{ "cells": [ { "cell_type": "markdown", "id": "05812d76-f652-440f-8f26-50c83c6e8390", "metadata": {}, "source": [ "Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities. In data science, some of the main important topics in calculus include:\n", "\n", "1) `Derivatives`: used to understand how a function changes with respect to its input.\n", "\n", "2) `Integrals`: used to calculate the total accumulated change of a function.\n", "\n", "3) `Multivariate calculus`: deals with functions of multiple variables, which is important for understanding more complex data sets.\n", "\n", "4) `Optimization`: used to find the best solution for a problem, such as finding the minimum or maximum of a function.\n", "\n", "5) `Differential equations`: used to model complex phenomena and make predictions about them.\n", "\n", "These concepts are used in many machine learning algorithms, like gradient descent, linear regression, and neural networks." ] }, { "cell_type": "markdown", "id": "5da6ced1-d436-43f7-88ba-01beb664fe76", "metadata": {}, "source": [ "## Derivatives\n", "\n", "In calculus, a derivative is a measure of how a function changes as its input (also called the independent variable) changes. It is represented by the symbol \"d/dx\" or \"∂/∂x\", where x is the input variable. The derivative of a function tells us the slope of the function at a given point, which can be used to determine the rate of change of the function at that point.\n", "\n", "For example, consider the simple function f(x) = x^2. The derivative of this function is f'(x) = 2x. This tells us that the slope of the function at any point x is 2x. If we graph the function, we can see that it is a parabola and the slope of the parabola at any point x is 2x.\n", "\n", "In data science, derivatives are used in machine learning algorithms like gradient descent. Gradient descent is an optimization algorithm used to find the minimum of a function (also called the cost function). The algorithm starts at a random point on the function and iteratively moves in the direction of the negative gradient (the derivative) until it reaches a minimum.\n", "\n", "Here is an example of how to calculate the derivative of a function in python:\n", "\n", "#### Example 1:" ] }, { "cell_type": "code", "execution_count": 2, "id": "dda90db3-e2dc-42c1-a624-9bff4795d49d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2*x\n" ] } ], "source": [ "from sympy import *\n", "x = Symbol('x')\n", "f = x**2\n", "derivative = f.diff(x)\n", "print(derivative)\n" ] }, { "cell_type": "markdown", "id": "cd728d8b-b99d-4498-88da-9f7e57031c73", "metadata": {}, "source": [ "We can visualize the function and its derivative using python libraries such as matplotlib or plotly. Here is an example using matplotlib:" ] }, { "cell_type": "code", "execution_count": 3, "id": "80630b84-4c14-427c-a9fc-fa455c4f0015", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "x = np.linspace(-10, 10, 100)\n", "y = x**2\n", "dy = 2*x\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x, y, 'r', linewidth=2)\n", "ax.plot(x, dy, 'g', linewidth=2)\n", "ax.legend(['y = x^2', 'dy/dx = 2x'])\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "1dccd4d9-e0a3-4707-bd2d-8d6ed2c7d269", "metadata": {}, "source": [ "#### Example 2:\n" ] }, { "cell_type": "markdown", "id": "f334cb41-3c8b-4c0b-a47e-aa78c112b925", "metadata": {}, "source": [ "Consider the function f(x) = sin(x). The derivative of this function is f'(x) = cos(x). This tells us that the slope of the function at any point x is cos(x).