Day1_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fea5a97b",
   "metadata": {},
   "source": [
    "# Day 1 - Python Workshop for civil engineers:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "587e43d8-879d-482d-be6e-3923d5ecbf11",
   "metadata": {},
   "source": [
    "# Basics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ceb2b74-328d-423f-a11f-dd199291024e",
   "metadata": {},
   "source": [
    "This is the first class of this workshop.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ffb923e9-84a6-48d3-a16a-e59bb9c541eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello World!\n"
     ]
    }
   ],
   "source": [
    "print(\"Hello World!\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ceb7ee45-ed75-4ca9-916f-e007b5dcf4b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "610"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "152+458"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3e9e052b-8782-474e-83db-a8e7d8d47dd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-6+17j)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(3+4j)*(2+3j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "579b1ab2-d178-4b5f-a474-d6b95f3cc1c3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Nelson\n"
     ]
    }
   ],
   "source": [
    "s = input()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7591e1d6-cdd3-43d0-8955-1d699aaa574e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nelson\n"
     ]
    }
   ],
   "source": [
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "39ff83d1-9354-4800-b8a6-c47167507a98",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 123\n"
     ]
    }
   ],
   "source": [
    "a = input()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4326e5e4-c849-4396-bd3b-6d43714f5d9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "123\n"
     ]
    }
   ],
   "source": [
    "print(a)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "577a1bac-5e35-4d66-b25c-78d5f57f3d72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Nelson123'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s + a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fa6ee96-0b8b-4114-a944-fead7402ab3b",
   "metadata": {},
   "source": [
    "## Data Types Exploration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "f57b1250-e2e1-49f0-a8de-96fbc80bb1b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 'one', y]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Data Types:\n",
    "# list\n",
    "list1 = [1, 2, 'one', x]\n",
    "\n",
    "#tuple\n",
    "tuple1 = (1, 2, 'one', x)\n",
    "\n",
    "# How to access:\n",
    "\n",
    "list1[3] = y\n",
    "list1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "a8dbefef-f89c-44bb-8abf-15ba751c6461",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Dictionary\n",
    "dict1 = {'a': 1, 'b': 2, 'c':3}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "6428395a-04a4-4969-b2da-22d0bc49c8f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 1, 'b': 2, 'c': 3}"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "2345bf4d-bcdf-4316-bbc7-162dd4904cb0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict['a']"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict['a']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "169337d8-11b8-4d18-a531-b930ef35fb98",
   "metadata": {},
   "source": [
    "# Example 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62d8a269-765c-460e-b810-6fc9f865acce",
   "metadata": {},
   "source": [
    "Q. Calculate distance(s) if a =1, u= 23, t = 12, g = 9.81."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bea9a628-a786-46d8-8673-18a4acb50c7a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "348.0\n"
     ]
    }
   ],
   "source": [
    "# Variable Assignment:\n",
    "a = 1\n",
    "u = 23\n",
    "t = 12\n",
    "\n",
    "# Process\n",
    "s = u*t + 1/2 * a * t**2\n",
    "\n",
    "# Ouput\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2433f7eb-fcf6-4602-b41a-40e847453f50",
   "metadata": {},
   "source": [
    "# Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27b3297e-de0d-4074-a78f-8c91ce0d4393",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import library\n",
    "import sympy as sp\n",
    "# sympy.function()  ########\n",
    "# sp.function()  ########\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eaa5bd4-bf6a-4438-b3de-a3b9c8431ef3",
   "metadata": {},
   "source": [
    "# Example 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0154beb9-d689-4712-84da-7f18129c4cbb",
   "metadata": {},
   "source": [
    "Q. Solve the equation sin(x) + cos^2(x) + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "bfaa13e3-968a-43a9-afd1-6c56a6fae36b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# library import\n",
    "import sympy as sp\n",
    "\n",
    "#Variable assignment\n",
    "x = sp.symbols('x')\n",
    "\n",
    "#process\n",
    "#make expression\n",
    "exp1 = sp.sin(x) + (sp.cos(x) )**2 + 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "80ba25fd-722a-4a4c-b98a-dcdfa930fa60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sin{\\left(x \\right)} + \\cos^{2}{\\left(x \\right)} + 1$"
      ],
      "text/plain": [
       "sin(x) + cos(x)**2 + 1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "95bd647b-23b2-4f39-8b04-34790f2ceef8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x: -pi/2}, {x: 2*atan(1/2 - sqrt(3)*I/2)}, {x: 2*atan(1/2 + sqrt(3)*I/2)}]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve the expression:\n",
    "sp.solve((exp1, 0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "844968b5-f8d8-44af-9eca-3ddef2ddcbd8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-pi/2, 2*atan(1/2 - sqrt(3)*I/2), 2*atan(1/2 + sqrt(3)*I/2)]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# solve the expression:\n",
    "sp.solve(exp1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "34522839-ab6f-434b-bd2d-9b9fbba23740",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x26d11bc6110>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# plot function/exp:\n",
