{ "cells": [ { "cell_type": "markdown", "id": "81b1d2f0", "metadata": {}, "source": [ "---\n", "title: \"Intro to Math 5486\"\n", "subtitle: \"Lecture 1: Introduction to Math 5486\"\n", "date: 2026-01-21\n", "abstract-title: Overview\n", "abstract: | \n", " (1) Syllabus, Canvas, and Admin;
\n", " (2) Intro/Reminders on Jupyter/Julia;
\n", " (3) Reminders on Math 5485 and prerequisites;
\n", " (4) Overview of Math 5486;\n", "format:\n", " html:\n", " other-links:\n", " - text: This notebook\n", " href: L1.ipynb\n", "---" ] }, { "cell_type": "markdown", "id": "63cf0867", "metadata": {}, "source": [ "::: {.callout-note}\n", "\n", "I encourage you to play around with the juptyer notebook for this lecture - you can copy the code with the ```this notebook``` button on the side of this page.\n", "\n", ":::\n", "\n", "::: {.callout-warning}\n", "\n", "These notes are mainly a record of what we discussed and are not a substitute for attending the lectures and reading books! If anything is unclear/wrong, let me know and I will update the notes.\n", "\n", ":::\n", "\n", "## Notebooks\n", "\n", "::: {.callout-tip}\n", "\n", "Follow the steps in /InstallingJulia.html and A1 to learn about notebooks and Julia. \n", "\n", ":::\n", "\n", "Notebooks are made up from \"cells\". \n", "\n", "* ```A``` adds a cell above the currently selected cell, \n", "* ```B``` adds a cell below,\n", "* ```M``` changes the cell from Julia to markdown,\n", "* Double click or ```enter``` to see the syntax and edit cells, \n", "* Press ```ctrl```+```enter``` to exit edit mode,\n", "\n", "::: {#exm-1}\n", "\n", "Add a new markdown cell below this one and write \"Hello world!\" \n", "\n", ":::" ] }, { "cell_type": "markdown", "id": "101cc19c", "metadata": {}, "source": [ "Hello, world!" ] }, { "cell_type": "markdown", "id": "cade2484", "metadata": {}, "source": [ "### Markdown\n", "\n", "Text in this cell can be **bold**, *italic*, ***bold italic***, quotes \n", "\n", ">\"The only source of knowledge is experience\" \n", ">-- Einstein\n", "\n", "```\n", "Preformatted text,\n", " useful for\n", "pseudocode\n", "```\n", "\n", "* Bullet points \n", " - level 2 bullet points \n", " - etc..\n", "* Another point\n", "\n", "
You can also use normal html formatting if you are familiar with that...
\n", "\n", "Markdown cheat sheet: [link](https://www.markdownguide.org/basic-syntax/) " ] }, { "cell_type": "markdown", "id": "4d3e351c", "metadata": {}, "source": [ "### LaTeX\n", "\n", "$\\LaTeX$ allows you to display math: e.g. $\\pi \\approx \\frac{22}{7}$ and $$f(x) = f(a) + f'(a) (x - a) + \\frac{1}{2} f''(a) (x-a)^2 + R(x).$$\n", "\n", "Multiline equations are also possible:\n", "\n", "\\begin{align}\n", " \\int_a^b f(x) \\mathrm{d}x\n", " %\n", " &\\approx \\int_a^b p_n(x) \\mathrm{d}x \\nonumber\\\\\n", " %\n", " &= \\sum_{j=0}^n w_j f(x_j) \n", "\\end{align}\n", "\n", "LaTex cheat sheet: [link](https://quickref.me/latex.html) \n", "Draw symbol to get latex syntax: [link](https://detexify.kirelabs.org/classify.html#google_vignette)" ] }, { "cell_type": "markdown", "id": "d7c3e721", "metadata": {}, "source": [ "### Julia\n", "\n", "You can use greek symbols in Julia code: type ```\\pi``` and ```tab``` to get the symbol. \n", "\n", "You can show the result of a calculation by not ending a line with a semi-colon:" ] }, { "cell_type": "code", "execution_count": 1, "id": "b01c3677", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "π = 3.1415926535897..." ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "π" ] }, { "cell_type": "markdown", "id": "acb6e78a", "metadata": {}, "source": [ "You can add comments with a ```#```:" ] }, { "cell_type": "code", "execution_count": 2, "id": "807b34b4", "metadata": {}, "outputs": [], "source": [ "# Define p\n", "p = 22/7;" ] }, { "cell_type": "markdown", "id": "5ded2970", "metadata": {}, "source": [ "You can also use ```@show``` to print variables (which also prints the calculation):" ] }, { "cell_type": "code", "execution_count": 3, "id": "540ca2f7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "abs(π - p) / π = 0.0004024994347707008\n" ] } ], "source": [ "@show