References/01 Numpy intro.ipynb

{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 01 Introduction to Numpy Module\n",
    "---\n",
    "\n",
    "## Introduction 🤔\n",
    "\n",
    "### What is NumPy?\n",
    "[![NumPy](https://img.shields.io/badge/Numpy-013243?style=flat&logo=numpy&logoColor=white)](https://numpy.org/) stands for numeric python which is a python package for the computation and processing of the multidimensional and single dimensional array elements.\n",
    "\n",
    "**Travis Oliphant** created NumPy package in 2005 by injecting the features of the ancestor module Numeric into another module Numarray.\n",
    "\n",
    "It is an extension module of Python which is mostly written in \"C\". It provides various functions which are capable of performing the numeric computations with a high speed.\n",
    "\n",
    "NumPy provides various powerful data structures, implementing multi-dimensional arrays and matrices. These data structures are used for the optimal computations regarding arrays and matrices.\n",
    "\n",
    "In this tutorial, we will go through the numeric python library NumPy.\n",
    "\n",
    "---\n",
    "\n",
    "### The need of NumPy?\n",
    "With the revolution of data science, data analysis libraries like NumPy, SciPy, Pandas, etc. have seen a lot of growth. With a much easier syntax than other programming languages, python is the first choice language for the data scientist.\n",
    "\n",
    "NumPy provides a convenient and efficient way to handle the vast amount of data. NumPy is also very convenient with Matrix multiplication and data reshaping. NumPy is fast which makes it reasonable to work with a large set of data.\n",
    "\n",
    "There are the following advantages of using NumPy for data analysis.\n",
    "\n",
    "* NumPy performs array-oriented computing.\n",
    "* It efficiently implements the multidimensional arrays.\n",
    "* It performs scientific computations.\n",
    "* It is capable of performing Fourier Transform and reshaping the data stored in multidimensional arrays.\n",
    "* NumPy provides the in-built functions for linear algebra and random number generation.\n",
    "---\n",
    "NumPy when combined with SciPy and Mat-plotlib is used as the replacement to MATLAB as Python is more complete and easier programming language than MATLAB.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np #Importing numpy module\n",
    "import matplotlib.pyplot as plt #Importing matplotlib for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8,  9,  5,  2,  5,  3,  7,  4,  6, 35, 46,  3,  6, 46,  3, 67])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([8,9,5,2,5,3,7,4,6,35,46,3,6,46,3,67]) #Makes an array of your desired numbers\n",
    "x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0.])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = np.zeros(2) #Makes an array of zeroes\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1.])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = np.ones(4) #Makes an array of ones\n",
    "z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.66451547, 0.87057818, 0.80232863, 0.1781389 , 0.87595003])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.random.random(5) #Makes an array of your random numbers\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.74000638,  0.75561225,  1.55452783,  0.25034893, -1.43271991])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.random.randn(5) #Makes an array of natural random numbersa #Calling a variable\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.11111111, 0.22222222, 0.33333333, 0.44444444,\n",
       "       0.55555556, 0.66666667, 0.77777778, 0.88888889, 1.        ])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = np.linspace(0,1,10) #Makes an array of your desired range with equal intervals\n",
    "q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = np.arange(0,10,1) #Makes an array/range of your desired range with equal intervals\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p+5 #Adding 5 to every element of array "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False, False, False, False, False,  True,  True,  True,\n",
       "        True])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p>5 #Gives you a boolean array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example of Sin funtion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-10,10,2000) #Making a linear space array\n",
    "y = np.exp(x) #Defining a fxn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y) #Ploting the data\n",
    "plt.xlabel('X',fontsize=20) #Labeling X axis\n",
    "plt.ylabel('exp(x)',fontsize=20) #Labeling Y axis\n",
    "plt.legend('y') #Legend \n",
    "plt.grid() #Grid on\n",
