Basics_of_Calculus/Basics_of_Calculus.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basics of Calculus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Calculus is the study of how things change. It provides a framework to construct relatively simple quantitative models of change, and to deduce their consequences. If you graph a quadratic you will notice that you do not get a straight line. Think of this like you moving on earth. Though the earth is round, as we walk down the street it looks pretty flat to us. \n",
    "\n",
    "If you look at a quadratic function $f$ at some particular argument, call it $z$, and very close to $z$, then $f$ will look like a straight line.  This slope is often written as\n",
    "\n",
    "$f'\\left( x \\right) = y' = \\frac{{df}}{{dx}} = \\frac{{dy}}{{dx}} = \\frac{d}{{dx}}\\left( {f\\left( x \\right)} \\right) = \\frac{d}{{dx}}\\left( y \\right)$\n",
    "\n",
    "\n",
    "### What is the rate of change?\n",
    "\n",
    "On if the important applications of derivatives is finding the rate of change. That is the fact that $f'\\left( x \\right)$ represents the rate of change of $f\\left( x \\right)$. \n",
    "\n",
    "We can think of it by using an example. Think of a car, in finding the velocity of the car, we are given the position of the car at time $t$. To compute the velocity of the car we just need find the rate at which the position is changing. This can be cacluated using the function below.\n",
    "\n",
    "$\\begin{align*}Velocity & = \\frac{{{\\mbox{change in position}}}}{{{\\mbox{time traveled}}}}\\end{align*}$\n",
    "\n",
    "$\\begin{align*}Rate  of  Change = \\frac{{f\\left( t \\right) - f\\left( a \\right)}}{{t - a}}\\end{align*}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"860\"\n",
       "            height=\"460\"\n",
       "            src=\"https://www.youtube.com/embed/K2jQ0AGbYaA\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1b4c0df5508>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('K2jQ0AGbYaA', width=860, height=460)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expression : cos(x)\n",
      "Limit of expression tends to 0 : 1\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "expr = cos(x)\n",
    "\n",
    "print(\"Expression : {}\".format(expr))\n",
    "\n",
    "limit_expr = limit(expr, x, 0)\n",
    "\n",
    "print(\"Limit of expression tends to 0 : {}\".format(limit_expr))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction to differentiation\n",
    "\n",
    "So far we've learned how to evaluate limits for points on a line. Now we're going to build on that knowledge and look at a calculus technique called differentiation. In differentiation, we use our knowledge of limits to calculate the derivative of a function in order to determine the rate of change at an individual point on its line. The word differentiation is derived from the word difference (subtraction). The known difference of function $f(x)$ at a point $x$ given a chnage of $\\Delta x$ is simply the difference between the values of the function at those points:\n",
    "\n",
    "\n",
    "The derivative of $f\\left( x \\right)$ with respect to x is the function $f'\\left( x \\right)$  and is defined as, $\\begin{equation}f'\\left( x \\right) = \\mathop {\\lim }\\limits_{h \\to 0} \\frac{{f\\left( {x + h} \\right) - f\\left( x \\right)}}{h} \\label{eq:eq2}\\end{equation}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"860\"\n",
       "            height=\"460\"\n",
       "            src=\"https://www.youtube.com/embed/a5WVw9vmGHU\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1b4c0db35c8>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('a5WVw9vmGHU', width=860, height=460)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expression : 2*x + 1\n",
      "7\n",
      "Expression : 1 - sin(x)\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "expr = diff(x**2 +x , x)\n",
    "\n",
    "print(\"Expression : {}\".format(expr))\n",
    "print(expr.subs(x,3))\n",
    "\n",
    "expr = diff(cos(x) +x , x)\n",
    "print(\"Expression : {}\".format(expr))\n",
    "print(expr.subs(x,0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Introduction to Integration\n",
    "\n",
    "\n",
    "Lets say we want to find the area under a function between the function line and the X axis. This is called the integral of the function and it's expressed like this. $\\int{{f\\left( x \\right)\\,dx}}$ . To calculate the integral of $f(x)$ with respect to $x$, we need to find the anti-derivative of $f(x)$ , which means we needs a function whose derivative is $f(x)$ . By calculating the parallel in reverse, we can figure out that this is one half X squared. \n",
    "\n",
    "To do so there are many techniques and methods. Lets discuss them in the video in detail. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"860\"\n",
       "            height=\"460\"\n",
       "            src=\"https://www.youtube.com/embed/5pwZchmmgF0\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1b4c0df57c8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('5pwZchmmgF0', width=860, height=460)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Area below the curve')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_range = np.linspace(0,2,1000)\n",
    "f = lambda x:np.exp(x)\n",
    "\n",
    "plt.plot(x_range, f(x_range))\n",
    "plt.fill_between(x_range, 0, f(x_range), alpha = 0.25)\n",
    "plt.title(\"Area below the curve\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expression : x**3/3 + x**2/2\n",
      "27/2\n",
      "Expression : x**2/2 + sin(x)\n",
      "sin(3) + 9/2\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import *\n",
    "\n",
    "x = symbols('x')\n",
    "expr = integrate(x**2 +x , x)\n",
    "\n",
    "print(\"Expression : {}\".format(expr))\n",
    "print(expr.subs(x,3))\n",
    "\n",
    "expr = integrate(cos(x) +x , x)\n",
    "print(\"Expression : {}\".format(expr))\n",
    "print(expr.subs(x,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises\n",
    "\n",
    "1. Determine where the following function is increasing and decreasing : $ A\\left( t \\right) = 17{t^3} - 45{t^2} - 130{t} + 150$. Integration can be used to find areas, volumes, central points and many useful things.\n",
    "\n",
    "2. Sketch the graph of $f\\left( x \\right) = 3 - {\\frac{1}{2}}x $ and identify all the minima and maxima of the function on each of the following intervals.\n",
    "\n",
    "a). $\\left( { - \\infty ,\\infty } \\right)$    \n",
    "\n",
    "b). $\\left[ { - 1,1} \\right]$  \n",
    "\n",
    "c).  $\\left[ {1,4} \\right]$\n",
    "\n",
    "\n",
    "3. Evaluate the following indefinite integrals:  $\\displaystyle \\int{{7{x^6} - 12{x^3} - 5\\,dx}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note** : The following tutorial is a brief introduction to Calculus. You Can dive more deeper using the various resources and books availabe [online](https://www.sydney.edu.au/stuserv/documents/maths_learning_centre/)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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