Priprema za prvi kolokvij.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probni prvi kolokvij\n",
    "\n",
    "## Nakić 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pomoću for petlji napišite ekvivalent donjeg koda\n",
    "```py\n",
    "q = [r**2 for r in [10**i for i in range(5)]]\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "unutarnja = [10**i for i in range(5)]\n",
    "q = [r**2 for r in unutarnja]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "unutarnja = []\n",
    "for i in range(5):\n",
    "    unutarnja.append(10**i)\n",
    "q = []\n",
    "for r in unutarnja:\n",
    "    q.append(r**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 100, 10000, 1000000, 100000000]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = []\n",
    "for i in range(5):\n",
    "    r = 10**i\n",
    "    q.append(r**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "q = []\n",
    "for i in range(0, 10, 2): q.append(10**i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 100, 10000, 1000000, 100000000]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "skup = {broj + 5 for broj in range(5, 99, 7) if broj % 3 == 1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{24, 45, 66, 87}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "skup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "skup = set()\n",
    "for broj in range(5, 99, 7):\n",
    "    if broj % 3 == 1:\n",
    "        skup.add(broj + 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{24, 45, 66, 87}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "skup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "rječnik = {ime: len(ime) for ime in 'Borna Ivka Mare Silvana'.split()}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Borna': 5, 'Ivka': 4, 'Mare': 4, 'Silvana': 7}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rječnik"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "rječnik = {}\n",
    "for ime in 'Borna Ivka Mare Silvana'.split():\n",
    "    rječnik[ime] = len(ime)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Borna': 5, 'Ivka': 4, 'Mare': 4, 'Silvana': 7}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rječnik"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "velika = [i + j for i in range(10) for j in range(i) if j % 3 != i % 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 3, 4, 5, 5, 6, 5, 7, 8, 6, 7, 9, 10, 7, 8, 9, 10, 11, 12, 13, 9, 10, 12, 13, 15, 9, 11, 12, 14, 15, 17]\n"
     ]
    }
   ],
   "source": [
    "print(velika)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "velika = []\n",
    "for i in range(10):\n",
    "    for j in range(i):\n",
    "        if j % 3 != i % 4:\n",
    "            velika.append(i + j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 3, 4, 5, 5, 6, 5, 7, 8, 6, 7, 9, 10, 7, 8, 9, 10, 11, 12, 13, 9, 10, 12, 13, 15, 9, 11, 12, 14, 15, 17]\n"
     ]
    }
   ],
   "source": [
    "print(velika)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nakić 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Napišite funkciju koja za ulaz prima broj $N$. Funkcija treba kreirati slučajan `numpy` niz duljine $N$ s uniformnom distribucijom, zatim treba naći broj $M$ brojeva u nizu koji leže između $0.5$ i $0.6$, te treba vratiti broj $\\frac{M}{N}$. Učinite funkciju interaktivnom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def proporcija(N):\n",
    "    niz = np.random.uniform(size=N)\n",
    "    M = ((niz > .5) & (niz < .6)).sum()\n",
    "    return M / N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d8c4a94326d743228c00c7ba296c5440",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=10, description='N', min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.proporcija>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import ipywidgets\n",
    "slajder = ipywidgets.IntSlider(min=1, max=100, step=1, value=10)\n",
    "ipywidgets.interact(proporcija, N=slajder)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nakić 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Riješite sljedeću ODJ koristeći Runge-Kutta metodu četvrtog stupnja\n",
    "na segmentu $[0,4]$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\left ( \\frac{d}{d x} y{\\left (x \\right )} = \\frac{1}{2 \\left(y{\\left (x \\right )} - 1\\right)}, \\quad y{\\left (0 \\right )} = \\sqrt{\\varepsilon} + 1\\right )$$"
