{ "cells": [ { "cell_type": "markdown", "id": "bf4b2dd0-e3d2-476d-a8d1-15a3c264d614", "metadata": {}, "source": [ "# Taylor Expansions and Series Solutions" ] }, { "cell_type": "markdown", "id": "b21aeacc-022c-49ed-85e9-b4c39c365038", "metadata": {}, "source": [ "**Instructor** : Camilla Marcellini (cmarcellini@ucsd.edu)" ] }, { "cell_type": "markdown", "id": "f109ec1c-6a2b-4603-a12c-d7c8e7da7c4a", "metadata": {}, "source": [ "**TAs**: Sam Schulz (s1schulz@ucsd.edu), Lauren Harvey (lrharvey@ucsd.edu), and Argen Smith (argen@ucsd.edu)" ] }, { "cell_type": "markdown", "id": "ab6cd24f-1d03-461c-b6a3-c1b26436cff4", "metadata": {}, "source": [ "Lecture notes adapted from 2024 Math Workshop Notes by Sam Schulz." ] }, { "cell_type": "markdown", "id": "812444d4-e5cb-423d-b309-2ae18269837c", "metadata": {}, "source": [ "## 1 | Introduction" ] }, { "cell_type": "markdown", "id": "0e531d22-0661-4889-8191-f3d873d0562e", "metadata": {}, "source": [ "Taylor expansions are a useful tool for when you have a function that is complicated to deal with. An example of this is the Coriolis parameter, which comes up in physical oceanography/geophysical fluid dynamics:\n", "\\begin{equation}\n", "f = 2 \\Omega \\cos(\\phi),\n", "\\end{equation}\n", "where $\\Omega$ is the rotation frequency of the earth ($2\\pi$/24 hr $\\sim 7 \\times 10^{-5}$ $\\text{s}^{-1}$). If an expression like this appears in an equation, especially a differential equation, it often can be useful to simplify it. With this motivation, let's use the function $f(x) = \\cos(x)$ as a guiding example.\n" ] }, { "cell_type": "markdown", "id": "d83a0e21-5ee8-4e6e-9f19-f3dda71b60c2", "metadata": {}, "source": [ "## 2 | Taylor Expansions" ] }, { "cell_type": "markdown", "id": "e550b87f-f0ea-4bea-9bae-cff0eb7bd1f2", "metadata": {}, "source": [ "A Taylor expansion (also called a Taylor series) is a method of rewriting a function as a sum of the function's derivatives evaluated at a single point. The formula (presented without proof) for the Taylor series of a function $f(x)$ about a point $x=a$ is:\n", "\\begin{align}\n", "f(x)&=f(a)+\\frac{f^{\\prime}(a)}{1!}(x-a)+\\frac{f^{\\prime \\prime}(a)}{2!}(x-a)^2+\\frac{f^{\\prime \\prime \\prime}(a)}{3!}(x-a)^3+\\cdots=\n", "\\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!}(x-a)^n.\n", "\\end{align}\n", "where the $'$ symbol denotes a derivative and the $!$ symbol is a factorial. The two lines of the above are equivalent, the second one is just there for those who feel comfortable with summation notation. We are assuming that the function $f(x)$ is infinitely differentiable at the point $x=a$, i.e. that we can take its derivative an $\\textit{infinite}$ number of times, to ensure the existence of the series. \n", "\n", "Equation (2) shows that a good approximation for $f(x)$ near $x=a$ is simply $f(a)$, and a closer one is $f(a)+\\frac{f^{\\prime}(a)}{1!}(x-a)+\\frac{f^{\\prime \\prime}(a)}{2!}(x-a)^2$. You can add more and more terms to get closer to the true value, but of course each term you add makes things more complicated. Typically, you see the first one or two terms kept. \n", "\n", "In each term of Eq. (2), everything is a constant except the part that depends on $(x-a)$. This means each term gets really small when $x$ is close to $a$, and the larger the exponent on this $(x-a)$ part, the smaller the term overall. This property makes Taylor expansions a useful tool when you want to approximate a function in the vicinity of a certain value. When $(x-a)$ is sufficiently small, the first term of the Taylor series, $f(a)$, will be the most important/largest, followed by the second, $\\frac{f^{\\prime \\prime}(a)}{2!