\n", "\n", "In data science, the sine function and its derivative, the cosine function, are often used in time series analysis and signal processing. For example, the sine function can be used to model periodic patterns in data, such as daily temperature fluctuations or stock prices. The derivative of the sine function, the cosine function, can be used to determine the rate of change of these patterns at any given point in time.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "4918eaad-5a81-4d72-bcea-a027b8bb3a2c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-np.pi, np.pi, 100)\n", "y = np.sin(x)\n", "dy = np.cos(x)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x, y, 'r', linewidth=2)\n", "ax.plot(x, dy, 'g', linewidth=2)\n", "ax.legend(['y = sin(x)', \"dy/dx = cos(x)\"])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "18d584ac-c481-4236-b97b-35820d427224", "metadata": {}, "source": [ "## Integral\n", "\n", "An integral is a measure of the total accumulated change of a function with respect to its input. It is represented by the symbol ∫, and the integral of a function from a to b is represented by the notation ∫a,b.\n", "\n", "Integrals can be classified into two types: definite and indefinite integrals. A definite integral has specific limits of integration and the result is a single value, while an indefinite integral does not have specific limits of integration and the result is a function.\n", "\n", "For example, consider the simple function f(x) = x^2. The definite integral of this function from a=0 to b=1 is ∫0,1 x^2 dx = (1/3)x^3 evaluated at the limits of integration.\n", "\n", "In data science, integrals are used in a variety of contexts, such as:\n", "\n", "In probability and statistics, integrals are used to calculate probability densities and cumulative distribution functions.\n", "In signal processing, integrals are used to calculate the area under a signal curve, which can be used to determine the total energy of the signal.\n", "In physics and engineering, integrals are used to calculate displacement, velocity, and acceleration.\n", "Here is an example of how to calculate the definite integral of a function in python:" ] }, { "cell_type": "code", "execution_count": 6, "id": "76b3410c-b91b-45dc-b28c-ada8bcb0602e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/3\n" ] } ], "source": [ "x = Symbol('x')\n", "f = x**2\n", "integral = integrate(f, (x, 0, 1))\n", "print(integral)\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "fd07b2a6-f1fb-4c9f-8ed4-5c10762083f3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "x = np.linspace(0, 1, 100)\n", "y = x**2\n", "\n", "fig, ax = plt.subplots()\n", "ax.fill_between(x, y)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "d269b93f-d875-466f-ab9f-4853b7f91495", "metadata": {}, "source": [ "This will plot the function y = x^2 and fill the area under the curve, representing the definite integral of the function.import numpy as np\n" ] }, { "cell_type": "markdown", "id": "74b93e16-3d15-4dff-acef-ac8e7131fe96", "metadata": {}, "source": [ "## Multivariate Calculus" ] }, { "cell_type": "markdown", "id": "ce46dd58-6f60-465c-b155-ed24e4b35534", "metadata": {}, "source": [ "In calculus, multivariate calculus deals with functions of multiple variables, as opposed to single variable functions. In data science, this is important for understanding more complex data sets that have multiple features or variables.