Classwork_Ex_5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ----------------------------------\n",
    "# Python: Exercise-5\n",
    "# ----------------------------------\n",
    "## Question No. 1: Write a program for the sum of first $n$ natural numbers. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10\n",
    "i = 1\n",
    "summ = 0\n",
    "while i <= n:\n",
    "    summ = summ + i\n",
    "    i = i + 1\n",
    "print('Sum of %d natural integers is %d'%(n,summ))    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question No. 2: Write a program for the sum of first $n$ odd numbers. \n",
    "## Solution: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of 11 odd positive integers is 36\n"
     ]
    }
   ],
   "source": [
    "n = 11\n",
    "i = 1\n",
    "summ = 0\n",
    "while i <= n:\n",
    "    summ = summ + i\n",
    "    i = i + 2\n",
    "print('Sum of %d odd positive integers is %d'%(n,summ))  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question No. 3: Write a program for the sum of first $n$ even numbers. \n",
    "## Solution: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum of 11 even positive integers is 30\n"
     ]
    }
   ],
   "source": [
    "n = 11\n",
    "i = 2\n",
    "summ = 0\n",
    "while i <= n:\n",
    "    summ = summ + i\n",
    "    i += 2\n",
    "print('Sum of %d even positive integers is %d'%(n,summ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question No. 4: Write a program to evaluate the value of the fucntion $f(x)=x^2-3x+2$ for all values of x between  $-1$ to $-3$ with step size $0.1$. Use for loop to perform the calcualtion. Plot the resulting fucntion using a 3-point-thick dashed red line.\n",
    "## Solution: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "import matplotlib.pyplot as plt\n",
    "X = []\n",
    "Y = []\n",
    "x = -1\n",
    "while x <=3:\n",
    "    X.append(round(x,2))\n",
    "    Y.append(round(x**2-3*x+2,2))\n",
    "    x = x + 0.1\n",
    "plt.plot(X,Y,'r--',linewidth = 3.0)  \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question No. 5: Write a program that evaluates the power series of \n",
    "## (a) $exp(x) = \\sum_{k=0}^N\\frac{x^k}{k!}$ \n",
    "## (b) $ sin(x) = \\sum_{k=0}^N (-1)^k\\frac{x^{2k+1}}{(2k+1)!}$ \n",
    "## for given $x$ and $N$\n",
    "## Solution: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exp(1.57) = 4.81 \n",
      "sin(1.57) = 1.00 \n"
     ]
    }
   ],
   "source": [
    "from math import*\n",
    "x = pi/2\n",
    "N = 50\n",
    "Expx = 0\n",
    "Sinx = 0\n",
    "for k in range(0,N+1):\n",
    "    Expx = Expx + x**k/factorial(k)\n",
    "    Sinx = Sinx + (-1)**k*(x**(2*k+1))/factorial(2*k+1)\n",
    "print('exp(%2.2f) = %2.2f '%(x, Expx))    \n",
    "print('sin(%2.2f) = %2.2f '%(x, Sinx))  \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/img05.JPG\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fn =  [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]\n"
     ]
    }
   ],
   "source": [
    "N = 11\n",
    "F = [] # storing the Fibonacci numbers in a list\n",
    "for n in range(0, N+1):\n",
    "    if n == 0:\n",
    "        F.append(0)\n",
    "    elif n == 1:\n",
    "        F.append(1)\n",
    "    else:\n",
    "        F.append(F[n-1]+F[n-2])\n",
    "print('Fn = ', F)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/img06.JPG\" width=\"700\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "from math import*\n",
    "from matplotlib.pyplot import*\n",
    "X = []\n",
    "Y = []\n",
    "x = -5\n",
    "dx = 0.1\n",
    "while x<=20:\n",
    "    if x <= 0:\n",
    "        y = -x + 1\n",
    "        Y.append(round(y,2))\n",
    "    elif 0 < x <= 3*pi:\n",
    "        y = x*sin(x) + 1\n",
    "        Y.append(round(y,2))\n",
    "    else:\n",
    "        y = -(x -3*pi) + 1\n",
    "        Y.append(round(y,2))\n",
    "    X.append(round(x,2))\n",
    "    x = x + dx\n",
    "plot(X,Y,'r',linewidth = 3.0)\n",
    "xlabel('x-value')\n",
    "ylabel('y-value')\n",
    "title('Plot of piecewise functions')\n",
    "show()"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}