0b6N27d+m8TZs2nfW5WrZsyQcffFC60/RfhYaGEh8fz549e+jVq9eFvaBTSExMJCYmhhUrVnDFFVcAJUeZrVmzhmnTppXb84iIZzNcLlJHjcZ57Bi+l11GzcFPmB1JTkPFx0PY7XbS0tJwOp0cOnSIL774gqlTp3Lbbbdx3333AdCxY0fatm1Lt27dmDZtGg0bNiQlJYVly5bRrVs3WrduzaBBg3jwwQdp3bo111xzDR988AFbt27lkrMcsdCrVy9mzJhB165dmThxIrVq1WL//v189NFHDBs2jFq1ajF+/Hgef/xxQkJC6NKlC3a7nU2bNnH06FGGDBlyyvXm5uaya9eu0ttJSUls2bKFiIgIateujcViYfDgwUyZMoX69etTv359pkyZQkBAAPfee2/5vcEi4tGOvPUWed99h8XXl/iZM7D+aVO/VC0qPh7iiy++IDY2Fi8vL8LDw2nevDkvvfQSffr0wWotObjPYrGwbNkyxowZwwMPPEBGRgYxMTHccMMNpZuFevXqxZ49exg6dCiFhYXcfffd9O3blw0bNpzx+QMCAli7di0jRoyge/fu5OTkEB8fz0033VQ6AtS/f38CAgKYMWMGw4cPJzAwkMsvv5zBgwefdr2bNm2iffv2pbdPFKQ+ffqUHqY/fPhwCgoKGDhwIEePHqVNmzYsX778pP2NREQuhH3nTjKenwVA9MgR+NarZ3IiOROLUR7HRbuR7OxsQkNDycrKOmmTTGFhIUlJSSQmJuKnE1GV6tSpEzExMSxevNjsKOVCP2cROVdGURF7e/SkcPt2Am+8gYRXXtGBEyY50+f3n2nER85Lfn4+r7zyCjfffDM2m4333nuPlStXsmLFCrOjiYhUusxXX6Nw+3asoaHEPvusSk81oOIj5+XE5rBJkyZht9tp2LAhS5YsoWPHjmZHExGpVAW//krmK68AEDN2LN5RUSYnknOh4iPnxd/fn5UrV5odQ0TEVC6Hg9SRI6G4mOCbbybk1r+ZHUnOkS5ZISIicp4yX56DfecubBERxDwzTpu4qhEVHxERkfOQ/9NPHH7jDQBiJ07AKyLC5ERyPlR8REREzpGroIDUkaPA5SLk77cTrP0bqx0VHxERkXOU/sILOPbtK7kA6ZgxZseRC6DiIyIicg7y1m/g6Fsl5yuLnTwJWzlcQFkqX7UqPmvXruX2228nLi4Oi8XC0qVLy9xvGAbjx48nLi4Of39/2rVrx6+//mpOWBERcRvO3DxSR48GIOyuuwi6/nqTE8mFqlbFJy8vj+bNmzNnzpxT3j99+nRmzZrFnDlz2LhxIzExMXTq1ImcnJxKTipnU7duXWbPnm12DBGRc5I+fTpFBw/iHR9P1IgRZseRi1Ctik+XLl2YNGkS3bt3P+k+wzCYPXs2Y8aMoXv37jRt2pRFixaRn5/Pu+++e9p12u12srOzy0zupm/fvlgslpOmP1/cs6IsXLiQsLCwk+Zv3LiRAQMGVPjzi4hcrNxvvuHYv/8NQOyUKdiCAk1OJBejWhWfM0lKSiItLY3OnTuXzvP19eXGG29k3bp1p33c1KlTCQ0NLZ0SEhIqI26lu+WWW0hNTS0zJSYmmpanZs2aBAQEmPb8IiLnwpmVRerTYwEI792bwDZXmZxILpbbFJ+0tDSA0quInxAdHV1636mMGjWKrKys0ik5OblCc5rF19eXmJiYMlO/fv3o1q1bmeUGDx5Mu3btSm+3a9eOxx9/nOHDhxMREUFMTAzjx48v85hjx44xYMAAoqOj8fPzo2nTpnz22WesXr2a+++/n6ysrNJRphOP/eumrv3799O1a1eCgoIICQnh7rvv5tChQ6X3jx8/nhYtWrB48WLq1q1LaGgoPXv21GZMEalQh6ZMofjQIXzq1CFqyJNmx5Fy4HaXrPjr2TMNwzjjGTV9fX3x9fW9oOcyDAOjoOCCHnuxLP7+lXam0EWLFjFkyBDWr1/P999/T9++fbn22mvp1KkTLpeLLl26kJOTw9tvv029evXYvn07NpuNa665htmzZzNu3Dh+//13AIKCgk5av2EYdOvWjcDAQNasWUNxcTEDBw6kR48erF69unS53bt3s3TpUj777DOOHj3K3XffzXPPPcfkyZMr5X0QEc+Ss3IlWR9/AlYrsc9Nxervb3YkKQduU3xiYmKAkpGf2NjY0vnp6eknjQKVF6OggN9btqqQdZ9Nwx83YzmPTUWfffZZmdLRpUsXAgPPbTt1s2bNeOaZZwCoX78+c+bMYdWqVXTq1ImVK1eyYcMGduzYQYMGDQC45JJLSh8bGhqKxWIp/fmcysqVK9m6dStJSUmlmxoXL15MkyZN2LhxI1deeSUALpeLhQsXEhwcDEDv3r1ZtWqVio+IlLviI0dIfWY8ADX6PUDAFVeYG0jKjdts6kpMTCQmJoYVK1aUznM4HKxZs4ZrrrnGxGRVQ/v27dmyZUvp9NJLL53zY5s1a1bmdmxsLOnp6QBs2bKFWrVqlZaeC7Fjxw4SEhLK7F/VuHFjwsLC2LFjR+m8unXrlpaev+YQESkvhmGQNmEizsOH8a1/KZGDBpkdScpRtRrxyc3NLXMkUlJSElu2bCEiIoLatWszePBgpkyZQv369alfvz5TpkwhICCAe++9t0LyWPz9afjj5gpZ97k89/kIDAzk0ksvLTPParViGEaZeUVFRSc91tvbu+xzWyy4XC6g5GrtF+t0myP/Ov9MOUREykv2smXkfPkleHkR+9xzWH18zI4k5ahaFZ9NmzbRvn370ttDhgwBoE+fPixcuJDhw4dTUFDAwIEDOXr0KG3atGH58uVlRgnKk8ViOa/NTVVNzZo1+eWXX8rM27Jly0kF40yaNWvGgQMH+OOPP0456uPj44PT6TzjOho3bsz+/ftJTk4uHfXZvn07WVlZXHbZZeecRUTkYhWlp5M28VkAIh9+GP8mTUxOJOWtWm3qateuXckOxX+ZFi5cCFB61FBqaiqFhYWsWbOGpk2bmhu6CuvQoQObNm3irbfeYufOnTzzzDMnFaGzufHGG7nhhhu44447WLFiBUlJSXz++ed88cUXQMnmqdzcXFatWkVmZib5+fknraNjx440a9aMXr168eOPP7Jhwwbuu+8+brzxRlq3bl0ur1VE5GwMwyBt7DhcWVn4NW5M5EM615g7qlbFR8rXzTffzNixYxk+fDhXXnklOTk53Hfffee9niVLlnDllVdyzz330LhxY4YPH146ynPNNdfw8MMP06NHD2rWrMn06dNPevyJy4+Eh4dzww030LFjRy655BI++OCDi36NIiLnKuuj/5K7Zg0Wb2/ipj2H5TxGv6X6sBh/3cnDw2VnZxMaGkpWVhYhISFl7issLCQpKYnExET8/PxMSigVTT9nEc9TdPAge/7eFVdeHlFDn6JG//5mR5LzdKbP7z/TiI+IiHg0w+Ui5emnceXl4d+iBRH33292JKlAKj4iIuLRjr7/Pvnf/4DFz4+456ZisdnMjiQVSMVHREQ8lmPfPtJnzAQg6qmn8Klb19xAUuFUfERExCMZTicpo8dgFBQQ0KYN4b0q5pxvUrWo+FwA7Q/u3vTzFfEMRxa9RcHmzVgDAoidPBmLVR+JnkA/5fNgO77d1+FwmJxEKtKJn69N2/lF3JZ91y4yZs8GIGrUSHxqxZsbSCpNtTpzs9m8vLwICAggIyMDb29vrPrrwO24XC4yMjIICAjAy0u/HiLuyCgqImXESAyHg8AbrifszjvNjiSVSP+znweLxUJsbCxJSUns27fP7DhSQaxWK7Vr1z7l9cNEpPrLfO01Cn/9FWtoKLHPTtLvuodR8TlPPj4+1K9fX5u73JiPj49G80TcVMEvv5I57xUAYsaOxTs6yuREUtlUfC6A1WrVGX1FRKoZl91OysgRUFxM8M03E3Lr38yOJCbQn7UiIuIRMl56Cceu3dgiI4kZ/4w2cXkoFR8REXF7+Zs3c+TNBQDETpyAV3i4yYnELCo+IiLi1lx5eaSMHAWGQeg//kFwhw5mRxITqfiIiIhbOzRzJkXJyXjFxhI9epTZccRkKj4iIuK2cr/9jmPvvQ9A3JTJ2IKDTU4kZlPxERERt+TMziZ1zBgAwnv1IrBtW5MTSVWg4iMiIm7p0OTJFB86hE+dOkQNfcrsOFJFqPiIiIjbyV6xgqyPPwGrldjnpmL19zc7klQRKj4iIuJWijMzSXtmPAA1+vUj4IorzA0kVYqKj4iIuA3DMEgZMwbnkSP4NmhA5KDHzI4kVYyKj4iIuI1j779P3pq1WHx8iJs5A6uPj9mRpIpR8REREbdg37OHQ9OmAxA19Cn8GjQwOZFURSo+IiJS7RkOBylDh2EUFhJ47bWE//OfZkeSKkrFR0REqr2Ml+dQuH07trAwYqdMwWLVx5ucmv5liIhItZa3YQOH588HIGbiBLyjo0xOJFWZio+IiFRbzuxsUkaOLLkA6R3dCenc2exIUsWp+IiISLWVNvFZilNS8a5dm5jRo82OI9WAio+IiFRLWZ9+RvZnn4HNRvz0aVgDA82OJNWAio+IiFQ7RQcPkjZxIgCRjzyCf4sW5gaSakPFR0REqhWjqIiDQ57ClZODf4sWRD78kNmRpBpR8RERkWol46WXKPj5Z6whIcTNnInFy8vsSFKNqPiIiEi1kfvNtxx+veTQ9dhJz+JTK97kRFLdqPiIiEi1UJSeTsqIEQCE33uPDl2XC6LiIyIiVZ7hdJIyfETJVdcbNSLqeAESOV8qPiIiUuVlvvoq+T/8gCUggPhZs7D6+podSaopFR8REanS8jduJHPOvwCIGTcW30sSTU4k1ZmKj4iIVFnFR49ycOgwcLkI7dqVsG7dzI4k1ZyKj4iIVEmGy0XKiBEUHzqET2IiMePGmh1J3ICKj4iIVEmZ8+aRt/YbLL6+xL8wS5ekkHKh4iMiIlVO7jff/G+/nvHj8WvUyORE4i7cqviMHz8ei8VSZoqJiTE7loiInIeigwdJGToMDIOwHj0I+0c3syOJG3G783w3adKElStXlt622WwmphERkfPhsts58MRgnFlZ+DVtSvSY0WZHEjfjdsXHy8tLozwiItXUoclTKPzlF2yhodR6cTZWHx+zI4mbcatNXQA7d+4kLi6OxMREevbsyZ49e864vN1uJzs7u8wkIiKV79hH/+XYv/8NFgtxzz+Pd7yuwyXlz62KT5s2bXjrrbf48ssvef3110lLS+Oaa67h8OHDp33M1KlTCQ0NLZ0SEhIqMbGIiAAUbNtG2oQJAEQOeoyg6641OZG4K4thGIbZISpKXl4e9erVY/jw4QwZMuSUy9jtdux2e+nt7OxsEhISyMrKIiQkpLKiioh4rKL0dPbeeRfF6ekEtWtHrbn/wmJ1q7/LpRJkZ2cTGhp61s9vt9vH588CAwO5/PLL2blz52mX8fX1xVfXfBERMYXLbufAoEEUp6fjU68ecTNnqPRIhXLrf112u50dO3YQGxtrdhQREfkLwzBIGzeOwp+3Yg0NJWHuv7AFBZkdS9ycWxWfoUOHsmbNGpKSkli/fj133nkn2dnZ9OnTx+xoIiLyF0cWLCTr40/AZqPW7BfwqVPH7EjiAdxqU9eBAwe45557yMzMpGbNmlx99dX88MMP1NEvk4hIlZK7di3pM2cCED1yJIFt25qcSDyFWxWf999/3+wIIiJyFvY9ezj41FBwuQi7607C/9nL7EjiQdxqU5eIiFRtxZmZJD84AFdODv6tWhEzdiwWi8XsWOJBVHxERKRSuPLzSX5kIEUHD+Jduza1Xn4Ji87MLJVMxUdERCqc4XRycOgwCrdtwxYWRu3XXsUrIsLsWOKBVHxERKRCGYbBoanPkfvVV1h8fKg1dy4+deuaHUs8lIqPiIhUqCOLFnH07bcBiJs+jYCWV5icSDyZio+IiFSYrE8/Jf25aQBEDRtGyC23mJxIPJ2Kj4iIVIic1atJGTkKgPDevYl44H6TE4mo+IiISAXI37SJg08MBqeTkL/fTvSokTpsXaoEFR8RESlXhTt2kPzwIxh2O0Ht2xM3ebIuPCpVhv4liohIubEnJbG//4O4cnPxb92K+BdmYfH2NjuWSCkVHxERKReOffvY36cvzsOH8b3sMhLmzcPq52d2LJEyVHxEROSiOfbvZ1+fvhSnp+NzaT1qz38dW3Cw2bFETqLiU0n2Zu3ljW1vmB1DRKTcOZKTS0pPWho+9epRZ+FCvGrUMDuWyCm51dXZq6pjhcfotawX2Y5swv3C6V6/u9mRRETKhePAQfb16UNxaio+l1xCnYUL