      ],
      "text/plain": [
       "⎛d               1                 ____________    ⎞\n",
       "⎜──(y(x)) = ────────────, y(0) = ╲╱ varepsilon  + 1⎟\n",
       "⎝dx         2⋅(y(x) - 1)                           ⎠"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy as sp\n",
    "sp.init_printing()\n",
    "y = sp.Function('y')\n",
    "x = sp.Symbol('x')\n",
    "epsilon = sp.Symbol('varepsilon')\n",
    "\n",
    "(sp.Eq(sp.Derivative(y(x),x),1/sp.factor(2*(y(x)-1))),\n",
    " sp.Eq(y(0), 1 + sp.sqrt(epsilon)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ovdje je $ε=10^{−3}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import ode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def desna_strana(x, y):\n",
    "    return 1 / (2*(y-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.00024858])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "epsilon = 10**-3\n",
    "jednadžba = ode(desna_strana)\n",
    "jednadžba.set_integrator('dopri5')\n",
    "jednadžba.set_initial_value(np.sqrt(epsilon) + 1)\n",
    "jednadžba.integrate(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pokušaj provjere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "sp.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{d}{d x} y{\\left (x \\right )} = \\frac{1}{2 \\left(y{\\left (x \\right )} - 1\\right)}$$"
      ],
      "text/plain": [
       "d               1      \n",
       "──(y(x)) = ────────────\n",
       "dx         2⋅(y(x) - 1)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = sp.Function('y')\n",
    "x = sp.Symbol('x')\n",
    "epsilon = sp.Symbol('varepsilon')\n",
    "\n",
    "jednadžba = sp.Eq(sp.Derivative(y(x),x),1/sp.factor(2*(y(x)-1)))\n",
    "jednadžba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left [ y{\\left (x \\right )} = - \\sqrt{C_{1} + x} + 1, \\quad y{\\left (x \\right )} = \\sqrt{C_{1} + x} + 1\\right ]$$"
      ],
      "text/plain": [
       "⎡           ________               ________    ⎤\n",
       "⎣y(x) = - ╲╱ C₁ + x  + 1, y(x) = ╲╱ C₁ + x  + 1⎦"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sva_rješenja = sp.dsolve(jednadžba)\n",
    "sva_rješenja"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALgAAAAaBAMAAAD2yYsRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHaZIu+JVM27RDKrZt2dj8xZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACnklEQVRIDbVVz2sTQRT+drP5talhERUPRbftWVpPtio0ICoeWuLNixJ78qTV2pOgAT2sIJKrUDT4D0Tw4jEUvUiUBUW8KBEUPIjGIlUs/nhvd2Z2J822qcQHM/O973vvm+lsdgv0H6k/G0f/Tj0qT/TgBkY9HZjTeiOrup4bGJOq/7PVjOh8meiwO1HZTLBqomKolFR6gIXtSy3/WFJFEp8rCcWoJpQYbRLM08ACjT4ie1IVvVBoTiEdZHzAuOsAqW+RcCmCAmXdEAwf/qq09wrtVEgHeyjNcYNdjoRkc5jK3GqrhlxdQQ3so2x6nqbCRMRvYm6MuTjqmNRgjD6+T3eSifVGLkAbsH4zYZR4DkOYi1bm5LUEJ89kyxhH3gd24a37EdhW5ZpzHsd1hoBDw3Rp3xXOKB6FCyDMRSuzmvnxVBV3UJwHzuKCc5nUNpVoMVuhtMhjLeQfPg9XZS5amdXMnbSLFaTrfL6bJKLQ4TkW9usyZa9opINnZABXA5n+ug+ed4uwaEXG826f8rwmy8EDbTiFNaTrlNImFOvMkf1F9DsaxWDfK9KcGHEtopUI/eSYhFkOrgW0CYXd5vn8Z45PDIEz1FOhNfyFT/QwD1u5VrsWLCHfDB7oRbODEflAuU7FeB05hzJrlaYMofBaKBEnF63coJtPoeHz78/+nu9YPh2vQiV67K1hIWCu+cjuJ9RlLlu5Rjcfnpsu8V0YyyNjb0jNPeAaLeg6bgSEMdU6yKDLXLayJM1TT34843ySRvT6zzKlh7VqNzWmyzyuSfOAG6oaPwls/OG6pz6aoc+itNshgVrj7y+Kft4lJV8Scs9PbqMl1HA58mVZyxMTe/QQa1ZNVKhd4h3y1YxzW8EzorjnvzlTbr0Vx/9c+xfoyLSa5Hv03gAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$y{\\left (x \\right )} = \\sqrt{C_{1} + x} + 1$$"
      ],
      "text/plain": [
       "         ________    \n",
       "y(x) = ╲╱ C₁ + x  + 1"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opće_rj = sva_rješenja[1]\n",
    "opće_rj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\sqrt{\\varepsilon} + 1 = \\sqrt{C_{1}} + 1$$"
      ],
      "text/plain": [
       "  ____________         ____    \n",
       "╲╱ varepsilon  + 1 = ╲╱ C₁  + 1"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "početni = opće_rj.subs({x: 0, y(x): 1 + sp.sqrt(epsilon)})\n",
    "početni"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$y{\\left (x \\right )} = \\sqrt{\\varepsilon + x} + 1$$"
      ],
      "text/plain": [
       "         ________________    \n",
       "y(x) = ╲╱ varepsilon + x  + 1"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partikularno = opće_rj.subs(sp.solve(početni)[0])\n",
    "partikularno"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Decimal('0.001000000000000000020816681711721685132943093776702880859375')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import decimal\n",
    "decimal.Decimal(10**-3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0x1.0624dd2f1a9fcp-10'"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(10**-3).hex()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC0AAAAPBAMAAACCUFuUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEJmJZjLNVN0i77urRHZ72Yd1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArklEQVQYGX2PMQ4BQRSG/2Vlis2G0IjGHkChoHcER9hO4wQuoFG4wboBR9hI1G5CRGI78b9/nk5MMV++LzPzdoH+bA5b4lfoKwz31sUomx6QHtAumUVtyfnKntUID3bR5c7erZE37KKL9XGB/M0uulivpug82UUX9cK7sYry7x2OCj43NC52Pjsh1XcaXazzV1ol54ou1rHFaJm8IiWA+uB2AXaAqG1yXC944ef6ADl3SYbbzLB1AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$0.001$$"
      ],
      "text/plain": [
       "0.001"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "10**-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'short'"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "sys.float_repr_style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$y{\\left (4 \\right )} = 3.0002499843769528198776145001049815577976516561481474503907$$"
      ],
      "text/plain": [
       "y(4) = 3.0002499843769528198776145001049815577976516561481474503907"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partikularno.subs({epsilon: sp.S(10)**-3, x: 4}).n(59)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nakić 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nacrtajte funkciju $v(x)$\n",
    "za $μ=1$, $μ=0.01$ te $μ=0.001$\n",
    "na segmentu $[0,1]$ koristeći $10000$ točaka."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$v{\\left (x \\right )} = \\frac{- e^{\\frac{x}{\\mu}} + 1}{- e^{\\frac{1}{\\mu}} + 1}$$"
      ],
      "text/plain": [
       "          x    \n",
       "          ─    \n",
       "          μ    \n",
       "       - ℯ  + 1\n",
       "v(x) = ────────\n",
       "          1    \n",
       "          ─    \n",
       "          μ    \n",
       "       - ℯ  + 1"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = sp.Function('v')\n",
    "mu = sp.Symbol('mu')\n",
    "\n",
    "definicija = sp.Eq(v(x), (1-sp.E**(x/mu))/(1-sp.E**(1/mu)))\n",
    "definicija"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "domena = np.linspace(0, 1, 10_000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb2d9de8400>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb2d9de82b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.plot([0, 1, 1], [0, 0, 1], label='$\\mu=0.001$')\n",
    "for mi in 0.01, 1, 0.1, 0.005:\n",
    "    slika = (1 - np.e ** (domena / mi)) / (1 - np.e ** (1 / mi))\n",
    "    plt.plot(domena, slika, label=f'$\\mu={mi}$')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb2d99c4b00>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb2d9b439e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([0, 1, 1], [0, 0, 1], label='$\\mu=0.001$')\n",
    "for mi in 0.01, 1:\n",
    "    slika = (1 - np.e ** (domena / mi)) / (1 - np.e ** (1 / mi))\n",
    "    plt.plot(domena, slika, label=f'$\\mu={mi}$')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\lim_{t \\to \\infty}\\left(\\frac{- e^{t \\left(- y + 1\\right)} + 1}{- e^{t} + 1}\\right)$$"
      ],
      "text/plain": [
       "    ⎛   t⋅(-y + 1)    ⎞\n",
       "    ⎜- ℯ           + 1⎟\n",
       "lim ⎜─────────────────⎟\n",
       "t─→∞⎜        t        ⎟\n",
       "    ⎝     - ℯ  + 1    ⎠"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi = sp.Symbol('mu')\n",
    "t = sp.Symbol('t')\n",
    "y = sp.Symbol('y', positive=True)\n",
    "sp.Limit(definicija.rhs, mi, 0, '+')\n",
    "sp.Limit(definicija.rhs.subs({1/mi: t, x: 1-y}), t, sp.oo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nakić 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pomoću `sympy`ja, izraz `log(x**y*a**b)` pojednostavite do izraza `b*log(a) + y*log(x)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "sp.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\log{\\left (a^{b} x^{y} \\right )}$$"
      ],