\n", "\n", "For example, consider a simple two-variable function f(x, y) = x^2 + y^2. This is a function of two variables, x and y. The partial derivative of this function with respect to x is ∂f/∂x = 2x, and the partial derivative with respect to y is ∂f/∂y = 2y. These partial derivatives tell us how the function changes with respect to each variable independently.\n", "\n", "In data science, multivariate calculus is used in machine learning algorithms like gradient descent. Gradient descent is an optimization algorithm used to find the minimum of a function (also called the cost function). In multivariate case, the gradient descent algorithm updates the values of all the variables (features) simultaneously based on their partial derivatives.\n", "\n", "Here is an example of how to calculate the partial derivative of a function in python:" ] }, { "cell_type": "code", "execution_count": 11, "id": "d1d6d034-9d72-4212-8fbe-057295464535", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2*x\n", "2*y\n" ] } ], "source": [ "\n", "x, y = symbols('x y')\n", "f = x**2 + y**2\n", "partial_x = f.diff(x)\n", "partial_y = f.diff(y)\n", "print(partial_x)\n", "print(partial_y)\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "d0c59f74-1ead-4694-bd2b-784b4fd06244", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "def f(x, y):\n", " return x**2 + y**2\n", "\n", "x = np.linspace(-5, 5, 30)\n", "y = np.linspace(-5, 5, 30)\n", "\n", "X, Y = np.meshgrid(x, y)\n", "Z = f(X, Y)\n", "\n", "fig = plt.figure()\n", "ax = plt.axes(projection='3d')\n", "ax.plot_surface(X, Y, Z, cmap='viridis')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "02f75089-3ba7-4aa0-a571-3fad9352bf16", "metadata": {}, "source": [ "## Optimization:" ] }, { "cell_type": "markdown", "id": "6bfc7ed9-1333-4e1b-b819-1329df2fb211", "metadata": {}, "source": [ "In mathematics and computer science, optimization is the process of finding the best solution for a problem, such as finding the minimum or maximum of a function. In data science, optimization algorithms are used to find the best parameters for a model to make accurate predictions.\n", "\n", "For example, consider a simple function f(x) = x^2. The minimum of this function is at x = 0, where f(x) = 0. An optimization algorithm like gradient descent can be used to find the minimum of this function. Gradient descent starts at a random point on the function and iteratively moves in the direction of the negative gradient (the derivative) until it reaches a minimum.\n", "\n", "In data science, optimization algorithms are used in a variety of contexts, such as:\n", "\n", "* In machine learning, optimization algorithms are used to find the best parameters for a model, such as the weights in a neural network.\n", "* In computer vision, optimization algorithms are used to find the best parameters for image processing algorithms, such as image compression.\n", "* In natural language processing, optimization algorithms are used to find the best parameters for language models, such as word embeddings.