8IqMNDuWyGlpxKcShPmF0btxbwCe/eFZtqRvMTeQiEg5cOzdy777elOckopP3brUXrgAr5o1zY4lckYqPpVkQLMBdKrTiWJXMYO/HkxaXprZkURELljh77+z95/HS0+dOtRetBDvqCizY4mclYpPJbFarEy6dhINwhtwuPAwj3/1OHlFeWbHEhE5b/k//cS+3vfhzMzEt1Ej6rzzNt7R0WbHEjknKj6VKMA7gJc6vES4bzg7juxgyOohFDmLzI4lInLOcr/7jv0P9MOVnY3/FVdQ561F2qdHqhUVn0oWHxTP3I5z8ffyZ13KOsauG4vLcJkdS0TkrLI//5wDDz+CUVBA4LXXUvuN+dhCQsyOJXJeVHxM0DSyKbPazcLL4sX/7fk/pm+cjmEYZscSETklwzDIfO11Dj45BKOoiODOnak1by7WgACzo4mcNxUfk1wXfx0Trp0AwDs73mHmppkqPyJS5RhFRaSNG0fGrFkAhN/Xm/gXZmH18TE5mciF0Xl8TPT3en/H7rQz8fuJvLX9LawWK0NaDdEVjEWkSnDm5HDwiSfIW/c9WK1EjxpFRO9/mh1L5KKo+JjsrgZ3YRgGz/7wLAt/XUhhcSGj2ozCatFgnIiYx56UxIFBg3Ds2o0lIID452cS3L692bFELpo+XauAuxvezdNtnsaChfd/f58Ra0fgcDrMjiUiHipn1Sr23nU3jl278YqKos7it1R6xG2o+FQRPRr1YNoN0/CyevHF3i8YuGogWfYss2OJiAcxnE7SX5jNgUcfw5Wbi3+rVtT98D/4N2lidjSRcqPiU4V0SezCv276F/5e/qxPXc8/l/2TvVl7zY4lIh6g+OhRkgc8xOFXXwVKdmKus3CBzsYsbkfFp4q5Ju4a3uryFjGBMezN3su9/3cv3xz4xuxYIuLG8r7/nqS/dyXvu++w+PkRN2MGMaNHY/H2NjuaSLlT8amCGkU04r1b36NFzRbkFOUwcNVAZm2apbM8i0i5MhwODs2Ywf4H+lGckYHPJZdQ94P3Cb39NrOjiVQYFZ8qKtI/kjdufoMeDXsAsODXBfT5og/JOckmJxMRd1D4+x/s7XkPR954EwyDsB49SFzyIX4NG5odTaRCWQydNa+M7OxsQkNDycrKIqSKnIp91b5VjF03lhxHDkHeQTzV+im61++uQ95F5LwZDgeZr71O5quvQlERttBQYidPIrhjR7OjiVyUc/381idnNXBTnZv48PYPaVGzBblFuUz4fgIPfPkASVlJZkcTkWqkYNsvJN11N5lz5kBREUE33UTiJ5+o9IhH0YjPX1TFEZ8Til3FvLPjHf615V8UFBfgY/Whf7P+9G3SF38vf7PjiUgVVXz0KBmzX+TYv/8NhoEtLIzosU8T8re/6Uzx4jbO9fNbxecvqnLxOeFAzgEm/TCJ71K+AyAqIIrHr3ic2y65DZvVZnI6EakqDKeTYx8uIWPWLJxZJecFC7n9dqJHjsCrRg2T04mULxWfC1Qdig+UXC35y71f8sLmF0jJSwGgYXhDHrviMW6sdaP+ihPxYIZhkPv1ajJemIV95y4AfBs0IGbs0wRceaXJ6UQqhorPBaouxecEu9POezve47Wtr5FTlANAg/AGPHj5g3Sq00kjQCIeJv/HH0mfNYuCTZsBsIaGUvPRgYTfey8WL12eUdyXis8Fqm7F54Rjhcd489c3+eC3D8gvzgegdnBtejbqyd/r/Z1Q31CTE4pIRTEMg/z168mc9wr569cDYPH1JeK+3tTo3x9bqH7/xf2p+Fyg6lp8TsiyZ/Hub+/yzo53Sq/15Wfzo0tiF+5scCeXR16uzWAibsIoLibnq6848uYCCrZsKZnp7U1Yt25EPjoQ75gYU/OJVCYVnwtU3YvPCflF+Xy25zPe//19dh7dWTq/dnBtbr3kVm695FbqhNQxMaGIXKjio0fJWrKEI+++S3FKKlAywhN2553U6PcA3nFxJicUqXwqPhfIXYrPCYZhsCVjC//+/d+s2r+KguKC0vsuDbuUG2rdQLuEdjSLbKb9gUSqMKOoiNzvviPr44/JXfUVhsMBgC08nLC77iKi9z/xqlnT5JQi5lHxuUDuVnz+LL8on6+Sv+L/9vwf36d8j9Nwlt4X7htO27i2XBlzJa2jW1MnpI42iYmYzHC5KNy2jexln5P12Wc4Dx8uvc+38WVE/LM3Ibf+Dauvr4kpRaoGFZ8L5M7F58+y7Fl8d/A7Vh9YzbcHvyXHkVPm/pr+NWkd3ZqmkU25rMZlXBZxGUE+QSalFfEcrsJC8r7/ntyvviZn9dc4MzJL77NFRBB6+22Edu2K72WX6Y8TkT9R8blAnlJ8/qzIVcSW9C2sT13PpkOb2JqxlSLXyVeCrxtSl8tqXEaD8AYkhiaSGJpIQnAC3lZvE1KLuAeXw0Hhtm3kb9hA3oYNFPy0BaOwsPR+a2AggTdcT+jtfyfo+uuweOv3TeRUPLr4zJ07lxkzZpCamkqTJk2YPXs2119//Tk91hOLz1/ZnXa2Zmzlx0M/sv3wdrYf2U5aXtopl/WyeFEruBZ1QuoQFxRHbGAssYGxxATGEBcUR6R/pC6mKnKcUVyMfc8eCrdvp/DX7ce//lqm6AB4xcQQ3KEDQR06EHjVlVh8fExKLFJ9eGzx+eCDD+jduzdz587l2muv5dVXX2X+/Pls376d2rVrn/XxKj6ndqTwCDsO72D74e3sztpNUlYSSVlJZXaWPhUvqxcRfhFlpnC/cCL8IqjhV4MQnxCCfIJKJu+SKdgnGB+b/qOX6slVUEDxoUMUHUqn6OBBHHv34khKKvm6b1/pTsl/ZouIIOCqqwi46koCr7oKn3r1tBlL5DxVWPHp27cvDzzwADfccMNFh6wIbdq0oWXLlsybN6903mWXXUa3bt2YOnXqWR9fEcXHcLkoyM85+4LVjGEYpBdksD93P/tzkjlUkE5afhpp+Yc4VHCIjILMMjtQnw9vqzdB3oH42/zxtfn+ZfL53/fW/83ztnpjs9rwsnhhs9iwWW3YLDa8rMdv/+l7L4sNm9ULL4sNq8V6fFTKgtViwYIFLBasWLAcv33i64nRqzLfWyxYsWKxwPFHlXnchbBwoY+7gMdc8Afs+T/udK/rVBFO/x78b75hGOB0YnE6