      "text/plain": [
       "   ⎛ b  y⎞\n",
       "log⎝a ⋅x ⎠"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, a = sp.symbols('x a', positive=True)\n",
    "y, b = sp.symbols('y b', real=True)\n",
    "izraz = sp.log(x**y * a**b)\n",
    "izraz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$b \\log{\\left (a \\right )} + y \\log{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "b⋅log(a) + y⋅log(x)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.expand_log(izraz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$b \\log{\\left (a \\right )} + y \\log{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "b⋅log(a) + y⋅log(x)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x, y, a, b = sp.symbols('x y a b')\n",
    "sp.expand_log(sp.log(x**y * a**b), force=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Čačić 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Što ispisuje sljedeći kod i zašto?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "[5, 3]\n"
     ]
    }
   ],
   "source": [
    "a = b = 5\n",
    "a += 3\n",
    "print(b)\n",
    "\n",
    "a = b = [5]\n",
    "a += [3]\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABIAAAAUBAMAAAByuXB5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NMolEIpm7EKvvVGZvmWXoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAcklEQVQIHWMQMmEAgcdqDGEMDBWdUxiAdBgD1waG+AQwi3sBA88BMItHgYH7C5jF/AvGAupk+gUWA7LyA2AsbYgpDAwcDTCWBFAByGQG3gaGcgjLg4FBHMxiVw3tVgCzmP///w9hAZXDdOBhCamAJYXUAD28Hbf6IzqfAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left [ 2\\right ]$$"
      ],
      "text/plain": [
       "[2]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mojalista = [2]\n",
    "list.__add__(mojalista, [3])\n",
    "mojalista"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Čačić 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulirajte bacanje pristranog novčića (vjerojatnost glave je 55%) 1000 puta. Kolika je vjerojatnost da u tih 1000 bacanja broj glava bude veći od broja pisama? Rezultat odredite numerički iz simulacije tako da ponovite pokus (svih 1000 bacanja) 100 000 puta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "broj_bacanja = 1000\n",
    "broj_pokusa = 100_000\n",
    "vjerojatnost_glave = .55\n",
    "\n",
    "pokusi = np.random.uniform(size=(broj_bacanja, broj_pokusa))\n",
    "glave = pokusi < vjerojatnost_glave"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$0.99901$$"
      ],
      "text/plain": [
       "0.99901"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "broj_glava = glave.sum(axis=0)\n",
    "broj_pisama = broj_bacanja - broj_glava\n",
    "(broj_glava > broj_pisama).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Domaća zadaća: dodajte interaktivnost. :-)\n",
    "Alternativno: nacrtajte graf ovisnosti o pristranosti novčića."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Čačić 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zadan je sljedeći DataFrame (u datoteci `pdzad.csv`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Writing pdzad.csv\n"
     ]
    }
   ],
   "source": [
    "%%file pdzad.csv\n",
    "2016-07-17\t450\t628.578622\tgirl\tred\n",
    "2014-02-17\t418\t226.950670\tboy\tred\n",
    "2016-03-03\t418\t208.042709\tgirl\tred\n",
    "2014-04-28\t26\t915.238500\tboy\tblue\n",
    "2014-09-07\t182\t744.946901\tboy\tgreen\n",
    "2014-07-21\t345\t542.665316\tgirl\tblue\n",
    "2014-01-21\t807\t396.394572\tboy\tyellow\n",
    "2016-01-23\t36\t792.745992\tboy\tblue\n",
    "2015-07-07\t44\t616.078044\tgirl\tbluedatum\n",
    "2014-08-18\t390\t527.061301\tboy\tyellow\n",
    "2014-04-02\t456\t4.716575\tgirl\tgreen\n",
    "2015-12-20\t584\t577.939367\tboy\tblue\n",
    "2015-03-18\t718\t919.344036\tgirl\tyellow\n",
    "2015-04-26\t792\t623.799887\tboy\tred\n",
    "2015-08-23\t938\t927.630485\tboy\tyellow\n",
    "2015-09-27\t14\t40.380074\tgirl\tblue\n",
    "2014-07-15\t26\t451.519075\tgirl\tblue\n",
    "2016-05-15\t116\t969.555910\tboy\tred\n",
    "2015-04-15\t209\t827.094101\tboy\tyellow\n",
    "2014-03-03\t202\t811.039542\tboy\tred\n",
    "2015-01-07\t254\t512.529009\tgirl\tblue\n",
    "2015-09-01\t2\t703.001673\tgirl\tyellow\n",
    "2016-04-26\t667\t187.608667\tboy\tred\n",
    "2016-01-23\t312\t884.018403\tgirl\tblue\n",
