docs/calculus/intro.ipynb

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    "# Introduction\n",
    "\n",
    "Calculus is a branch of mathematics that gives tools to study rate of change of functions trough two main areas:\n",
    "derivatives and integrals.\n",
    "\n",
    "In the context of machine learning and data science, you can for instance use derivatives to optimize the parameters of a model with gradient descent. You might use integrals to calculate area under the curve.\n",
    "\n",
    "## Functions\n",
    "A function is a rule that takes one or more inputs and produces a single output. For example, the function $f(x) = x + 1$ takes a single input $x$, adds one to it, and produces a single output.\n",
    "In algebra, functions are written using symbols and formulas. For example, the function $f(x) = x + 1$ can be written as $f:x \\rightarrow x + 1$.\n",
    "The input to a function is called the **argument** or **input variable**. The output is called the **value** or **output variable**.\n",
    "\n",
    "Functions are often written using the following notation:\n",
    "\n",
    "$$y = f(x)$$\n",
    "\n",
    "The notation above is read as \"$y$ equals $f$ of $x$\" or \"$y$ is a function of $x$\".\n",
    "The notation above is useful because it allows us to define a function without specifying its name. For example, we can define a function $f$ as follows:\n",
    "\n",
    "$$f(x) = x^2$$\n",
    "\n",
    "We can then use the function $f$ to compute the square of any number. For example, $f(2) = 2^2 = 4$ and $f(3) = 3^2 = 9$.\n",
    "\n",
    "$$\n",
    "\\mathrm{f}(x) = \\sqrt{x + {6}} \\\\\n",
    "\\mathrm{f}(6) = \\sqrt{10 + {6}} \\\\\n",
    "\\mathrm{f}(6) = 4.0\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{gathered}\n",
    "f(x)=\\frac{x-3}{x+2} \\\\\n",
    "f(3)=\\frac{3-3}{3+2}=\\frac{0}{5}=0\n",
    "\\end{gathered}\n",
    "$$\n",
    "\n",
    "### Domain and Range of a Function\n",
    "The **domain** of a function is the set of all possible inputs to the function. The **range** of a function is the set of all possible outputs of the function.\n",
    "For example, the function $f(x) = x^2$ has a domain of all real numbers and a range of all non-negative real numbers.\n",
    "The domain of a function is often written as $D(f)$ and the range is often written as $R(f)$.\n",
    "\n",
    "$$ \n",
    "y = f(x) \\\\\n",
    "y = x^2\n",
    "$$"
   ]
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sb\n",
    "\n",
    "func = lambda x: x ** 2\n",
    "\n",
    "x = [-1,-2,-3, -4, 1, 2, 3, 4]\n",
    "y = [func(i) for i in x]\n",
    "\n",
    "sb.lineplot(x=x, y=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Piecewise Functions\n",
    "A piecewise function is a function that is defined by multiple sub-functions, each sub-function applying to a different interval of the main function's domain.\n",
    "For example, the function $f(x) = |x|$ is defined by two sub-functions:\n",
    "\n",
    "$$\n",
    "f(x) = \\begin{cases}\n",
    "x & \\text{if } x \\geq 0 \\\\\n",
    "-x & \\text{if } x < 0\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "\n",
    "## Expoents\n",
    "An exponent is a number that indicates how many times a base number is multiplied by itself.\n",
    "For example, $2^3$ is the same as $2 \\times 2 \\times 2$ and $2^4$ is the same as $2 \\times 2 \\times 2 \\times 2$.\n",
    "The number $2$ is called the **base** and the number $3$ is called the **exponent**.\n",
    "Exponents are often written using the following notation:\n",
    "\n",
    "$$2^3 = 2 \\times 2 \\times 2 = 8$$\n",
    "\n",
    "The notation above is read as \"two to the power of three\" or \"two cubed\".\n",
    "\n",
    "### Negative Exponents\n",
    "A negative exponent indicates that the base number should be divided by itself a certain number of times.\n",
    "For example, $2^{-3}$ is the same as $\\frac{1}{2^3}$ and $2^{-4}$ is the same as $\\frac{1}{2^4}$.\n",
    "The number $2$ is called the **base** and the number $-3$ is called the **exponent**.\n",
    "Negative exponents are often written using the following notation:\n",
    "\n",
    "$$2^{-3} = \\frac{1}{2^3} = \\frac{1}{8}$$\n",
    "\n",
    "The notation above is read as \"two to the power of negative three\" or \"two to the power of minus three\".\n",
    "### Fractional Exponents\n",
    "A fractional exponent indicates that the base number should be multiplied by itself a certain number of times.\n",
    "For example, $2^{\\frac{1}{2}}$ is the same as $\\sqrt{2}$ and $2^{\\frac{1}{3}}$ is the same as $\\sqrt[3]{2}$.\n",
    "The number $2$ is called the **base** and the number $\\frac{1}{2}$ is called the **exponent**.\n",
    "Fractional exponents are often written using the following notation:\n",
    "\n",
    "$$2^{\\frac{1}{2}} = \\sqrt{2} = 1.414213562373095$$\n",
    "\n",
    "The notation above is read as \"two to the power of one half\" or \"two to the power of one over two\".\n",
    "\n",
    "## Logarithms\n",
    "A logarithm is the inverse of an exponent. For example, the logarithm of $2^3$ is $3$.\n",
    "The logarithm of a number $x$ to the base $b$ is written as $\\log_b(x)$.\n",
    "For example, $\\log_2(8) = 3$ because $2^3 = 8$.\n",
    "\n",
    "### Common Logarithms\n",
    "\n",
    "The common logarithm of a number $x$ is the logarithm of $x$ to the base $10$. The common logarithm of $x$ is written as $\\log(x)$.\n",
    "For example, $\\log(100) = 2$ because $10^2 = 100$.\n",
    "\n",
    "### Natural Logarithms\n",
    "The natural logarithm of a number $x$ is the logarithm of $x$ to the base $e$. The natural logarithm of $x$ is written as $\\ln(x)$.\n",
    "For example, $\\ln(100) = 4.60517$ because $e^{4.60517} = 100$.\n",
    "\n",
    "## Polynomials\n",
    "\n",
    "A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.\n",
    "\n",
    "For example, $x^2 + 2x + 1$ is a polynomial because it consists of the variables $x$ and the coefficients $1$ and $2$.\n",
    "\n",
    "The degree of a polynomial is the highest degree of its terms. For example, the polynomial $x^2 + 2x + 1$ has a degree of $2$ because its highest degree term is $x^2$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "notes",
   "language": "python",
   "name": "python3"
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