odgJxcVQ7MRwOrEYgMsFTmfJV5cLXMb/vi+db2AxDAyXE5ynWM7lAqcLw3CVPEduPkZuLkZePuTkYuTmYeTkYhw+givzMOTknvlN8PfH1qAetgaX4tWoPrZGDbDWScBiPfXI6KnehVO9N6f/OZ5i2XL4OZxy/mkynOtrKFnFuec91WNLfhdVGqs6/4Dg0/6bv1Dn+vl93ucvz8nJoXPnziQkJHD//ffTp08f4uPjLypseXE4HGzevJmRI0eWmd+5c2fWrVt3ysfY7Xbsdnvp7ezs7HLPVZCfQ8DMs482VUeJx6dTKQYybTYO26wcsdk4YrNx1Fry/WGblaM2G9lWK7lWCzlWK3nHJyjZ7+io/RhHOVZJr0TMYjEMwnIhPBfCcg1C8yEsr+T74ALwd4C/3cDPcfx7B/g5wMsJXi6z059aoTccCYbMEAupEZASUfI1NcJCepgDw/Ib8FvJL8kvxycpNzbDwGaADQMvA6wY2AAvo+SrrfTr/5axYWA1wAsDH8PAz3X8q2Hge5rJz1Vyf5DLRbDrxFcXQS4XgYaBNvKfXv7Q/QQEmXNG8fMuPkuWLOHw4cO8/fbbLFy4kGeeeYaOHTvSr18/unbtireJO95lZmbidDqJjo4uMz86Opq0tFPvozJ16lQmTJhQGfE8jhcQ43QS43QCJ+8sfSpOIM9qIc9iJcdqJd9qwW7531RosWC3/u97x4l5FitFFnBaLBQDxRYLTkpuFx3/6jw+v9gCxVhwWsBJyW0AFxYMKJkslH7vOv7XpgG4/jS/ZLKcYvnj88/zj87zGXqtqGXP1/ms29duUCsTEjIgPtMg6hhEHYOaWeBTXH6ZXBZwWo//rCzgOv6960/fG3+5/dfvyzyudL4FlxXyfSHP78RXC3m+kO8HxwLhSLCFI0FQ4MtpRz+k4jktJb/fFzYGWj4shkHg8VIU4nQR4XIS4XRRw+mkhrPs9zHFTiJcLhPTepaL3sfnp59+4s0332T+/PkEBQXxz3/+k4EDB1K/fv3yynjOUlJSiI+PZ926dbRt27Z0/uTJk1m8eDG//fbbSY851YhPQkKCNnWJXATD4cC+4zfsW7dh37qVoj92Unww5fQPsFqx1aiBrUYE1oiI0u9tYWFYgoKwBgZgDQjAEhiANSAQS0AAFh/vkotuenlhOT7h5VXuw+fn41T/nRqnqYennX8e/yWfzzpOn+N0Ky+P13Luy54uyXm9FsPAabhwGk5chhOn4aTYVfK1ZJ7r+LzisvNcTopLly+myFWE3Wk/Pjmwu+yltx1Ox/++dzkoKC4ktyiX3KI88opLvp7qqNiz8bX5EhsQS2xANLEBscQERpMQlEDd4DokBNVyu6Nnq9Wmrj9LTU1l+fLlLF++HJvNxt/+9jd+/fVXGjduzPTp03nyyScvZvXnLTIyEpvNdtLoTnp6+kmjQCf4+vriW8En/7JYraYN6YlUBsPppODnreR9+w153/9A4S+/YBSd/J+/V1QUvg0b4lu/Pj61a+OdUAufhAS8Y2N1mLa4DbvTTo4jh1xHLrlFuWTbszlceJgjhUc4XHCYw4Ul05GCI2QUZJBZkIndaWdvzl725uw9aX1eFi8SQhKoF1qPemH1aFyjMU0jmxIVEFX5L84NnPeIT1FREZ988gkLFixg+fLlNGvWjP79+9OrVy+Cg4MBeP/993nkkUc4evRohYQ+kzZt2tCqVSvmzp1bOq9x48Z07drVtJ2bRdyRMyeHnFWryFu7ltzv1uHKyipzvy0iAv+WVxBwxRX4NWmKb8MGeIWHm5RWpOpyOB2k5aVxMPcgqXmpHMw9SEpuCvuy97H72G7yi/NP+bgo/yiaRDahSY0mtIxuSfOazT36iNgKG/GJjY3F5XJxzz33sGHDBlq0aHHSMjfffDNhYWHnu+pyMWTIEHr37k3r1q1p27Ytr732Gvv37+fhhx82JY+IO3Hl55Pz9ddkL/ucvLVry4zqWENCCLz2GoKuu46A1q3xrl1bR9eInAMfmw+1Q2pTO+Tkg2AMw+BQ/iH2HNvDnqw9/HH0D345/Au7j+0mvSCd9OR0vk7+GijZXNYiqgVtYtrQJrYNTSOb6jxqp3DeIz6LFy/mrrvuws/Pr6IyXbS5c+cyffp0UlNTadq0KS+88MI5H36vER+RsgzDoPDnnzn63vtkL1+OUfC/czf51KtHcOdOBF1/A/7NLi/Zz0ZEKlx+UT6/HfmNXzJ/YVvmNjambeRw4eEyy0T6R9I+oT0danfgqpir3H40yGNPYHixVHxESrjy8sj69DOOvv8+9j8dGOCdkEDI3/5GyN/+hm+D+hrVEakCDMMgKSuJ9WnrWZ9aMuUW/e+cUoHegXRI6MDt9W7nqpirsFltJqatGCo+F0jFRzxdUXo6Rxcv5uh77+PKLfmP0+LrS0iXLoT1uBv/Fi1UdkSquCJnERvTNvJV8ld8tf8rMgoySu+LDojm9nq3c2eDO4kPqhrn4SsPKj4XSMVHPJUjOZnD898g67//Lb2sgk/duoT17EFYt27YTNpvT0QujstwsTVjK5/t+YzPkz4n21Fyol6rxUr7hPbc2+heroy5str/QaPic4FUfMTTFB06ROa8eRz7cEnJJR8A/yuuoMaABwm68UZTz4sjIuXL4XSwOnk1H/7xId+nfl86v2F4Qx5q/hA31b6p2u4QreJzgVR8xFM4s7LIfO01jr79Dsbxk3gGXnstkY88jH+rVtX+rz8RObPdx3bz3m/v8cnuT0ovOF0/vD4PNXuITnU6VbsCpOJzgVR8xN0ZTifHPlxCxuzZOI+fa8u/ZUuinhxMwJVXmpxORCpblj2LxdsX886Od0p3iG5cozEjrhxBy+iWJqc7dyo+F0jFR9xZ/ubNpE2ejH37DgB8Lq1H1NChJZu0NMIj4tGy7Fm8veNtFm9fTF5RHgC31L2FIa2GEBsUa3K6s1PxuUAqPuKOnDk5pM+YybF//xsAa3AwNQc9Rvg99+hSESJSRmZBJnN+msNHOz/CwMDP5sdjVzzGPy/7Z5U+DF7F5wKp+Ii7yVm5krQJEynOKDmcNfTOO4gaMgSviAiTk4lIVfbbkd+YtmEamw5tAqBZzWY8e82zXBJ2icnJTk3F5wKp+Ii7cGZnkzZ+AtnLlgHgU6cOMc9OJPCqq0xOJiLVhWEYLNm5hJmbZpJXlIeP1YdBVwzivib3Vbmdn8/187tqpRaRcpG3YQN7unYrKT02GzUeeojETz5W6RGR82KxWLizwZ0s7bqUa+OvxeFy8Pzm53l01aMcKTxidrwLohGfv9CIj1RnhsNBxstzODx/PhgG3nVqEz9jBv7NmpkdTUSqOcMw+HDnh0zbMA27006UfxQz283kiqgrzI4GaMRHxOM4Dhxg7729OPz662AYhN55B5d89JFKj4iUC4vFwl0N7uLdW98lMTSR9IJ0HvjyAf67879mRzsvKj4ibiD3m29JuuNOCn/5BWtoKPEvvkjcpElYAwPNjiYibqZBeAPev/V9OtXpRLGrmHHrxjF943ScLqfZ0c6Jio9INWa4XGTOm0fygAG4srLwa9aMS5b+l5CbO5sdTUTcWIB3ADNvnMkjzR8BYPH2xQxbOwyH02FysrNT8RGpppzZ2Rx49DEyXnwJDIOwHj2o8/ZivGOr/onGRKT6s1qsDGwxkBk3zsDb6s2KfSsYuHIguY5cs6OdkYqPSDXkSE5mb897yP36ayw+PsROnkzshPFYfXzMjiYiHuaWurcwr+M8ArwCWJ+2nn7L+5FlzzI71mmp+IhUMwVbtrC3R08ce/bgFRNDnXffJeyO7mbHEhEP1ia2DQtuWUCEXwTbD29nwIoBVbb8qPiIVCPZX3zJvj59cR45gm/jy6j7wQf4N21idiwRERrXaMz8zvNLy8/DKx4m25FtdqyTqPiIVAOGYXD4jTc4OHgwht1OULt21F28GO/oKLOjiYiUqh9en9c7v064bzi/HP6FR1c+SmFxodmxylDxEaniDMMg/blppM+YCUD4P/9JrX/N0aHqIlIlNQhvwOudXyfYJ5gtGVsYtnYYxa5is2OVUvERqcIMp5PUp5/myKJFAESNHEHM02Ow2KruFZJFRBpGNGROhzn42nxZnbyaST9MoqpcKELFR6SKcjkcHHxyCFlLPgKrldipU6nRt6/ZsUREzknL6JZMu2EaVouVJTuX8MYvb5gdCVDxEamSXPn5HHhkIDnLl2Px9iZ+9guE/aOb2bFERM7LTbVvYvRVowF46ceXWJ282tQ8oOIjUuW48vLYP2AAed99h8Xfn4RXXyGks87ELCLVU49GPejRsAcGBiO/GcnuY7tNzaPiI1KFuPLzSX7oYQo2bcYaHEztN98g8JprzI4lInJRRlw1glbRrcgryuPxrx439Rw/Kj4iVYQrP5/khx8hf9MmrEFB1H5jPgFXXGF2LBGRi+Zt9WZWu1nEBcaRlpfGr4d/NS2Ll2nPLCKlXAUFJD8ykPwNG7AGBlJ7/uv4N2tmdiwRkXIT4RfBSx1ewuF0cHnNy03LoeIjYjJXYSHJAweSv3491oAAEl5/Hf8WLcyOJSJS7hpGNDQ7gjZ1iZjJKCri4JNDyP/+BywBASTMf52Altq8JSJSUVR8RExiuFykPv10yRXWfX1JeGUeAS1bmh1LRMStqfiImMAwDNKnTSPr40/AZiP+hRcIvOoqs2OJiLg9FR8RExx+5RWOLHoLgLgpkwnu0N7kRCIinkHFR6SSHX3/fTJefAmA6NGjCO3a1eREIiKeQ8VHpBLlfPU1aROfBSBy4CNE3HefyYlERDyLio9IJSnY9gsHn3oKXC7C7rqTyEGDzI4kIuJxVHxEKoHjwEGSH3kEo6CAwOuuI2bcOCwWi9mxREQ8joqPSAVzZmWR/NBDODMz8W3UiPjZs7F4e5sdS0TEI6n4iFQgw+HgwKDHcezejVdMDAmvvoItKNDsWCIiHkvFR6SCGIZB6oQJpdffSnj1Fbyjo82OJSLi0VR8RCrI0cVvk7XkI7BaiZ/9An4Nzb9GjYiIp1PxEakAud99x6HnngMgatgwgq6/3uREIiICKj4i5c6xdy8Hh5Qcth7arRsRffuYHUlERI5T8REpR86cHJIffQxXVhb+zZsTM2G8DlsXEalC3Kr41K1bF4vFUmYaOXKk2bHEQxhOJylDh5UcwRUdTfzLL2H19TU7loiI/ImX2QHK28SJE3nwwQdLbwcFBZmYRjxJxuwXyV2zBouvL7XmzME7KsrsSCIi8hduV3yCg4OJiYk55+Xtdjt2u730dnZ2dkXEEjeXvWIFh19/HYDYyZPxv7ypyYlERORU3GpTF8C0adOoUaMGLVq0YPLkyTgcjjMuP3XqVEJDQ0unhISESkoq7sKxdy+po0YDENGnD6G33WpyIhEROR2LYRiG2SHKywsvvEDLli0JDw9nw4YNjBo1iq5duzJ//vzTPuZUIz4JCQlkZWUREhJSGbGlGnPl57O3R0/sO3fi36oVdRYu0OUoRERMkJ2dTWho6Fk/v6t88Rk/fjwTJkw44zIbN26kdevWJ81fsmQJd955J5mZmdSoUeOcnu9c3zgRwzBIGTGC7E8+xRYZSeJHS7Rfj4iISc7187vK7+Pz2GOP0bNnzzMuU7du3VPOv/rqqwHYtWvXORcfkXN19L33yP7kU7DZqPXCLJUeEZFqoMoXn8jISCIjIy/osT/99BMAsbGx5RlJhIItWzg09fiZmZ96ioArrzQ5kYiInIsqX3zO1ffff88PP/xA+/btCQ0NZePGjTz55JP8/e9/p3bt2mbHEzdSfPQoBwY/CUVFBHfuTMT9fc2OJCIi58htio+vry8ffPABEyZMwG63U6dOHR588EGGDx9udjRxI4ZhkDpyFMVpafjUrUvslMk6M7OISDXiNsWnZcuW/PDDD2bHEDd3ZOGikpMU+vgQ/+JsbDpBpohIteJ25/ERqSgF27aRPmsWANGjRuLXsKHJiURE5Hyp+IicA2dODgefHFK6X0/YWY40FBGRqknFR+QsDMMgddw4ig4cwDsujthJz2q/HhGRakrFR+Qsjv37P+R8/gV4eRE/63lsOrGliEi1peIjcgaFv//BoSlTAIga/AT+LVqYG0hERC6Kio/Iabjy8zk4ZAiG3U7gddcR8cADZkcSEZGLpOIjchqHnpuGY/duvGrWJG7ac1is+nUREanu9D+5yCnkrFrFsX//G4C46dPw0rXeRETcgoqPyF8UZ2SQ+vRYACLuv5/Atm1NTiQiIuVFxUfkTwzDIGX0GJxHj+LbqBE1nxxsdiQRESlHKj4if3