    "2014-10-11\t792\t585.769718\tgirl\tpurple\n",
    "2014-03-30\t507\t373.570850\tgirl\tyellow\n",
    "2015-03-27\t78\t635.718898\tgirl\tpurple\n",
    "2014-12-27\t100\t41.486492\tgirl\tpurple\n",
    "2016-04-17\t683\t138.001860\tgirl\tred\n",
    "2016-03-08\t300\t925.708079\tboy\tgreen\n",
    "2016-01-16\t925\t971.141551\tboy\tred\n",
    "2016-06-23\t317\t223.288738\tboy\tgreen\n",
    "2016-01-26\t783\t819.096804\tboy\tblue\n",
    "2015-01-28\t71\t309.760628\tboy\tblue\n",
    "2016-03-27\t325\t444.532115\tboy\tpurple\n",
    "2015-07-10\t552\t517.586297\tboy\tred\n",
    "2014-05-19\t740\t988.004758\tboy\tyellow\n",
    "2014-06-07\t463\t61.233638\tboy\tgreen\n",
    "2016-06-02\t518\t256.335606\tboy\tyellow\n",
    "2014-03-14\t528\t114.734319\tgirl\tred\n",
    "2015-06-08\t207\t731.211508\tboy\tyellow\n",
    "2015-10-09\t211\t715.706315\tboy\tred\n",
    "2014-07-08\t672\t302.847557\tboy\tyellow\n",
    "2014-05-06\t375\t957.917383\tgirl\tyellow\n",
    "2016-06-09\t530\t205.990431\tgirl\tpurple\n",
    "2016-09-06\t294\t682.120222\tgirl\tblue\n",
    "2015-09-15\t166\t190.032588\tboy\tred\n",
    "2015-01-12\t591\t978.913511\tboy\tblue\n",
    "2015-10-21\t571\t259.954915\tgirl\tgreen\n",
    "2015-09-29\t75\t414.686734\tboy\tpurple"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Za najkasniji (datumi su u prvom stupcu) redak koji u predzadnjem stupcu ima `girl` a u zadnjem `yellow`, nađite umnožak drugog i trećeg stupca."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['datum', 'prvi', 'drugi', 'spol', 'boja']"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'datum prvi drugi spol boja'.split()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "header = 'datum prvi drugi spol boja'.split()\n",
    "df = pd.read_csv('pdzad.csv', delimiter='\\t', names=header,\n",
    "                 index_col=0, parse_dates=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 50 entries, 2016-07-17 to 2015-09-29\n",
      "Data columns (total 4 columns):\n",
      "prvi     50 non-null int64\n",
      "drugi    50 non-null float64\n",
      "spol     50 non-null object\n",
      "boja     50 non-null object\n",
      "dtypes: float64(1), int64(1), object(2)\n",
      "memory usage: 2.0+ KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prvi</th>\n",
       "      <th>drugi</th>\n",
       "      <th>spol</th>\n",
       "      <th>boja</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>datum</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-03-18</th>\n",
       "      <td>718</td>\n",
       "      <td>919.344036</td>\n",
       "      <td>girl</td>\n",
       "      <td>yellow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-09-01</th>\n",
       "      <td>2</td>\n",
       "      <td>703.001673</td>\n",
       "      <td>girl</td>\n",
       "      <td>yellow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-03-30</th>\n",
       "      <td>507</td>\n",
       "      <td>373.570850</td>\n",
       "      <td>girl</td>\n",
       "      <td>yellow</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-05-06</th>\n",
       "      <td>375</td>\n",
       "      <td>957.917383</td>\n",
       "      <td>girl</td>\n",
       "      <td>yellow</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            prvi       drugi  spol    boja\n",
       "datum                                     \n",
       "2015-03-18   718  919.344036  girl  yellow\n",
       "2015-09-01     2  703.001673  girl  yellow\n",
       "2014-03-30   507  373.570850  girl  yellow\n",
       "2014-05-06   375  957.917383  girl  yellow"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subdf = df[(df['spol'] == 'girl') & (df['boja'] == 'yellow')]\n",
    "subdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "prvi           2\n",
       "drugi    703.002\n",
       "spol        girl\n",
       "boja      yellow\n",
       "Name: 2015-09-01 00:00:00, dtype: object"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subdf.loc[subdf.index.max()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$1406.0033460000002$$"
      ],
      "text/plain": [
       "1406.0033460000002"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "traženi = subdf.loc[subdf.index.max()]\n",