abs(π-p)/π;" ] }, { "cell_type": "markdown", "id": "1d889bc5", "metadata": {}, "source": [ "You can use ```println()``` to output variables (and you can also add text):" ] }, { "cell_type": "code", "execution_count": 4, "id": "3f4494bc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The relative error when approximating π by 22/7 is 0.0004024994347707008\n" ] } ], "source": [ "println( \"The relative error when approximating π by 22/7 is \", abs(π-p)/π)" ] }, { "cell_type": "markdown", "id": "3e551058", "metadata": {}, "source": [ "#### Arrays {.unnumbered}\n", "\n", "Arrays are indexed at 1:" ] }, { "cell_type": "code", "execution_count": 5, "id": "3f944269", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = [1 2 3 4 5];\n", "a[1]" ] }, { "cell_type": "markdown", "id": "0677504e", "metadata": {}, "source": [ "#### Vectors {.unnumbered}" ] }, { "cell_type": "code", "execution_count": 6, "id": "22e27a5f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4-element Vector{Int64}:\n", " 2\n", " 4\n", " 6\n", " 8" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b = [2, 4, 6, 8]" ] }, { "cell_type": "markdown", "id": "6080fd07", "metadata": {}, "source": [ "Vector of objects:" ] }, { "cell_type": "code", "execution_count": 7, "id": "8c0c1215", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Any}:\n", " [1 2 … 4 5]\n", " [2, 4, 6, 8]\n", " \"hello world\"" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = [ a , b , \"hello world\" ]" ] }, { "cell_type": "code", "execution_count": 8, "id": "9614c954", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"hello world\"" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c[3]" ] }, { "cell_type": "markdown", "id": "f234f1a8", "metadata": {}, "source": [ "#### Matrices {.unnumbered}\n", "\n", "You can either specify the columns:" ] }, { "cell_type": "code", "execution_count": 9, "id": "5811f004", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Int64}:\n", " 1 2\n", " 4 5" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = [ [1, 4] [2, 5] ]" ] }, { "cell_type": "markdown", "id": "6ab69ee9", "metadata": {}, "source": [ "Or the rows: " ] }, { "cell_type": "code", "execution_count": 10, "id": "16437508", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Int64}:\n", " 1 2\n", " 4 5" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Y = [ 1 2 ; 4 5 ]" ] }, { "cell_type": "markdown", "id": "802fedae", "metadata": {}, "source": [ "#### Linear Algebra {.unnumbered}\n", "\n", "In order to use a certain package, you need to use the ```using``` keyword:" ] }, { "cell_type": "code", "execution_count": 11, "id": "171680e0", "metadata": {}, "outputs": [], "source": [ "using LinearAlgebra" ] }, { "cell_type": "markdown", "id": "3114bc3d", "metadata": {}, "source": [ "Recall that" ] }, { "cell_type": "code", "execution_count": 12, "id": "6ddba0e9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Int64}:\n", " 1 2\n", " 4 5" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X " ] }, { "cell_type": "code", "execution_count": 13, "id": "be9811a2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-3.0" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "det(X)" ] }, { "cell_type": "code", "execution_count": 14, "id": "b69a8098", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tr( X )" ] }, { "cell_type": "code", "execution_count": 15, "id": "f139c771", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " -1.66667 0.666667\n", " 1.33333 -0.333333" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(-1/3) * [ 5 -2 ; -4 1 ]" ] }, { "cell_type": "code", "execution_count": 16, "id": "c51f9663", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " -1.66667 0.666667\n", " 1.33333 -0.333333" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "inv( X )" ] }, { "cell_type": "code", "execution_count": 17, "id": "b234a340", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2-element Vector{Float64}:\n", " -0.4641016151377544\n", " 6.464101615137754" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ϵ = eigvals( X )" ] }, { "cell_type": "code", "execution_count": 18, "id": "98ed8a58", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " -0.806898 -0.343724\n", " 