    "plt.show() #Used to plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-5,5,100) #Making a linear space array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def x_square(x): #Defining a function\n",
    "    return x**2 \n",
    "\n",
    "plt.plot(x, x_square(x)) #PLoting\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array Indexing/Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  4,  6,  8, 10])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1 = np.array([2,4,6,8,10]) #Defining an array\n",
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[3] #Calls 3rd element of array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6,  8, 10])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[2:] #Calls all elements after 2nd postion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4, 6])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[:-2] #Calls all elements before 2nd postion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True,  True,  True])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1>5 #Checks if given conditon is true of false"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6,  8, 10])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[x1>5] #Checks and gives you values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 8])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[x1%4==0] #Checks and gives you values on given condition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculus / Statistical Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "y1 = np.linspace(0,10,2) #Defining a variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean, standard deviation, and percentiles of arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(y1) #Gives you the mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(y1) #Gives you the median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(y1) #Gives you the std deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.0"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(y1,90) #Gives you the percentile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0., 10.])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1 #Gives you the array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Integrals and derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.linspace(1,10,1000) #Defiining an array\n",
    "b = np.sin(a) #Defining a function\n",
    "dydx = np.gradient(b,a) #Calling np.gradient for derivative\n",
    "y_intergal = np.cumsum(b) * (a[1]-a[0]) #Calling np.cumsum for integration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x206b3f80eb0>]"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#PLotting the data\n",
    "plt.plot(a,b)\n",
    "plt.plot(a,dydx)\n",
    "plt.plot(a,y_intergal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic fluid flow examples in a pipe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Liquid *n-hexane* flows at a rate of **m = 0.75 kg/s** in a pipe with inside diameter **D = 5 cm**. What are the volumetric flow rate, molar flow rate and velocity? What would these quantities be same if **Diameter of pipe is chaning from 5 cm to 2 cm.**\n",
    "\n",
    "**Assume the liquid n-hexane density as 689 kg/m3**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mass_flow_rate = 0.75 #Mass flow rate in kg/s\n",
    "Density = 659 # Density in kg/m3\n",
    "Dia_of_pipe = 5 #Defining a pipe diameter\n",
    "Dia_of_pipe * 10**-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0011380880121396055"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Volumetric_Flow = Mass_flow_rate/Density #Finding volumetric flow rate\n",
    "Volumetric_Flow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.70908183053288"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Molar_flow_rate = Mass_flow_rate * 10**3 / 86.117\n",
    "Molar_flow_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.001963495408493621"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Area_of_pipe = (np.pi/4) * (Dia_of_pipe*10**-2)**2\n",
    "Area_of_pipe\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.579623464978071"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Velocity = Volumetric_Flow/Area_of_pipe\n",
    "Velocity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> #### Now solving using Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02      , 0.02030303, 0.02060606, 0.02090909, 0.02121212,\n",
       "       0.02151515, 0.02181818, 0.02212121, 0.02242424, 0.02272727,\n",
       "       0.0230303 , 0.02333333, 0.02363636, 0.02393939, 0.02424242,\n",
       "       0.02454545, 0.02484848, 0.02515152, 0.02545455, 0.02575758,\n",
       "       0.02606061, 0.02636364, 0.02666667, 0.0269697 , 0.02727273,\n",
       "       0.02757576, 0.02787879, 0.02818182, 0.02848485, 0.02878788,\n",
       "       0.02909091, 0.02939394, 0.02969697, 0.03      , 0.03030303,\n",
