LA2_MAT120_Sabira.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lJVynZg7satV",
        "outputId": "717614ad-2db0-41d7-8aac-f1281abdffd5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "First derivative of the given function :  8*x**3 + 3*x**2 + 4\n",
            "Second derivative of the given function :  6*x*(4*x + 1)\n",
            "Third derivative of the given function :  6*(8*x + 1)\n"
          ]
        }
      ],
      "source": [
        "#Task-01 (a)\n",
        "\n",
        "from sympy import*\n",
        "x= symbols('x')\n",
        "\n",
        "f = 2*x**4+x**3+4*x\n",
        "df = diff(f,x)\n",
        "df2 = diff (f,x,2)\n",
        "df3 = diff (f,x,3)\n",
        "\n",
        "print('First derivative of the given function : ', df)\n",
        "\n",
        "#Viva part\n",
        "\n",
        "df2 = diff (f,x,2)\n",
        "df3 = diff (f,x,3)\n",
        "\n",
        "print('Second derivative of the given function : ', df2)\n",
        "print('Third derivative of the given function : ', df3)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Task-01 (b)\n",
        "\n",
        "from sympy import*\n",
        "x= symbols('x')\n",
        "\n",
        "f = 2*x**4+x**3+4*x\n",
        "df = diff(f,x)\n",
        "print('First derivative :',df)\n",
        "\n",
        "df = lambdify(x,df)\n",
        "print('Value of the first derivative when x=4 :',df(4))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7yaaVvTGtAWl",
        "outputId": "211e1deb-bec9-495e-b3eb-eabd41a09d1e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "First derivative : 8*x**3 + 3*x**2 + 4\n",
            "Value of the first derivative when x=4 : 564\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Task-01 (c)\n",
        "from sympy import*\n",
        "x= symbols('x')\n",
        "\n",
        "f = 2*x**4+x**3+4*x\n",
        "df = diff(f,x)\n",
        "print('First derivative :',df)\n",
        "\n",
        "dF = lambdify(x,df)\n",
        "\n",
        "from numpy import*\n",
        "#test_numbers = arange(-5,7) #-5,6\n",
        "#a=df(test_numbers)\n",
        "\n",
        "x_vals = [val/10 for val in range(-50, 61)] #-5,6\n",
        "y_vals = [df.subs(x, val) for val in x_vals]\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.plot(x_vals , y_vals)\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('dy')\n",
        "plt.title('Graph for the given function')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "id": "K_bN9uCpyeL9",
        "outputId": "e78a531a-40a8-4018-c3b1-6ffae8b31a50"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "First derivative : 8*x**3 + 3*x**2 + 4\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Task-02 (a)\n",
        "\n",
        "from sympy import*\n",
        "x=symbols('x')\n",
        "\n",
        "f= ((1+x**0.5)**(1/3))/(x**0.5)\n",
        "integrate(f,x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 42
        },
        "id": "L0ngEjGh3UN7",
        "outputId": "64f26655-1a59-460c-d373-903fa8df0a2f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.5*(x**0.5 + 1)**1.33333333333333"
            ],
            "text/latex": "$\\displaystyle 1.5 \\left(x^{0.5} + 1\\right)^{1.33333333333333}$"
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Task-02 (b)\n",
        "\n",
        "from numpy import*\n",
        "from scipy.integrate import*\n",
        "f = lambda x: exp(sin(x))\n",
        "quad (f, 1, 2)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9FpL6Zr16WMT",
        "outputId": "5ee9b895-5a78-4979-b629-5e03446bce0a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2.6046615488029587, 2.891755222836866e-14)"
            ]
          },
          "metadata": {},
          "execution_count": 1
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Task-03\n",
        "\n",
        "from sympy import*\n",
        "\n",
        "x = symbols('x')\n",
        "y = Function('y')\n",
        "\n",
        "y1 = Derivative(y(x), x)\n",
        "y2 = Derivative(y(x), x, 2)\n",
        "\n",
        "df = y2 - (6 * y1) + (5 * y(x))\n",
        "\n",
        "solve = dsolve(df, y(x), ics = {y(0) : 1, y1.subs(x,0) : 0 })\n",
        "print(f\"An eqn that solves initial value condition is: {solve}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "O83fy8AtugJ_",
        "outputId": "4bd7e6ba-2966-41ec-8f09-2606208cb87d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "An eqn that solves initial value condition is: Eq(y(x), (5/4 - exp(4*x)/4)*exp(x))\n"
          ]
        }
      ]
    }
  ]
}