    "sp.plot(exp1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7391034-4411-47a6-b406-4e46b68e82a2",
   "metadata": {},
   "source": [
    "# Example 3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eae7af08-3575-4260-a16d-b97e60c43874",
   "metadata": {},
   "source": [
    "Q. Solve the following system of equation:\n",
    "\n",
    "3x + 4y^2 - 1 =0; <br>\n",
    "2x + 12y - 15 = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "1073b1d8-0dee-4d04-bf06-b38351ec3756",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import lib\n",
    "# DOne\n",
    "\n",
    "\n",
    "#Assign variables:\n",
    "x = sp.symbols('x')\n",
    "y = sp.symbols('y')\n",
    "\n",
    "#2nd technique\n",
    "x, y = sp.symbols('x y')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "10355758-d29f-4fa0-bcb5-bfb31694e02b",
   "metadata": {},
   "outputs": [],
   "source": [
    "exp2 = 3*x + 4 *y**2 -1\n",
    "exp3 = 2*x + 12*y - 15\n",
    "\n",
    "ans = sp.solve((exp2,exp3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "0812694d-78ed-4c8c-a10f-e0ad0438825a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x: -6 - 3*sqrt(5)*I/2, y: 9/4 + sqrt(5)*I/4},\n",
       " {x: -6 + 3*sqrt(5)*I/2, y: 9/4 - sqrt(5)*I/4}]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "07c10cba-92df-4016-ab64-391bd367cc06",
   "metadata": {},
   "outputs": [],
   "source": [
    "a1 = ans[0]\n",
    "a1\n",
    "a2 = ans[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "8dee992f-5be6-44ce-9143-07b8d3f103b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Values of x:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -6 - \\frac{3 \\sqrt{5} i}{2}$"
      ],
      "text/plain": [
       "-6 - 3*sqrt(5)*I/2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -6 + \\frac{3 \\sqrt{5} i}{2}$"
      ],
      "text/plain": [
       "-6 + 3*sqrt(5)*I/2"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Values of y:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{9}{4} + \\frac{\\sqrt{5} i}{4}$"
      ],
      "text/plain": [
       "9/4 + sqrt(5)*I/4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{9}{4} - \\frac{\\sqrt{5} i}{4}$"
      ],
      "text/plain": [
       "9/4 - sqrt(5)*I/4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Values of x:\")\n",
    "display(a1[x])\n",
    "display(a2[x])\n",
    "\n",
    "print(\"Values of y:\")\n",
    "display(ans[0][y])\n",
    "display(ans[1][y])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fafbd7b-4f98-4d2a-9f74-ecddcd62ef78",
   "metadata": {},
   "source": [
    "# Example 4:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "27c67d58-95c7-4176-ab06-559dc0833894",
   "metadata": {},
   "source": [
    "Find the centriod of given parabolic figure:<br>\n",
    "![image.png](https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRsHMk29SWgld8ndthVJibsdrzW_0kY2Bjb2PfSenA-_2gWgQtsdcAE2wgklGFmBoaYNyc&usqp=CAU)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a02efee-fbc6-400e-a82a-4b010a7b5b7e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "377e947f-a019-4a7e-a9ba-f415a0d657a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# assign variables / define symbols\n",
    "x, y, k = sp.symbols('x, y, k')\n",
    "a, b = sp.symbols('a, b', constant = True)\n",
    "\n",
    "# make exp\n",
    "# evaluate\n",
    "# output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "61c48211-6ad9-4670-ae4d-50a7679965b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{b}{a^{2}}$"
      ],
      "text/plain": [
       "b/a**2"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find k\n",
    "#  y = kx**2\n",
    "k = y/ x**2\n",
    "# Substitute x,y = a,b\n",
    "k_val = k.subs([(x, a), (y, b) ])\n",
    "k_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "c4062b5e-1c27-46f3-a26e-64ed0d306802",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{b x^{2}}{a^{2}}$"
      ],
      "text/plain": [
       "b*x**2/a**2"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  integrate  --    kx2 dx\n",
    "\n",
    "itr1 = k_val * x**2\n",
    "itr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "92e15ea0-d7b6-493b-922c-afce6a2768e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int\\limits_{0}^{a} \\frac{b x^{2}}{a^{2}}\\, dx$"
      ],
      "text/plain": [
       "Integral(b*x**2/a**2, (x, 0, a))"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "area = sp.Integral(itr1, (x, 0, a) ) \n",
    "area\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "45269a2d-564e-4761-a95d-76c866cb3fcf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a b}{3}$"
      ],
      "text/plain": [
       "a*b/3"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = area.doit()\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "bc387d28-64f5-4b6a-98d4-5161f4e1200b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\int\\limits_{0}^{a} \\frac{b x^{3}}{a^{2}}\\, dx$"
      ],
      "text/plain": [
       "Integral(b*x**3/a**2, (x, 0, a))"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "itr2 = x* itr1\n",
    "upper = sp.Integral(itr2, (x, 0, a) )\n",
    "upper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "eb591cc6-707c-4274-847a-3a729686a143",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_avg:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 a}{4}$"
      ],
      "text/plain": [
       "3*a/4"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#compute x_bar\n",
    "\n",
    "x_bar = upper.doit() / A\n",
    "print ('x_avg:') \n",
    "x_bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d13308e0-6bd3-4277-80ac-ea6d3946068c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "616c1899-b99d-40ab-95e2-808a14d67c2e",
   "metadata": {},
   "source": [
    "Please complete this problem to find y coordinate of centriod too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1546bfe-951c-4b4a-ade7-f830d1239dee",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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