0.59069 -0.939071" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = eigvecs( X )" ] }, { "cell_type": "code", "execution_count": 19, "id": "8ac234e6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.220446049250313e-16" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v1 = v[1:2,1]; # gets the first column of v\n", "norm( ( X - ϵ[1] * Diagonal([1, 1]) ) * v1 )" ] }, { "cell_type": "markdown", "id": "bf4967ef", "metadata": {}, "source": [ "#### Functions {.unnumbered}" ] }, { "cell_type": "code", "execution_count": 20, "id": "2481948e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1.0" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1 = x -> cos( x );\n", "f1( π )" ] }, { "cell_type": "code", "execution_count": 21, "id": "46453422", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1.0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f2(x) = cos(x)\n", "f2(π)" ] }, { "cell_type": "markdown", "id": "1fbd56ec", "metadata": {}, "source": [ "In order to do entry-wise evaluation, you can use a dot (this is called *vectorisation*): " ] }, { "cell_type": "code", "execution_count": 22, "id": "81127980", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Float64}:\n", " -1.0\n", " 1.0\n", " -1.0" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1.( [-π, 0, π] )" ] }, { "cell_type": "markdown", "id": "7ea0bf41", "metadata": {}, "source": [ "You can also specify the vectorisation at the start with ```@.```:" ] }, { "cell_type": "code", "execution_count": 23, "id": "4e496669", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3-element Vector{Float64}:\n", " -1.0\n", " 1.0\n", " -1.0" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@. f1( [-π, 0, π] )" ] }, { "cell_type": "markdown", "id": "e1385c3f", "metadata": {}, "source": [ "In order to plot functions we need the ```Plots``` package and, in order to write $\\LaTeX$ in the titles and labels, we need ```LaTeXStrings```." ] }, { "cell_type": "code", "execution_count": 24, "id": "d9d7c567", "metadata": {}, "outputs": [], "source": [ "using Plots\n", "using LaTeXStrings" ] }, { "cell_type": "code", "execution_count": 25, "id": "1f440871", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(x) = x/exp(x)\n", "plot( g, -5, 1, label=\"hello\" )" ] }, { "cell_type": "code", "execution_count": 26, "id": "b87be9e9", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = -5:.01:1;\n", "Y = X .* exp.(X) ;\n", " \n", "plot( X, Y, label = L\"f(w) = w e^w\", \n", " xlabel = L\"w\", \n", " ylabel = \"not latex\", \n", " title = \"L\\\"\\\" is a LaTeX string and \\\"\\\" a normal string\") " ] }, { "cell_type": "markdown", "id": "ae5a28d9", "metadata": {}, "source": [ "Element-wise operations can also be written using the following:" ] }, { "cell_type": "code", "execution_count": 27, "id": "822f385d", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#| label: fig-1\n", "#| fig-cap: \"Ploting two functions on one graph\"\n", "\n", "X = range(0, 10, length=100)\n", "Y1 = @. sin(X) / X\n", "Y2 = cos.(X)\n", "plot( X, [Y1 Y2], \n", " xlabel=L\"x\", \n", " label=[L\"\\frac{\\sin x}{x}\" L\"\\cos x\"], \n", " linewidth=[4 2], \n", " lc=[:green :blue]) " ] }, { "cell_type": "markdown", "id": "8459def6", "metadata": {}, "source": [ "In @fig-1, you can see two graphs! \n", "\n", "::: {.callout-note}\n", "\n", "If you are looking at the code, don't worry about the ```@fig-1``` or the ```::: {.callout-note}``` syntax - this adds the html/css elements so that the webpage looks nicer. \n", "\n", ":::\n" ] }, { "cell_type": "code", "execution_count": 28, "id": "b7cbd6eb", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# ! is like \"hold on\" in Matlab (if you are familar with that!)\n", "\n", "plot( X, Y1, xlabel=L\"x\", label=L\"\\frac{\\sin x}{x}\", linewidth=4, lc=:green) \n", "plot!( X, Y2, label=L\"\\cos x\", linewidth=2, lc=:blue) " ] }, { "cell_type": "code", "execution_count": 29, "id": "25baee30", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f3(x) = 1 / (1 + x^2);\n", "f4(x) = 1 / (1 + sin(x)^2);\n", "plot(f3, -π, π, \n", " lw=3, \n", " label = L\"f_1(x) = \\frac{1}{1+x^2}\");\n", "plot!