}(x-a)^2$, followed by the third, and so on.\n" ] }, { "cell_type": "markdown", "id": "0bb767b3-3942-45ce-8016-bc19ad22d846", "metadata": {}, "source": [ "### 2.2 Building Intuition on Taylor Series" ] }, { "cell_type": "markdown", "id": "7690a859-33bf-4d78-a6f5-c2e87801a027", "metadata": {}, "source": [ "Physical functions are complex and difficult to calculate. One of the key techniques in Applied Mathematics is to approximate functions within certain domains. One of the most useful tools for local approximation is the Taylor series, which is built from derivatives. You already know that the first derivative gives the slope at a point, which lets us approximate a function near that point with a straight line. But instead of stopping there, can we extend this idea to higher-order polynomials—curves that better capture the behavior of the function—to reduce the error? \n", "\n", "This is exactly the idea behind the Taylor series, and why they are so commonly used in Applied Mathematics.\n", "In Figure (1), we can see this in action: adding extra terms that involve higher derivatives improves the approximation of the function $f(x)=\\cos(x)$." ] }, { "cell_type": "code", "execution_count": 7, "id": "1c393e16-410c-401e-a3ec-312440e4c7d6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from math import factorial\n", "\n", "def taylor_series_cosine(x_,n):\n", " to_return=0\n", " for i in np.arange(n):\n", " to_return+=((-1)**(i))*(x_**(2*i))/factorial(2*i)\n", " return to_return\n", "\n", "x_=np.linspace(-8,8,200)\n", "\n", "plt.figure(figsize=(10,6))\n", "\n", "plt.plot(x_,np.cos(x_),linewidth=3,label='cos(x)')\n", "plt.plot(x_,taylor_series_cosine(x_,1),label = 'first 1 term')\n", "plt.plot(x_,taylor_series_cosine(x_,2),label = 'first 2 terms')\n", "plt.plot(x_,taylor_series_cosine(x_,3),label = 'first 3 terms')\n", "plt.plot(x_,taylor_series_cosine(x_,5),label = 'first 5 terms')\n", "plt.plot(x_,taylor_series_cosine(x_,10),label = 'first 10 terms')\n", "\n", "plt.ylim([-1.5,1.5])\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "e8e4d936-f280-4882-a4e6-65f9a86e8e8f", "metadata": {}, "source": [ "Figure (1): A demonstration of the Taylor expansion. The blue curve is the function $f(x)=\\cos(x)$ and the other lines are curves containing successively more terms of the Taylor approximation about $x=0$." ] }, { "cell_type": "markdown", "id": "ffa4d94c-f9fb-417b-8ea9-62434a9b9f3a", "metadata": {}, "source": [ "### 2.3 Exercises" ] }, { "cell_type": "markdown", "id": "dc4ff3cf-2920-4fc0-9720-8a56b83cf24a", "metadata": {}, "source": [ "Exercise 1: Find the expression for (or just the first two terms of) the Taylor expansion of $e^x$ around $x=0$.\n", "\n", "Exercise 2: Find the expression for (or just the first two terms of) the Taylor expansion of $\\cos(x)$ around $x=0$.\n", "\n", "Exercise 3: Find the expression for (or just the first two terms of) the Taylor expansion of $\\cos(x)$ around $x=\\pi/3$.\n" ] }, { "cell_type": "markdown", "id": "b4f2a0c7-bc4c-49e3-bded-08e50d9de704", "metadata": {}, "source": [ "### 2.4 List of common Taylor expansions:" ] }, { "cell_type": "markdown", "id": "e5357abc-5e63-4135-8d82-a0f7326b973b", "metadata": {}, "source": [ "1. $e^x=1+x+\\frac{x^2}{2!}+\\frac{x^3}{3!}+\\ldots$\n", "2. $\\ln (1+x)=x-\\frac{x^2}{2}+\\frac{x^3}{3}-\\ldots[$ only convergent for $-1