\n", "\n", "\n", "Here is an example of how to use the optimization algorithm gradient descent in python:" ] }, { "cell_type": "code", "execution_count": 16, "id": "e1e97577-6b3f-43a5-a489-698e05cfaa13", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.111107929003464e-10\n", "3.7345640119929e-19\n" ] } ], "source": [ "import numpy as np\n", "\n", "def f(x):\n", " return x**2\n", "\n", "def grad(x):\n", " return 2*x\n", "\n", "x = 3\n", "learning_rate = 0.1\n", "iterations = 100\n", "\n", "for i in range(iterations):\n", " x = x - learning_rate*grad(x)\n", "\n", "print(x)\n", "print(f(x))\n" ] }, { "cell_type": "markdown", "id": "63d4e582-df09-44af-b780-5f0cf106ba53", "metadata": {}, "source": [ "Another example is to find the maximum of a function, for example f(x) = -x^2, the maximum of this function is at x = 0, where f(x) = 0. In this case, you can use optimization algorithm like gradient ascent which is the same as gradient descent but with a positive gradient to find the maximum of the function.\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "id": "557b5899-6f47-4236-bbb3-8be01c5bc899", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "x = np.linspace(-10, 10, 100)\n", "y = x**2\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x, y, 'r', linewidth=2)\n", "ax.scatter(0, 0, c='green', s=100)\n", "ax.annotate('Minimum', xy=(0, 0), xytext=(-1, 50),\n", " arrowprops={'arrowstyle': '->', 'color': 'green'})\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "6b78a5a0-7efe-4203-8b02-d6ff1d0fc825", "metadata": {}, "source": [ "## Differential equations:" ] }, { "cell_type": "markdown", "id": "b58c083f-8d8a-404d-afa1-3ef9df39d460", "metadata": {}, "source": [ "A differential equation is an equation that describes the relationship between a function and its derivatives. It is used to model complex phenomena and make predictions about them. \n", "\n", "In data science, differential equations are used in a variety of contexts, such as:\n", "\n", "* In finance, differential equations are used to model stock prices and interest rates.\n", "* In physics and engineering, differential equations are used to model physical systems, such as the motion of a particle or the flow of a fluid.\n", "* In biology and medicine, differential equations are used to model the spread of diseases and the behavior of populations.\n", "\n", "For example, consider the simple differential equation dy/dx = x. This equation describes the relationship between the function y and its derivative dy/dx. To find the specific function y that satisfies this equation, we can use a technique called integration, which essentially \"undoes\" the derivative. Integrating both sides of the equation with respect to x gives us y = (1/2)x^2 + C, where C is an arbitrary constant of integration.\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "6d17bd89-62a2-422f-a74e-94568d45ad81", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0. 0.5]\n" ] } ], "source": [ "from scipy.integrate import solve_ivp\n", "\n", "def dy_dx(x, y):\n", " return x\n", "\n", "solution = solve_ivp(dy_dx, [0, 1], [0], t_eval=[0, 1])\n", "y = solution.y[0]\n", "print(y)\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "8cce1cf6-e262-4eda-adc0-6194e7f60bf9", "metadata": {}, "outputs": [ { "data": { "image/png": 