    "traženi['prvi'] * traženi['drugi']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Čačić 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nacrtajte u polarnom koordinatnom sustavu grafove $r=\\frac{\\left|\\sin\\vartheta\\right|}{\\vartheta}$ i $r=\\ln(1+\\vartheta)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = np.linspace(0, 2*np.pi)[1:]\n",
    "r1 = np.abs(np.sin(theta)) / theta\n",
    "r2 = np.log(1 + theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fb2d42c6908>]"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb2d3aee2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.polar(theta, r1)\n",
    "plt.polar(theta, r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Čačić 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Napišite funkciju koja prima simboličku funkciju, integrira je simbolički po varijabli `x` (ako može), dobiveni rezultat derivira simbolički i uspoređuje s originalnim ulazom. Na kraju treba ispisati jednadžbe koje proizlaze iz integriranja odnosno deriviranja."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "sp.init_printing()\n",
    "x = sp.Symbol('x')\n",
    "from IPython.display import display\n",
    "\n",
    "def provjeri_integral(fja):\n",
    "    integral = sp.Integral(fja, x)\n",
    "    intfja = integral.doit()\n",
    "    prva = sp.Eq(integral, intfja, evaluate=False)\n",
    "    \n",
    "    derivacija = sp.Derivative(intfja, x)\n",
    "    derfja = derivacija.doit()\n",
    "    druga = sp.Eq(derivacija, derfja, evaluate=False)\n",
    "    \n",
    "    if derfja == fja:\n",
    "        print('Sintaksno su jednake')\n",
    "    else:\n",
    "        print('Nisu sintaksno jednake')\n",
    "\n",
    "    display(prva)\n",
    "    display(druga)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nisu sintaksno jednake\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\int x \\left(x + 1\\right)\\, dx = \\frac{x^{3}}{3} + \\frac{x^{2}}{2}$$"
      ],
      "text/plain": [
       "                  3    2\n",
       "⌠                x    x \n",
       "⎮ x⋅(x + 1) dx = ── + ──\n",
       "⌡                3    2 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{d}{d x}\\left(\\frac{x^{3}}{3} + \\frac{x^{2}}{2}\\right) = x^{2} + x$$"
      ],
      "text/plain": [
       "  ⎛ 3    2⎞         \n",
       "d ⎜x    x ⎟    2    \n",
       "──⎜── + ──⎟ = x  + x\n",
       "dx⎝3    2 ⎠         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "provjeri_integral(x*(x+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sintaksno su jednake\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\int \\sin{\\left (x \\right )}\\, dx = - \\cos{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "⌠                    \n",
       "⎮ sin(x) dx = -cos(x)\n",
       "⌡                    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{d}{d x}\\left(- \\cos{\\left (x \\right )}\\right) = \\sin{\\left (x \\right )}$$"
      ],
      "text/plain": [
       "d                   \n",
       "──(-cos(x)) = sin(x)\n",
       "dx                  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "provjeri_integral(sp.sin(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sintaksno su jednake\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\int \\sqrt{\\sin{\\left (x \\right )}}\\, dx = \\int \\sqrt{\\sin{\\left (x \\right )}}\\, dx$$"
      ],
      "text/plain": [
       "⌠                 ⌠              \n",
       "⎮   ________      ⎮   ________   \n",
       "⎮ ╲╱ sin(x)  dx = ⎮ ╲╱ sin(x)  dx\n",
       "⌡                 ⌡              "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{d}{d x} \\int \\sqrt{\\sin{\\left (x \\right )}}\\, dx = \\sqrt{\\sin{\\left (x \\right )}}$$"
      ],
      "text/plain": [
       "  ⎛⌠              ⎞             \n",
       "d ⎜⎮   ________   ⎟     ________\n",
       "──⎜⎮ ╲╱ sin(x)  dx⎟ = ╲╱ sin(x) \n",
       "dx⎝⌡              ⎠             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "provjeri_integral(sp.sqrt(sp.sin(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Domaća zadaća: pokušajte centrirati te dvije jednadžbe.\n",
    "Ustanovite programski zna li sympy integrirati vašu funkciju."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}