       "       0.03060606, 0.03090909, 0.03121212, 0.03151515, 0.03181818,\n",
       "       0.03212121, 0.03242424, 0.03272727, 0.0330303 , 0.03333333,\n",
       "       0.03363636, 0.03393939, 0.03424242, 0.03454545, 0.03484848,\n",
       "       0.03515152, 0.03545455, 0.03575758, 0.03606061, 0.03636364,\n",
       "       0.03666667, 0.0369697 , 0.03727273, 0.03757576, 0.03787879,\n",
       "       0.03818182, 0.03848485, 0.03878788, 0.03909091, 0.03939394,\n",
       "       0.03969697, 0.04      , 0.04030303, 0.04060606, 0.04090909,\n",
       "       0.04121212, 0.04151515, 0.04181818, 0.04212121, 0.04242424,\n",
       "       0.04272727, 0.0430303 , 0.04333333, 0.04363636, 0.04393939,\n",
       "       0.04424242, 0.04454545, 0.04484848, 0.04515152, 0.04545455,\n",
       "       0.04575758, 0.04606061, 0.04636364, 0.04666667, 0.0469697 ,\n",
       "       0.04727273, 0.04757576, 0.04787879, 0.04818182, 0.04848485,\n",
       "       0.04878788, 0.04909091, 0.04939394, 0.04969697, 0.05      ])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Mass_flow_rate = 0.75 #Mass flow rate in kg/s\n",
    "Density = 659 # Density in kg/m3\n",
    "Dia_of_pipe = np.linspace(2,5,100) #Defining a pipe diameter\n",
    "Dia_of_pipe * 10**-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0011380880121396055"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Volumetric_Flow = Mass_flow_rate/Density #Finding volumetric flow rate\n",
    "Volumetric_Flow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.70908183053288"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Molar_flow_rate = Mass_flow_rate * 10**3 / 86.117\n",
    "Molar_flow_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00031416, 0.00032375, 0.00033349, 0.00034337, 0.00035339,\n",
       "       0.00036356, 0.00037388, 0.00038433, 0.00039493, 0.00040568,\n",
       "       0.00041657, 0.00042761, 0.00043878, 0.00045011, 0.00046157,\n",
       "       0.00047319, 0.00048494, 0.00049684, 0.00050889, 0.00052107,\n",
       "       0.00053341, 0.00054588, 0.00055851, 0.00057127, 0.00058418,\n",
       "       0.00059723, 0.00061043, 0.00062377, 0.00063726, 0.00065089,\n",
       "       0.00066467, 0.00067859, 0.00069265, 0.00070686, 0.00072121,\n",
       "       0.00073571, 0.00075035, 0.00076513, 0.00078006, 0.00079513,\n",
       "       0.00081035, 0.00082571, 0.00084122, 0.00085687, 0.00087266,\n",
       "       0.0008886 , 0.00090469, 0.00092091, 0.00093729, 0.0009538 ,\n",
       "       0.00097046, 0.00098726, 0.00100421, 0.00102131, 0.00103854,\n",
       "       0.00105592, 0.00107345, 0.00109112, 0.00110893, 0.00112689,\n",
       "       0.00114499, 0.00116324, 0.00118163, 0.00120017, 0.00121885,\n",
       "       0.00123767, 0.00125664, 0.00127575, 0.00129501, 0.00131441,\n",
       "       0.00133395, 0.00135364, 0.00137347, 0.00139345, 0.00141357,\n",
       "       0.00143384, 0.00145425, 0.0014748 , 0.0014955 , 0.00151634,\n",
       "       0.00153733, 0.00155846, 0.00157974, 0.00160116, 0.00162272,\n",
       "       0.00164443, 0.00166628, 0.00168828, 0.00171042, 0.00173271,\n",
       "       0.00175514, 0.00177771, 0.00180043, 0.00182329, 0.0018463 ,\n",
       "       0.00186945, 0.00189274, 0.00191618, 0.00193977, 0.0019635 ])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Area_of_pipe = (np.pi/4) * (Dia_of_pipe*10**-2)**2\n",
    "Area_of_pipe\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.62264666, 3.51531496, 3.41268357, 3.31448201, 3.22045895,\n",
       "       3.13038065, 3.04402948, 2.96120263, 2.88171089, 2.80537757,\n",
       "       2.73203754, 2.66153632, 2.59372926, 2.52848083, 2.46566388,\n",
       "       2.4051591 , 2.34685438, 2.29064434, 2.23642982, 2.18411749,\n",
       "       2.13361937, 2.08485253, 2.03773874, 1.99220412, 1.94817887,\n",
       "       1.90559701, 1.86439613, 1.82451715, 1.78590412, 1.74850403,\n",
       "       1.71226658, 1.6771441 , 1.6430913 , 1.61006518, 1.57802488,\n",
       "       1.54693156, 1.51674825, 1.4874398 , 1.45897271, 1.43131509,\n",
       "       1.40443653, 1.37830805, 1.35290199, 1.32819197, 1.3041528 ,\n",
       "       1.2807604 , 1.25799178, 1.23582495, 1.21423891, 1.19321352,\n",
       "       1.17272955, 1.15276856, 1.1333129 , 1.11434566, 1.09585061,\n",
       "       1.07781223, 1.06021559, 1.04304639, 1.0262909 , 1.00993593,\n",
       "       0.99396881, 0.97837738, 0.96314995, 0.94827527, 0.93374253,\n",
       "       0.91954133, 0.90566166, 0.89209389, 0.87882874, 0.86585727,\n",
       "       0.85317089, 0.8407613 , 0.8286205 , 0.81674079, 0.80511474,\n",
       "       0.79373517, 0.78259516, 0.77168805, 0.76100737, 0.75054691,\n",
       "       0.74030066, 0.7302628 , 0.72042772, 0.71079   , 0.70134439,\n",
       "       0.69208582, 0.68300939, 0.67411034, 0.66538408, 0.65682617,\n",