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PP5dWr7abBwCABkQZ8RX33OMaT59uLwcAAA2MMuIrrr/ezB+RpLfekr77zmocAAAaSr3KyMyZMxUTE6Pw8HDFxcVp7dq1J31/SUmJJk2apE6dOiksLEznn3++5s+fX6/AASs01LUI2vHj0vPP280DAEADcbuMLFmyRGPGjNGkSZO0efNmDRgwQElJScrOzq71MzfccIP+85//aN68efrqq6+0ePFiXXzxxacVPCDdeacpJZI0d65UXGw3DwAADcDhdLp3a0a/fv3Uu3dvzTphAa7Y2FgNHz5caWlp1d6/cuVK3Xjjjdq5c6datGhRr5CFhYWKjIxUQUGBIiIi6vU1/MZtt7me4jtjhjR6tNU4AADUpq5/v906M1JaWqrMzEwlJiZWOZ6YmKj169fX+JkVK1aoT58+evrpp3XOOefooosu0rhx43TkJIt3lZSUqLCwsMqGn40Z4xr//e9mZVYAAHyYW2UkPz9f5eXliqp4XsrPoqKilJubW+Nndu7cqXXr1umLL77QsmXLNG3aNL3xxhsafZL/R5+WlqbIyMjKLTo62p2Y/q1nT2nQIDP+9ltpxQqrcQAAOF31msDqcDiq7DudzmrHKhw/flwOh0MLFy7UpZdeqiFDhui5557Tiy++WOvZkQkTJqigoKBy28MD4qoaN841fvZZezkAAGgAbpWRVq1aKTg4uNpZkLy8vGpnSyq0a9dO55xzjiIjIyuPxcbGyul06vvvv6/xM2FhYYqIiKiy4QRXXy117WrG69ebDQAAH+VWGQkNDVVcXJwyMjKqHM/IyFBCQkKNn7nsssu0d+9eHTp0qPLY119/raCgIHXo0KEekSGHQ7r/ftf+1Kn2sgAAcJrcvkwzduxYzZ07V/Pnz9f27dt13333KTs7W6k/P+p+woQJSklJqXz/zTffrJYtW+r222/Xtm3btGbNGv3lL3/RH//4RzVt2rThfpJAc9NNrkXQli2TvvnGbh4AAOrJ7TKSnJysadOmacqUKerZs6fWrFmj9PR0derUSZKUk5NTZc2RZs2aKSMjQwcPHlSfPn10yy23aNiwYZrOkuanJyzMtUS802nurAEAwAe5vc6IDawzUosDB6ToaLP4WdOmUna21KqV7VQAAEhqpHVG4GXOPlsaNcqMjxyRTliIDgAAX0EZ8XVjxkhBP//HOH26dPiw1TgAALiLMuLrzj1XSk424/x8ad48q3EAAHAXZcQfjB/vGj/zjFRaai8LAABuooz4g+7dpWHDzHjPHmnhQrt5AABwA2XEX0yc6Bo/+SQP0AMA+AzKiL/o318aONCMv/5aWrrUbh4AAOqIMuJPTjw78re/mcXQAADwcpQRfzJokNS3rxlnZUkrV1qNAwBAXVBG/InDUf3sCAAAXo4y4m+uvVbq0sWM162T1qyxmwcAgFOgjPiboCBpwgTX/qOP2ssCAEAdUEb80Y03ShdcYMYffMDZEQCAV6OM+KOQEOmvf3XtT55sLQoAAKdCGfFXN9/sOjvyf/8nrV5tNw8AALWgjPirX54dYe4IAMBLUUb82c03SxdeaMacHQEAeCnKiD9j7ggAwAdQRvzdTTe5zo58+KHZAADwIpQRf1fT2RGeWQMA8CKUkUBw003SRReZ8erVUkaG3TwAAJyAMhIIQkKqzheZOJGzIwAAr0EZCRTJyVKPHmacmSktXWo3DwAAP6OMBIqgIOmJJ1z7Dz0klZXZywMAwM8oI4FkyBDpssvM+MsvpX/9y24eAABEGQksDoeUlubanzxZKimxFgcAAIkyEngGDJCSksw4O1uaPdtuHgBAwKOMBKIT54488YR06JC9LACAgEcZCUS9epm7ayTpxx+l556zmwcAENAoI4HqscfM+iOS9PTTUm6u3TwAgIBFGQlUF14opaaacXGx9MgjdvMAAAIWZSSQPfywFBFhxnPnSlu32s0DAAhIlJFA1rq1NGGCGR8/Lj3wgN08AICARBkJdPfeK0VHm3F6uvT++3bzAAACDmUk0DVtKv3tb679ceOk8nJ7eQAAAYcyAunmm6Xevc34s8+kV16xmwcAEFAoIzAP0Xv2Wdf+pEnmDhsAADyAMgJj4EDpN78x4x9+kJ56ym4eAEDAoIzA5dlnpSZNzPjpp6Vdu+zmAQAEBMoIXDp3NnfXSOZpvuPG2c0DAAgIlBFU9de/SlFRZrx0qfTBB3bzAAD8HmUEVUVESE8+6dq/5x6prMxeHgCA36OMoLqUFOnSS81461Zp1iy7eQAAfo0yguqCgqTp0137Dz8s5efbywMA8GuUEdSsXz9pxAgzPnhQmjjRahwAgP+ijKB2aWlS8+Zm/M9/Shs22M0DAPBLlBHUrl07acoU135qKpNZAQANjjKCk7v7bqlnTzP+7DNpxgyrcQAA/ocygpMLCTF30zgcZv+vfzXLxQMA0EAoIzi1/v2lO+4w40OHpPvus5sHAOBXKCOom7Q0qXVrM379dWnlSrt5AAB+gzKCumnRQnrmGdf+6NHSkSP28gAA/AZlBHWXkiL96ldmvHOn9OijdvMAAPwCZQR153BIs2dLoaFm/9lnpU8/tZsJAODzKCNwT2ys9NBDZlxeLo0cKR07ZjcTAMCnUUbgvgcflLp1M+OsLGnqVKtxAAC+rV5lZObMmYqJiVF4eLji4uK0du3aOn3uo48+UkhIiHpWLKIF3xQaKs2bZx6oJ0mTJ0tff201EgDAd7ldRpYsWaIxY8Zo0qRJ2rx5swYMGKCkpCRlZ2ef9HMFBQVKSUnRoEGD6h0WXqRvX2nMGDMuKZFGjZKOH7caCQDgmxxOp9Ppzgf69eun3r17a9asWZXHYmNjNXz4cKWlpdX6uRtvvFEXXnihgoODtXz5cmVlZdX5exYWFioyMlIFBQWKiIhwJy4aU3Gx1L27ubNGkmbOlP70J7uZAABeo65/v906M1JaWqrMzEwlJiZWOZ6YmKj169fX+rkFCxbo22+/1SOPPFKn71NSUqLCwsIqG7zQmWdKc+a49v/yF2nXLnt5AAA+ya0ykp+fr/LyckVFRVU5HhUVpdzc3Bo/s2PHDo0fP14LFy5USEhInb5PWlqaIiMjK7fo6Gh3YsKTBg0yl2gkc6bk9tu5XAMAcEu9JrA6Kh6a9jOn01ntmCSVl5fr5ptv1qOPPqqLLrqozl9/woQJKigoqNz27NlTn5jwlKlTpU6dzHj1aukf/7CbBwDgU+p2quJnrVq1UnBwcLWzIHl5edXOlkhSUVGRNm3apM2bN+vuu++WJB0/flxOp1MhISFatWqVrrzyymqfCwsLU1hYmDvRYFNEhLRggVTxn+X48dI110idO9vNBQDwCW6dGQkNDVVcXJwyMjKqHM/IyFBCQkK190dERGjLli3Kysqq3FJTU9W5c2dlZWWpX79+p5ce3mPgQOnPfzbjo0el226TysqsRgIA+Aa3zoxI0tixY3XrrbeqT58+io+P15w5c5Sdna3U1FRJ5hLLDz/8oJdffllBQUHq2rVrlc+3adNG4eHh1Y7DDzz5pHma744d0oYNZrn48eNtpwIAeDm3y0hycrL279+vKVOmKCcnR127dlV6ero6/TxnICcn55RrjsBPnXGG9OKL0oABZhLrI49ISUlSjx62kwEAvJjb64zYwDojPubBB6WnnzbjLl2kTZukpk3tZgIAeFyjrDMC1MmUKa6zIdu2mfVHAACoBWUEDS8sTFq0SAoPN/vPPy+9/bbdTAAAr0UZQePo0kV67jnX/h//KNWyMB4AILBRRtB4UlOlYcPM+McfWZ0VAFAjyggaj8MhzZsntW1r9leuZHVWAEA1lBE0rtatpZdecu0/8IC5uwYAgJ9RRtD4EhOl++8349JS6YYbpIMHrUYCAHgPygg8429/kyqW/9+1Sxo5UvL+JW4AAB5AGYFnhIZKS5ZIZ59t9pculWbMsJsJAOAVKCPwnE6dqs4fuf9+5o8AACgj8LBhw1zzR44dM/NHDhywmwkAYBVlBJ6Xlib172/Gu3ZJt97K+iMAEMAoI/C8Jk3M/JGWLc3+O+9Ijz1mNxMAwBrKCOzo2FFavFgK+vm/gpMn8/waAAhQlBHYM3iwueW3wh/+IH3zjb08AAArKCOw64EHpOuvN+OCAum666RDh+xmAgB4FGUEdjkc0oIF0sUXm/0vvmBBNAAIMJQR2Ne8ubRsmXmVpNdek554wm4mAIDHUEbgHS6+WHrlFXOmRJL++lfpzTftZgIAeARlBN7j2murTmhNSZE2b7aXBwDgEZQReJcHHzSLoEnS4cOmoOTm2s0EAGhUlBF4F4dDmjPHtULr999Lw4dLR49ajQUAaDyUEXif8HAzoTU62ux/8ol0220sGQ8AfooyAu/Utq20YoV0xhlmf8kSaeJEu5kAAI2CMgLv1bOnKSEVS8Y/9ZQ0e7bVSACAhkcZgXf7zW+kGTNc+6NH8wwbAPAzlBF4vz/9ySwbL5l5I8nJUmam3UwAgAZDGYFvSEszJUQyt/wOHSp9+63dTACABkEZgW8ICpJefFG6/HKzv2+flJgo5eRYjQUAOH2UEfiO8HDprbekSy4x+zt3StdcIx08aDUWAOD0UEbgW1q0kN57T+rUyex//rk0bJi5dAMA8EmUEfiec86RVq2SWrc2++vWmfkkx47ZzQUAqBfKCHzTRRdJ774rNW9u9t9+WxoxQiovt5sLAOA2ygh8V1ycmUMSGmr2Fy+W7riDZeMBwMdQRuDbBg6U3nhDCgkx+wsWSHffLTmddnMBAOqMMgLfN2yYOStSsWz8rFnS/fdTSADAR1BG4B9+9zvp5Zclh8Ps//3v0qRJFBIA8AGUEfiPW26R/vlP135amvTQQxQSAPBylBH4l5Ejpeefd+3/7W/S+PEUEgDwYpQR+J+77qpaSJ5+Who3jkICAF6KMgL/dNdd0gsvuPafe04aM4ZCAgBeiDIC//X//p80b55rUuv06dKf/sTCaADgZSgj8G9//KNZe6SikLzwgvSHP7B0PAB4EcoI/N+IEdLCha6F0V59VbruOunIEbu5AACSKCMIFDfdJC1fLoWHm/133pGuuUYqLLQaCwBAGUEgGTpUWrnS9XC9NWvMcvJ5eXZzAUCAo4wgsPz619IHH0gtW5r9Tz+VEhKkb76xmwsAAhhlBIGnTx9p7VqpQwez/+23Uny89N//2s0FAAGKMoLAFBsrffyx1LWr2c/PN5ds3nnHbi4ACECUEQSuDh3MGZIrrjD7hw9Lv/2tNGeO1VgAEGgoIwhsZ51lJrUmJ5v98nLpzjvN8vEsjgYAHkEZAcLCpEWLpPvvdx2bOlX6n/+RDh2ylwsAAgRlBJCkoCDp2Wel2bOl4GBzbMUK6fLLpT177GYDAD9HGQFOdOed5rJNZKTZ/+wz6dJLpQ0b7OYCAD9GGQF+6aqrTPk47zyzn5tr1ieZN89uLgDwU5QRoCYXXyx98okpIZJUWiqNGiWNHm3GAIAGQxkBatOqlZSRIf35z65jM2dKgwZJ+/bZywUAfqZeZWTmzJmKiYlReHi44uLitHbt2lrfu3TpUg0ePFitW7dWRESE4uPj9d5779U7MOBRTZpI06dL8+dLoaHm2Lp1Uu/e5hUAcNrcLiNLlizRmDFjNGnSJG3evFkDBgxQUlKSsrOza3z/mjVrNHjwYKWnpyszM1MDBw7UsGHDtHnz5tMOD3jM7bebBdLOOcfs791rFkubOlVyOq1GAwBf53A63ftf0n79+ql3796aNWtW5bHY2FgNHz5caWlpdfoal1xyiZKTk/Xwww/X6f2FhYWKjIxUQUGBIiIi3IkLNKzcXOmmm6QPP3QdGz5cWrDALKAGAKhU17/fbp0ZKS0tVWZmphITE6scT0xM1Pr16+v0NY4fP66ioiK1aNGi1veUlJSosLCwygZ4hbZtzTySiRNdx5Yvl+LipMxMa7EAwJe5VUby8/NVXl6uqKioKsejoqKUm5tbp68xdepUFRcX64Ybbqj1PWlpaYqMjKzcoqOj3YkJNK6QEOmJJ6S335bOPtsc27nTPPl36lTp+HG7+QDAx9RrAqvD4aiy73Q6qx2ryeLFizV58mQtWbJEbdq0qfV9EyZMUEFBQeW2hxUw4Y2GDpU2bzaLoknSsWPmmTZDhnC3DQC4wa0y0qpVKwUHB1c7C5KXl1ftbMkvLVmyRCNHjtRrr72mq6666qTvDQsLU0RERJUN8EqdOpm7ah580HXsvfek7t3NSq4AgFNyq4yEhoYqLi5OGRkZVY5nZGQoISGh1s8tXrxYt912mxYtWqShQ4fWLyngrZo0kZ58Ulq1yswpkaS8PCkpSbr7bqm42G4+APBybl+mGTt2rObOnav58+dr+/btuu+++5Sdna3U1FRJ5hJLSkpK5fsXL16slJQUTZ06Vf3791dubq5yc3NVUFDQcD8F4A0GDzbPshkyxHXs+eelXr3Maq4AgBq5XUaSk5M1bdo0TZkyRT179tSaNWuUnp6uTp06SZJycnKqrDnywgsvqKysTKNHj1a7du0qt3vvvbfhfgrAW7RpYya2Pv+81LSpObZjh3TZZdLDD5t5JQCAKtxeZ8QG1hmBT/rqKyklRfrvf13HevQwa5L06mUvFwB4SKOsMwLADZ07Sx99JD36qBQcbI599pnUt6/00ENSSYndfADgJSgjQGMKCTGXZz75xNxhI0nl5Wadkl69pA0b7OYDAC9AGQE8IS5O2rhRmjzZFBRJ2r5dSkgwd9wwoRtAAKOMAJ4SGio98ohZNj4uzhxzOs1k19hY6Y03eOgegIBEGQE8rXt3c3nmmWekM84wx3JypN//XvrNb6Rdu+zmAwAPo4wANoSEmKXjt20zy8pXSE+XunQxl3OOHLEWDwA8iTIC2NSpk/Tvf5tLNO3amWNHj5o7cLp0kd56i0s3APweZQSwzeGQrr9e+vJL6f77XRNcv/tOGj7cLCu/bZvNhADQqCgjgLeIiJCefdasRTJokOt4xYP37rpL+vFHe/kAoJFQRgBv06WLlJEhvf661LGjOVZeLs2aJV1wgZn4yoJpAPwIZQTwRg6H9LvfmUs3TzwhNWtmjhcWSg88YFZ3ffllU1IAwMdRRgBv1rSpNHGiedjeqFGmpEjS7t3SiBFmFdd33mGSKwCfRhkBfEHbttI//ylt3ixdc43r+JYtZm2SX/9aWrPGXj4AOA2UEcCX9Oghvfuu9MEH5oF7FdauNYVk8GDp44/t5QOAeqCMAL5o4EDz8L033pAuush1/P33zfNuhgwxz8IBAB9AGQF8VcX6JFu3Si++KJ13nuvf3n1XuvRSc0ln3TprEQGgLigjgK8LCTGTWb/80swrqbgdWDJrlAwYIF1xhTlrwkRXAF6IMgL4iyZNzB03X38tzZkjxcS4/m31ajOfpG9f6bXXpLIyezkB4BcoI4C/CQuT7rhD+uor6aWXzJokFTIzpeRkc+z556XDh+3lBICfUUYAf9WkiZSSYuaULFki9e7t+redO6W775aio806Jj/8YC8ngIBHGQH8XXCwdMMN0qZN0n/+IyUmuv7tp5+ktDTp3HOlW27hDhwAVlBGgEDhcEhXXmkmtW7eLP3hD+bsiWTmkCxaZO7A6dfPLDV/9KjdvAACBmUECEQ9e0r/+pf03XfSQw9JLVu6/u2//zV350RHS+PHS7t22UoJIEBQRoBA1r699Nhj0p495rbgHj1c/5afLz31lHT++dLVV0tvvikdO2YvKwC/RRkBYB7IN2qUuXyzbp10002uSzhOp7RqlXmKcIcO0oMPmjt1AKCBOJxO718FqbCwUJGRkSooKFBERITtOEBg2LdPmjdPmju35ks18fHS7bebybGRkZ7PB8Dr1fXvN2UEwMkdP27uwvnnP6Xly6tfqgkPl667Trr1VrOwWkiIlZgAvA9lBEDDy8uTFi6UFiyQtmyp/u9t2phF1f7wB7Paq8Ph+YwAvAZlBEDjcTqlTz81D+hbuFA6cKD6e847zxST5GSpe3eKCRCAKCMAPKOkRFq5UnrlFenf/zb7v9S5sykl118vdetGMQECBGUEgOcVFJhbgBctkv7v/8x8k1+64AJTSq6/XurTh2IC+DHKCAC79u0zxWTJEmntWnNp55c6dJCuvdZsAwdKoaGezwmg0VBGAHiPvXulpUtNOVmzpuYzJs2bS0lJ0tCh5rV1a8/nBNCgKCMAvFNenvTWW9KyZeaW4dLS6u9xOMxzcoYOlYYMkXr1koJYoxHwNZQRAN6vqMg8uG/FCuntt2u+K0cyZ0kGDzbL0icmSm3bejYngHqhjADwLWVl0scfS++8Y7Yvvqj9vd26SVddJQ0aJP3qV+YSDwCvQxkB4Nt275bS082Zkw8+MGdRahISIvXrJ11xhdkSEqQzzvBkUgC1oIwA8B/HjpmzJitXSu+/L23aVPPdOZJ5wF+/fuaMyYABppzwvxuAFZQRAP7rp5+kDz80E2Dff1/6+uva3xsUJPXo4SomCQlSdLTHogKBjDICIHDs3WvKyYcfmsXWvvnm5O+PjjalpH9/cxalVy/zwD8ADYoyAiBw7d1rFlpbu9asa/LFF7Vf1pHMpZ2ePU0x6dvXrAzbubMUHOyxyIA/oowAQIUDB6QNG6T16832ySdScfHJP9OsmRQXZ7bevc120UUUFMANlBEAqE1ZmbRliyklGzaY1y+/PPXnzjjDzD/p2dP12q0bd+8AtaCMAIA7DhyQMjPNnTobN5rX7OxTf87hkC680JSSbt2k7t3Na0wMZ1EQ8CgjAHC68vKkzZulTz81RSUzU/ruu7p9Njxcio2VLrlE6tLFbLGx0nnnmbVRgABAGQGAxnDwoPT559Jnn0lZWWbbtk06erRunw8NNWdSYmPNJNnOnc1clM6dpbPOarzcgAWUEQDwlPJyczvxli1m++ILaetWc6y8vO5fp3VrU1RO3M4/32wUFfggyggA2FZSIn31lSknX34pbd9utq+/NqvKuqNlS1cxiYkxl3tiYswWHc2lH3glyggAeKuyMmnXLlNUTtx27JByctz/esHBUocOUqdO0rnnmtdOnaSOHV1b06YN/mMAp0IZAQBfdOiQubyzY4fZvv3WtX3/ff2/bqtWprBER7tezznHbB06mNdmzRru5wBEGQEA/3P0qLmbZ9cus+3caV537zbH9+8/va8fESG1b2+2du1cr23bmteKcUSEuaUZOIW6/v3mIiMA+IrwcOnii81Wk6IiU0x27zZrpFRsu3dLe/aYZfLLymr/+oWFZjvVAnBhYaaUREWZ1zZtzLjitXVrs7VpY+a6MJ8Fp8B/QwDAXzRvLnXtaraalJdL+/aZYvL999IPP5jt++/NlpNj9g8fPvn3KSlxlZ66aNHCXCZq3dq8VmwtW1bfWrQwW5Mm7v3s8GlcpgEAuDid5gzL3r1my801JaXidd8+M963T8rPP/kDCE9H8+amlJx9ttlOHJ91VtXXyEgzPussM27alMtIXoLLNAAA9zkcZk5IRETtl4MqlJVJP/5oVqrdt8/1WnHsxx9dW36+uQRUV0VFrstO7goJMaXkxK3iZ6oYN2/uev3luFkz15gl/T2CMgIAqJ+QENfE1rooLTWTbCvKyf79Vbeffqq67d9vnhnk7posZWWur3m6mjY15eTE7cwzq7+euJ1xhuv1l+MTtyZNOIPzM8oIAMAzQkPdKy+SuQx0+LApJwcOmOX4T3w9cEAqKDBbxbGK/cJC83qySbuncuSI2X78sf5fozZBQaaUNG1a8xYeXvW1YlzbFhZW+2tNmxed9alXGZk5c6aeeeYZ5eTk6JJLLtG0adM0YMCAWt+/evVqjR07Vlu3blX79u31wAMPKDU1td6hAQABwuFwnXGIjnb/806nKRMVdwpVFJSKy0AVxyr2i4rMWi8V4+Jis19x7MiRhvvZjh93fW0bgoJcxSQ0VLr6aunll61EcbuMLFmyRGPGjNHMmTN12WWX6YUXXlBSUpK2bdumjh07Vnv/rl27NGTIEN1xxx165ZVX9NFHH+muu+5S69atdf311zfIDwEAQI0cDtdlkbZtT//rlZebMzWHDrmKSnFx1e3w4aqvxcWmxBw+7Noq9k98rdhKS08/Z10cP+76npIpaZa4fTdNv3791Lt3b82aNavyWGxsrIYPH660tLRq73/wwQe1YsUKbd++vfJYamqqPvvsM3388cd1+p7cTQMACBjl5WaBuyNHan49cTtyxNxqffSoea3Yr9gqjv/yWGmpGZ/4evXV0uzZDfqjNMrdNKWlpcrMzNT48eOrHE9MTNT69etr/MzHH3+sxMTEKseuvvpqzZs3T8eOHVOTGu4lLykpUUlJSZUfBgCAgBAc7Lo0FSCC3Hlzfn6+ysvLFRUVVeV4VFSUcnNza/xMbm5uje8vKytTfn5+jZ9JS0tTZGRk5RZdn+uEAADAJ7hVRio4fnErktPprHbsVO+v6XiFCRMmqKCgoHLbs2dPfWICAAAf4NZlmlatWik4OLjaWZC8vLxqZz8qtG3btsb3h4SEqGXLljV+JiwsTGFhYe5EAwAAPsqtMyOhoaGKi4tTRkZGleMZGRlKSEio8TPx8fHV3r9q1Sr16dOnxvkiAAAgsLh9mWbs2LGaO3eu5s+fr+3bt+u+++5TdnZ25bohEyZMUEpKSuX7U1NTtXv3bo0dO1bbt2/X/PnzNW/ePI0bN67hfgoAAOCz3F5nJDk5Wfv379eUKVOUk5Ojrl27Kj09XZ06dZIk5eTkKDs7u/L9MTExSk9P13333afnn39e7du31/Tp01ljBAAASOKpvQAAoJHU9e93ve6mAQAAaCiUEQAAYBVlBAAAWEUZAQAAVlFGAACAVZQRAABgldvrjNhQcfcxT+8FAMB3VPzdPtUqIj5RRoqKiiSJp/cCAOCDioqKFBkZWeu/+8SiZ8ePH9fevXvVvHnzkz4d2F2FhYWKjo7Wnj17WEytkfG79gx+z57B79kz+D17RmP+np1Op4qKitS+fXsFBdU+M8QnzowEBQWpQ4cOjfb1IyIi+C+6h/C79gx+z57B79kz+D17RmP9nk92RqQCE1gBAIBVlBEAAGBVQJeRsLAwPfLIIwoLC7Mdxe/xu/YMfs+ewe/ZM/g9e4Y3/J59YgIrAADwXwF9ZgQAANhHGQEAAFZRRgAAgFWUEQAAYFVAl5GZM2cqJiZG4eHhiouL09q1a21H8jtr1qzRsGHD1L59ezkcDi1fvtx2JL+Tlpamvn37qnnz5mrTpo2GDx+ur776ynYsvzRr1ix17969cnGo+Ph4vfvuu7Zj+bW0tDQ5HA6NGTPGdhS/M3nyZDkcjipb27ZtrWQJ2DKyZMkSjRkzRpMmTdLmzZs1YMAAJSUlKTs723Y0v1JcXKwePXpoxowZtqP4rdWrV2v06NHasGGDMjIyVFZWpsTERBUXF9uO5nc6dOigJ598Ups2bdKmTZt05ZVX6re//a22bt1qO5pf2rhxo+bMmaPu3bvbjuK3LrnkEuXk5FRuW7ZssZIjYG/t7devn3r37q1Zs2ZVHouNjdXw4cOVlpZmMZn/cjgcWrZsmYYPH247il/78ccf1aZNG61evVq/+tWvbMfxey1atNAzzzyjkSNH2o7iVw4dOqTevXtr5syZevzxx9WzZ09NmzbNdiy/MnnyZC1fvlxZWVm2owTmmZHS0lJlZmYqMTGxyvHExEStX7/eUiqgYRQUFEgyfyTReMrLy/Xqq6+quLhY8fHxtuP4ndGjR2vo0KG66qqrbEfxazt27FD79u0VExOjG2+8UTt37rSSwycelNfQ8vPzVV5erqioqCrHo6KilJubaykVcPqcTqfGjh2ryy+/XF27drUdxy9t2bJF8fHxOnr0qJo1a6Zly5apS5cutmP5lVdffVWffvqpNm7caDuKX+vXr59efvllXXTRRdq3b58ef/xxJSQkaOvWrWrZsqVHswRkGangcDiq7DudzmrHAF9y99136/PPP9e6detsR/FbnTt3VlZWlg4ePKg333xTI0aM0OrVqykkDWTPnj269957tWrVKoWHh9uO49eSkpIqx926dVN8fLzOP/98vfTSSxo7dqxHswRkGWnVqpWCg4OrnQXJy8urdrYE8BV//vOftWLFCq1Zs0YdOnSwHcdvhYaG6oILLpAk9enTRxs3btT//u//6oUXXrCczD9kZmYqLy9PcXFxlcfKy8u1Zs0azZgxQyUlJQoODraY0H+deeaZ6tatm3bs2OHx7x2Qc0ZCQ0MVFxenjIyMKsczMjKUkJBgKRVQP06nU3fffbeWLl2qDz74QDExMbYjBRSn06mSkhLbMfzGoEGDtGXLFmVlZVVuffr00S233KKsrCyKSCMqKSnR9u3b1a5dO49/74A8MyJJY8eO1a233qo+ffooPj5ec+bMUXZ2tlJTU21H8yuHDh3SN998U7m/a9cuZWVlqUWLFurYsaPFZP5j9OjRWrRokd566y01b9688oxfZGSkmjZtajmdf5k4caKSkpIUHR2toqIivfrqq/rwww+1cuVK29H8RvPmzavNdzrzzDPVsmVL5kE1sHHjxmnYsGHq2LGj8vLy9Pjjj6uwsFAjRozweJaALSPJycnav3+/pkyZopycHHXt2lXp6enq1KmT7Wh+ZdOmTRo4cGDlfsV1yBEjRujFF1+0lMq/VNyefsUVV1Q5vmDBAt12222eD+TH9u3bp1tvvVU5OTmKjIxU9+7dtXLlSg0ePNh2NMBt33//vW666Sbl5+erdevW6t+/vzZs2GDl72DArjMCAAC8Q0DOGQEAAN6DMgIAAKyijAAAAKsoIwAAwCrKCAAAsIoyAgAArKKMAAAAqygjAADAKsoIAACwijICAACsoowAAACrKCMAAMCq/w+EscAEKUcboQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "t = np.linspace(0, 5, 100)\n", "y = np.exp(-t)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(t, y, 'r', linewidth=2)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "d9a80630-ead7-45c9-88ce-ed27dc4c4c0f", "metadata": {}, "source": [ "## Summary: \n", "\n", "Data science is a field that heavily relies on the concepts of calculus. In this post, we will introduce the basics of derivatives, integrals, multivariate calculus, optimization, and differential equations and how they are used in data science. Through simple examples and visualizations, we will explore how these concepts are applied in time series analysis, signal processing, machine learning, computer vision, and natural language processing. By understanding the fundamentals of calculus, data scientists can better analyze and understand complex data sets, optimize models, and make accurate predictions.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.15" } }, "nbformat": 4, "nbformat_minor": 5 }