L0nXfJ++YbLL6+xM+YjtXHx+xIIiJSjlR8RI6z79pF+owZAEQNHYpv/fomJxIRkfKm4iMCuBwODg4dVnroevg/e5kdSUREKoCKjwiQ8eKL2H/7DVt4OLFTJuuSFCIibkrFRzxe3g/rOfLmAgBiJz2Ld1SUyYlERKSiqPiIR3NmZZEyciQYBmF33UXwTTeZHUlERCqQio94tLQJEylOS8OnTh2iR400O46IiFQwFR/xWNlffEH2smVgsxE3YzrWgACzI4mISAVT8RGPVJyZSdr4CQDUGPAg/s2amZxIREQqg4qPeBzDMEh9ZjzOY8dKzs78yCNmRxIRkUqi4iMeJ/uTT8hdtQq8vUuuuq6zM4uIeAwVH/EoRWlppE2aDEDNRx/Fr2FDkxOJiEhlUvERj2EYBqlPj8WVk4Nfs2bU6N/P7EgiIlLJVHzEYxz7z3/I+/ZbLD4+xE2dgsXLy+xIIiJSyVR8xCM4Dhwk/blpANR88kl869UzOZGIiJhBxUfcnuFykTp6NK78fPxbtSLivt5mRxIREZOo+IjbO/rOu+Rv2IDF379kE5fNZnYkERExiYqPuDV7UhLpzz8PQNSwofjUrm1yIhERMZOKj7gtw+kkddRojMJCAtpeTXjPnmZHEhERk6n4iNs6snAhBVu2YA0MJG7yZCxW/XMXEfF0+iQQt2TfuZOM2S8CED16FN5xcSYnEhGRqkDFR9yOUVREyshRGEVFBN54A6Hdu5sdSUREqggVH3E7ma+9RuGvv2INDSV24rNYLBazI4mISBWh4iNupXD7djLnvQJAzNNP4x0dZXIiERGpSlR8xG24HA5SRo6C4mKCO3Ui5LZbzY4kIiJVjIqPuI3MOf/C/scf2CIiiBn/jDZxiYjISVR8xC0U/Pwzh+fPByBm/DN41ahhciIREamKVHyk2nMVFpZs4nK5CLn9dkI6dzY7koiIVFEqPlLtZbwwG0dSEl41axLz9Biz44iISBWm4iPVWv7GjRx56y0AYic9iy001OREIiJSlan4SLXlyssjZdRoMAxC77yDoBtvNDuSiIhUcSo+Um0dmjmTogMH8IqLJXrkSLPjiIhINVBtis/kyZO55pprCAgIICws7JTL7N+/n9tvv53AwEAiIyN5/PHHcTgclRtUKkXut99x7L33AYibPBlbUJDJiUREpDrwMjvAuXI4HNx11120bduWN95446T7nU4nt956KzVr1uTbb7/l8OHD9OnTB8MwePnll01ILBXFmZ1N6tNPAxDeqxeBbduanEhERKqLalN8JkyYAMDChQtPef/y5cvZvn07ycnJxB2/Evfzzz9P3759mTx5MiEhIad8nN1ux263l97Ozs4u3+BS7g5NmUpxWhredWoT9dQQs+OIiEg1Um02dZ3N999/T9OmTUtLD8DNN9+M3W5n8+bNp33c1KlTCQ0NLZ0SEhIqI65coJxVq8hauhSsVuKmPoc1IMDsSCIiUo24TfFJS0sjOjq6zLzw8HB8fHxIS0s77eNGjRpFVlZW6ZScnFzRUeUCFR89Suq4ZwCo8cD9BLS8wuREIiJS3ZhafMaPH4/FYjnjtGnTpnNe36muzWQYxhmv2eTr60tISEiZSaoewzBIGz8B5+HD+Na/lMhBg8yOJCIi1ZCp+/g89thj9OzZ84zL1K1b95zWFRMTw/r168vMO3r0KEVFRSeNBEn1k71sGTlffgleXsROfQ6rr6/ZkUREpBoytfhERkYSGRlZLutq27YtkydPJjU1ldjYWKBkh2dfX19atWpVLs8h5ig6lE7axGcBiHz4YfybNjE5kYiIVFfV5qiu/fv3c+TIEfbv34/T6WTLli0AXHrppQQFBdG5c2caN25M7969mTFjBkeOHGHo0KE8+OCD2nxVjRmGQeq4sbiysvBr0oTIhwaYHUlERKqxalN8xo0bx6JFi0pvX3FFyY6tX3/9Ne3atcNms/F///d/DBw4kGuvvRZ/f3/uvfdeZs6caVZkKQdZS5aQt2YtFh8f4p6bisXb2+xIIiJSjVkMwzDMDlGVZGdnExoaSlZWlkaKTOY4cJCkv/8dV34+UcOGUaPfA2ZHEhGRKupcP7/d5nB2cS+Gy0XqmDG48vPxb9mSiL59zI4kIiJuQMVHqqSj77xL/vr1WPz9iZs6BYvNZnYkERFxAyo+UuXYd+8m/fi+WVHDhuJTp47JiURExF2o+EiVYjgcpAwbjmG3E3jttYSf5TxPIiIi50PFR6qUjJfnULh9O7awMGKnTMFi1T9REREpP/pUkSojf+NGDs+fD0DMxAl4R0eZnEhERNyNio9UCc6cHA6OGAGGQegd3Qnp3NnsSCIi4oZUfKRKSHv2WYpTUvFOSCB61Giz44iIiJtS8RHTZf3f/5H9yadgsxE3fRq2oECzI4mIiJtS8RFTFaWkkDZ+AlByAdKA45ciERERqQgqPmIaw+UiZeQoXDk5+DVvRuTDD5kdSURE3JyKj5jm8Ovzyd+wAUtAAPHTp+sCpCIiUuFUfMQU+T/+SMZLLwEQM2aMzs4sIiKVQsVHKp3z2DEODh0KTicht99OaPd/mB1JREQ8hIqPVCrDMEh5+umSQ9fr1CbmmWewWCxmxxIREQ+h4iOV6ui775K7chV4exP//Cwdui4iIpVKxUcqTeGOHaQ/Nw2A6GFD8W/axOREIiLiaVR8pFK48vI4+OQQjKIigtq3J7x3b7MjiYiIB1LxkQpnGAap4yfg2LsXr+hoYqdM1n49IiJiChUfqXBH33uP7E9LLkkRP3MGXuHhZkcSEREPpeIjFarg5585NPU5AKKGDCHgyitNTiQiIp5MxUcqTPGRIxx4YjAUFRHcqRMRD9xvdiQREfFwKj5SIQynk5ShQylOS8Onbl1ip07Rfj0iImI6FR+pEBkvv0zeuu+x+PtT6+WXsAUFmR1JRERExUfKX/aKFRx+5VUAYidOxLd+fZMTiYiIlFDxkXJVuGMHKcNHABDeuzeht99mciIREZH/UfGRclN8+DDJjz6KUVBA4DXXED1iuNmRREREylDxkXLhcjg4MOhxilNS8alTh/gXZmHx8jI7loiISBkqPnLRDMMgbfwECn78EWtwMLXmzcMWGmp2LBERkZOo+MhFO7JwEVkffQRWK/EvvIDvJYlmRxIRETklFR+5KNlffEH69OkARI8YTtB115qcSERE5PRUfOSC5W/cSMqw4WAYhPfqRfh995kdSURE5IxUfOSC2HftIvnRxzCKigju1JHo0aN0ZmYREanyVHzkvBUdOsT+AQNwZWfj36IFcTNmYLHZzI4lIiJyVio+cl6KDx9mf9/7Sw5br1uXWvPmYvXzMzuWiIjIOVHxkXPmPHaM/Q/0w5GUhFdsLLXfmI9XeLjZsURERM6Zio+cE2duLvsHPIT999+x1YykzoI38Y6PNzuWiIjIeVHxkbNy5uaR/PDDFG7dii0sjNpvvIFP3bpmxxIRETlvuqaAnJEzK4v9Dw6gcOtWrEFBJMyfj1+DBmbHEhERuSAqPnJaxYcPs79ff+y//YYtNJSEN97Av2kTs2OJiIhcMBUfOaWiQ4dKdmTevRtbZCS133xDIz0iIlLtaR8fOUnhb7+xt0dPHLt34xUTQ53Fb6n0iIiIW6g2xWfy5Mlcc801BAQEEBYWdsplLBbLSdMrr7xSuUGrudy1a9l3by+K09LwueQS6rz9Nr6JuuioiIi4h2qzqcvhcHDXXXfRtm1b3njjjdMut2DBAm655ZbS26GhoZUR76wMpxNXbi62KpLnVI68+y6HJk0Gl4uAq6+m1ouzq3ReERGR81Vtis+ECRMAWLhw4RmXCwsLIyYmphISnTvDMDg0eQp569aR8Nqr+NSubXakMlwFBaRNfJas//4XgNA7uhP7zDNYfHxMTiYiIlK+qs2mrnP12GOPERkZyZVXXskrr7yCy+U64/J2u53s7OwyU3lzHjtGzuqvcezdy96e91CwdWu5P8eFsiclsbdHz5LSY7USNfQpYidNUukRERG35FbF59lnn+U///kPK1eupGfPnjz11FNMmTLljI+ZOnUqoaGhpVNCQkK55/IKD6fue+/j2/gynEeOsO++PuSsXFnuz3M+DJeLI++8Q1L3O7D/8UfJkVsLFlCjf39dZV1ERNyWxTAMw6wnHz9+fOkmrNPZuHEjrVu3Lr29cOFCBg8ezLFjx866/ueff56JEyeSlZV12mXsdjt2u730dnZ2NgkJCWRlZRESEnL2F3EenLl5HHzySfK++QaAiL59iRryZKWPrjiSk0kdO478H34AIODqq4mbPg3vqKhKzSEiIlJesrOzCQ0NPevnt6n7+Dz22GP07NnzjMvUvYhLI1x99dVkZ2dz6NAhoqOjT7mMr68vvr6+F/wc58MWFEjC3H9xaPoMji5ezJGFC8nfuJG4GdPxveSSCn9+V34+ma+9xpE3F2A4HFj8/Yka+hTh99yDxepWg38iIiKnZGrxiYyMJDIyssLW/9NPP+Hn53faw9/NYPH2JmbMaALbXk3qqNEU/vore/7elYj77iNy4CPYgoLK/TlddjvHlizh8KuvUXzoEAABba8m9plndM0tERHxKNXmqK79+/dz5MgR9u/fj9PpZMuWLQBceumlBAUF8emnn5KWlkbbtm3x9/fn66+/ZsyYMQwYMKDSRnTOR3CHDvh9vJS08RPIXb2aI2++SdYnn1Cjbx/C7r4bWzlsZis+epSs/y7lyMKFFKenA+AdH0/UyBEEd+yofXlERMTjmLqPz/no27cvixYtOmn+119/Tbt27fjiiy8YNWoUu3btwuVycckll9C/f38effRRvLzOvd+d6zbC8pS7Zg1pU6ZQtG8/ANaAAEK7dSPktlvxb9HivDZDOXNyyPv+e7I//5yclaugqAgAr5gYajzYn7A778RaBYugiIjIxTjXz+9qU3wqixnFB8BwOMj67P84smAB9p07S+fbwsMJuOoq/Jo0wfeSRGwREdiCg7F4e+PMzcOVk41jfzL2nTsp3L6dgp9/Bqez9PF+TZoQ1uNuQrt1w6pD1EVExE2p+Fwgs4rPCYZhkPfdOrI//YSclatw5eWd9zp8EhMJuuEGQrt1xe+yyyogpYiISNVSLY7qkpNZLBaCrruWoOuuxXA4KPjlF/I3bsK+cyeOfftwZmfhysrGKCrCGhyMNTAQ75gYfBs0wLd+fQKuuhKfWrXMfhkiIiJVkopPFWbx8SGgZUsCWrY0O4qIiIhb0MlbRERExGOo+IiIiIjHUPERERERj6HiIyIiIh5DxUdEREQ8hoqPiIiIeAwVHxEREfEYKj4iIiLiMVR8RERExGOo+IiIiIjHUPERERERj6HiIyIiIh5DxUdEREQ8hoqPiIiIeAwvswNUNYZhAJCdnW1yEhERETlXJz63T3yOn46Kz1/k5OQAkJCQYHISEREROV85OTmEhoae9n6LcbZq5GFcLhcpKSkEBwdjsVjMjmOq7OxsEhISSE5OJiQkxOw4bkvvc+XRe1059D5XDr3PZRmGQU5ODnFxcVitp9+TRyM+f2G1WqlVq5bZMaqUkJAQ/VJVAr3PlUfvdeXQ+1w59D7/z5lGek7Qzs0iIiLiMVR8RERExGOo+Mhp+fr68swzz+Dr62t2FLem97ny6L2uHHqfK4fe5wujnZtFRETEY2jER0RERDyGio+IiIh4DBUfERER8RgqPiIiIuIxVHzkvNntdlq0aIHFYmHLli1mx3Ere/fupV+/fiQmJuLv70+9evV45plncDgcZker9ubOnUtiYiJ+fn60atWKb775xuxIbmXq1KlceeWVBAcHExUVRbdu3fj999/NjuX2pk6disViYfDgwWZHqTZUfOS8DR8+nLi4OLNjuKXffvsNl8vFq6++yq+//soLL7zAK6+8wujRo82OVq198MEHDB48mDFjxvDTTz9x/fXX06VLF/bv3292NLexZs0aHn30UX744QdWrFhBcXExnTt3Ji8vz+xobmvjxo289tprNGvWzOwo1YoOZ5fz8vnnnzNkyBCWLFlCkyZN+Omnn2jRooXZsdzajBkzmDdvHnv27DE7SrXVpk0bWrZsybx580rnXXbZZXTr1o2pU6eamMx9ZWRkEBUVxZo1a7jhhhvMjuN2cnNzadmyJXPnzmXSpEm0aNGC2bNnmx2rWtCIj5yzQ4cO8eCDD7J48WICAgLMjuMxsrKyiIiIMDtGteVwONi8eTOdO3cuM79z586sW7fOpFTuLysrC0D/divIo48+yq233krHjh3NjlLt6CKlck4Mw6Bv3748/PDDtG7dmr1795odySPs3r2bl19+meeff97sKNVWZmYmTqeT6OjoMvOjo6NJS0szKZV7MwyDIUOGcN1119G0aVOz47id999/n82bN7Np0yazo1RLGvHxcOPHj8disZxx2rRpEy+//DLZ2dmMGjXK7MjV0rm+z3+WkpLCLbfcwl133UX//v1NSu4+LBZLmduGYZw0T8rHY489xtatW3nvvffMjuJ2kpOTeeKJJ3jnnXfw8/MzO061pH18PFxmZiaZmZlnXKZu3br07NmTTz/9tMwHhdPpxGaz0atXLxYtWlTRUau1c32fT/xHlpKSQvv27WnTpg0LFy7EatXfKBfK4XAQEBDAf/7zH/7xj3+Uzn/iiSfYsmULa9asMTGd+xk0aBBLly5l7dq1JCYmmh3H7SxdupR//OMf2Gy20nlOpxOLxYLVasVut5e5T06m4iPnZP/+/WRnZ5feTklJ4eabb+bDDz+kTZs21KpVy8R07uXgwYO0b9+eVq1a8fbbb+s/sXLQpk0bWrVqxdy5c0vnNW7cmK5du2rn5nJiGAaDBg3iv//9L6tXr6Z+/fpmR3JLOTk57Nu3r8y8+++/n0aNGjFixAhtWjwH2sdHzknt2rXL3A4KCgKgXr16Kj3lKCUlhXbt2lG7dm1mzpxJRkZG6X0xMTEmJqvehgwZQu/evWndujVt27bltddeY//+/Tz88MNmR3Mbjz76KO+++y4ff/wxwcHBpftPhYaG4u/vb3I69xEcHHxSuQkMDKRGjRoqPedIxUekClm+fDm7du1i165dJxVKDc5euB49enD48GEmTpxIamoqTZs2ZdmyZdSpU8fsaG7jxKkC2rVrV2b+ggUL6Nu3b+UHEjkNbeoSERERj6E9JkVERMRjqPiIiIiIx1DxEREREY+h4iMiIiIeQ8VHREREPIaKj4iIiHgMFR8RERHxGCo+IiIi4jFUfERERMRjqPiIiIiIx1DxEREREY+h4iMibi0jI4OYmBimTJlSOm/9+vX4+PiwfPlyE5OJiBl0kVIRcXvLli2jW7durFu3jkaNGnHFFVdw6623Mnv2bLOjiUglU/EREY/w6KOPsnLlSq688kp+/vlnNm7ciJ+fn9mxRKSSqfiIiEcoKCigadOmJCcns2nTJpo1a2Z2JBExgfbxERGPsGfPHlJSUnC5XOzbt8/sOCJiEo34iIjbczgcXHXVVbRo0YJGjRoxa9Ystm3bRnR0tNnRRKSSqfiIiNsbNmwYH374IT///DNBQUG0b9+e4OBgPvvsM7OjiUgl06YuEXFrq1evZvbs2SxevJiQkBCsViuLFy/m22+/Zd68eWbHE5FKphEfERER8Rga8RERERGPoeIjIiIiHkPFR0RERDyGio+IiIh4DBUfERER8RgqPiIiIuIxVHxERETEY6j4iIiIiMdQ8RERERGPoeIjIiIiHkPFR0RERDzG/wOLX4BR01dvEgAAAABJRU5ErkJggg==\n"
191 |      },
192 |      "metadata": {},
193 |      "output_type": "display_data"
194 |     }
195 |    ],
196 |    "source": [
197 |     "# Plotting\n",
198 |     "plt.plot(x_values, function_and_approximations[0, :], label=\"Degree 1\")\n",
199 |     "plt.plot(x_values, function_and_approximations[4, :], label=\"Degree 5\")\n",
200 |     "plt.plot(x_values, function_and_approximations[9, :], label=\"Degree 10\")\n",
201 |     "plt.plot(x_values, function_and_approximations[20, :], label=\"Function\")\n",
202 |     "\n",
203 |     "# Add labels and legend for clarity\n",
204 |     "plt.xlabel('x')\n",
205 |     "plt.ylabel('y')\n",
206 |     "plt.legend()\n",
207 |     "\n",
208 |     "# Display the plot\n",
209 |     "plt.show()"
210 |    ],
211 |    "metadata": {
212 |     "collapsed": false
213 |    }
214 |   },
215 |   {
216 |    "cell_type": "code",
217 |    "execution_count": null,
218 |    "outputs": [],
219 |    "source": [],
220 |    "metadata": {
221 |     "collapsed": false
222 |    }
223 |   }
224 |  ],
225 |  "metadata": {
226 |   "kernelspec": {
227 |    "display_name": "Python 3",
228 |    "language": "python",
229 |    "name": "python3"
230 |   },
231 |   "language_info": {
232 |    "codemirror_mode": {
233 |     "name": "ipython",
234 |     "version": 2
235 |    },
236 |    "file_extension": ".py",
237 |    "mimetype": "text/x-python",
238 |    "name": "python",
239 |    "nbconvert_exporter": "python",
240 |    "pygments_lexer": "ipython2",
241 |    "version": "2.7.6"
242 |   }
243 |  },
244 |  "nbformat": 4,
245 |  "nbformat_minor": 0
246 | }
247 | 


--------------------------------------------------------------------------------