       "       0.64843232, 0.64019834, 0.63212021, 0.62419401, 0.61641597,\n",
       "       0.60878241, 0.60128977, 0.59393462, 0.58671359, 0.57962346])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Velocity = Volumetric_Flow/Area_of_pipe\n",
    "Velocity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Dia_of_pipe,Velocity,'+--') #Ploting the data\n",
    "plt.xlabel('Diameter of Pipe',fontsize=20) #Labeling X axis\n",
    "plt.ylabel('Velocity of fluid in pipe',fontsize=20) #Labeling Y axis\n",
    "plt.grid() #Grid on\n",
    "plt.show() #Used to plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dealing with 2D functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function in 2 dimensions. Try this..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0,10,1000) #Defining an array\n",
    "y = np.linspace(0,5,1000) #Defining an array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xv,yv = np.meshgrid(x,y) #Creating a mesh\n",
    "zv = xv**2+yv**2 #calling the function\n",
    "plt.contourf(xv,yv,zv,levels=40) #Calling contour\n",
    "plt.colorbar() #calling color bar for intensity\n",
    "plt.show() #used to plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Linear Algebra"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1,2,3],[1,2,3],[1,2,3]]) #Craeating an array\n",
    "b1 = np.array([1,2,3]) #Craeating an array\n",
    "b2 = np.array([4,2,3]) #Craeating an array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [2, 2, 2],\n",
       "       [3, 3, 3]])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.T #used for transpose"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(b1,b2) #Used for dot product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  9, -6])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross(b1,b2) #used for cross product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Systems of Equations\n",
    "\n",
    "$ 3x + 2y + z = 4$\n",
    "\n",
    "$ 5x -5y + 4z = 3$\n",
    "\n",
    "$ 6x +z = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[3,2,1],[5,-5,4],[6,0,1]])\n",
    "C = np.array([4,3,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.49056604,  1.26415094,  2.94339623])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.solve(A,C) #used to find values of x y z variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding Eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 1.61168440e+01, -1.11684397e+00, -1.30367773e-15]),\n",
       " array([[-0.23197069, -0.78583024,  0.40824829],\n",
       "        [-0.52532209, -0.08675134, -0.81649658],\n",
       "        [-0.8186735 ,  0.61232756,  0.40824829]]))"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.eig(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples to practice\n",
    "\n",
    "### Question 1\n",
    "\n",
    "Let $f(x,y) = e^{-(x^2+y^2)} \\cdot \\sin(x)$ for $-2 \\leq x \\leq 2$ and $-2 \\leq y \\leq 2$\n",
    "\n",
    "1. Make a contour plot of $f$\n",
    "2. Find the volume $|f(x,y)|$ in the specified $x$ and $y$ range\n",
    "3. Find the volume $|f(x,y)|$ only in the region where $\\sqrt{x^2+y^2}>0.5$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x206b449c9a0>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-2,2,1000)\n",
    "y = np.linspace(-2,2,1000)\n",
    "xv,yv = np.meshgrid(x,y)\n",
    "f = np.exp(-xv**2-yv**2)*np.sin(xv)\n",
    "g = np.exp(-x**2-y**2)*np.sin(x)\n",
    "plt.contourf(xv,yv,f,levels=1000)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x206b4217df0>]"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4861858145125453"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diff(x)[0]*np.diff(y)[0]*sum(np.abs(f.ravel()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "92700.93306683759"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(np.abs(f.ravel()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.344765293020408"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diff(x)[0]*np.diff(y)[0]*sum(np.abs(f[xv**2+yv**2>0.25].ravel()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2\n",
    "\n",
    "After examining a circuit full of resistors, you find that the voltage at 4 specified points is given by\n",
    "\n",
    "$ 3V_1 + 2V_2 + 3V_3 + 10V_4 = 4$\n",
    "\n",
    "$ 2V_1 - 2V_2 + 5V_3 + 8V_4 = 1$\n",
    "\n",
    "$ 3V_1 + 3V_2 + 4V_3 + 9V_4 = 3$\n",
    "\n",
    "$ 3V_1 + 4V_2 - 3V_3 - 7V_4 = 2$\n",
    "\n",
    "Find all the voltages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[3,2,3,10],[2,-2,5,8],[3,3,4,9],[3,4,-3,-7]])\n",
    "B = np.array([4,1,3,2])\n",
    "C = np.linalg.solve(A,B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.78378378,  0.03603604, -0.67567568,  0.36036036])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C"
   ]
  }
 ],
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