(f4, -π, π, \n", " lw = 3, \n", " label = L\"f_2(x) = \\frac{1}{1+\\sin^2(x)}\", \n", " size = (600, 250), legend = :outertopright )" ] }, { "cell_type": "markdown", "id": "6654f203", "metadata": {}, "source": [ "## Math 5485 Quiz\n", "\n", "* See [lecture notes](https://jack.thomaslabs.co.uk/teaching/Math5485/) if you want/need to recap anything\n", "\n", "::: {#exr-1}\n", "\n", "What is the relative error in approximating $\\pi$ by $3$? (write down a formula, no need to simplify)\n", "\n", ":::\n", "\n", "::: {#exr-2}\n", "\n", "Let $x_n = \\frac{\\sin n}{n^2}$. For what $p$ do we have $x_n = \\mathcal O( n^p )$ as $n \\to \\infty$? \n", "\n", ":::\n", "\n", "::: {#exr-3}\n", "\n", "Write down the 3rd order Taylor polynomial of $f(x) = x - \\sin x$ about $x = 0$.\n", "\n", ":::\n", "\n", "::: {#exr-4}\n", "\n", "Let $y_n = \\frac1n - \\sin \\frac1n$. For what $p$ do we have $y_n = \\mathcal O( n^p )$ as $n \\to \\infty$? \n", "\n", ":::\n", "\n", "::: {#exr-5}\n", "\n", "Let $F(x) := \\frac{e^x - 1}{x}$ and notice that $F(x) \\approx G(x) := 1 + \\frac{x}{2} + \\frac{x^2}{6}$\n" ] }, { "cell_type": "code", "execution_count": 30, "id": "604e6061", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0, 1.0)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "F(x) = ( exp(x) - 1 )/x\n", "G(x) = 1 + x/2 + x^2/6\n", "\n", "ϵ = 1e-16\n", "F(ϵ), G(ϵ)" ] }, { "cell_type": "markdown", "id": "82372b93", "metadata": {}, "source": [ "\n", "Which result do you trust more and why?\n", "\n", ":::\n", "\n", "::: {#exr-6}\n", "\n", "What does the relative condition number $\\kappa_f(x)$ of a function $f$ measure? \n", "\n", ":::\n", "\n", "::: {#exr-7}\n", "\n", "Consider the following plot " ] }, { "cell_type": "code", "execution_count": 31, "id": "b3a56dd6", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#| echo: false\n", "f5 = x -> x^(-2)\n", "plot( f5, 0.1, 10, xaxis=:log, yaxis=:log )" ] }, { "cell_type": "markdown", "id": "6614e883", "metadata": {}, "source": [ "
\n", "\n", "Is the decay algebraic $x^{-p}$ or exponential $e^{-a x}$?\n", "\n", ":::\n", "\n", "::: {#exr-8}\n", "\n", "Write down the Intermediate Value Theorem.\n", "\n", ":::\n", "\n", "::: {#exr-9}\n", "\n", "Consider some function $f$ and a polynomial interpolation $p$. How could one use $p$ to approximate \n", "\n", "\\begin{align}\n", " \\int_a^b f(x) \\mathrm{d}x \\approx \\sum_{j=0}^n w_j f(x_j) ?\n", "\\end{align}\n", "\n", "What are $x_j$ and $w_j$?\n", "\n", ":::\n", "\n", "::: {#exr-10}\n", "\n", "Suppose $u : [0,T] \\to \\mathbb R$ solves the *initial value problem* \n", "\n", "\\begin{align}\n", " u'(t) &= f\\big( t, u(t) \\big) \\qquad \\text{on } (0,T) \\nonumber \\\\\n", " u(0) &= u_0. \n", "\\end{align}\n", "\n", "Fix *mesh points* $t_j = j \\frac{T}{n}$ for $j=0,\\dots,n$ and show that \n", "\n", "\\begin{align}\n", " u(t_{j+1}) - u( t_j ) = \\int_{t_j}^{t_{j+1}} f\\big( s, u(s) \\big) \\mathrm{d}s \n", "\\end{align}\n", "\n", ":::\n", "\n", "::: {#exr-11}\n", "\n", "Write down what you get when you apply the rectangular rule to $(4)$. \n", "\n", ":::\n", "\n", "::: {#exr-11}\n", "\n", "A simple numerical method for solving $(3)$ is to approximate the integral in $(4)$ with the rectangular rule (this is known as *Euler's method*)\n", "\n", "\\begin{align}\n", " u(t_{j+1}) \\approx u(t_j) + \\frac{T}{n} f\\big( t_j, u(t_j) \\big).\n", "\\end{align}\n", "\n", "We implement this here:" ] }, { "cell_type": "code", "execution_count": 32, "id": "61f7c9e5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Euler (generic function with 1 method)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function Euler( u0, f, T, n )\n", " h = T/n \n", " t = 0:h:T \n", " u = zeros(n+1)\n", " u[1] = u0\n", " for j = 1:n\n", " u[j+1] = u[j] + h * f( t[j], u[j] )\n", " end\n", " return u\n", "end " ] }, { "cell_type": "markdown", "id": "6ebbda29", "metadata": {}, "source": [ "We now use this method to numerically solve the initial value problem for $u_0 = 0$ and $f(t, u) := -t \\cos(u)$:" ] }, { "cell_type": "code", "execution_count": 33, "id": "73d43e2a", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(t,u) = -t * cos(u) \n", "u0 = 0\n", "T = 10\n", "n = 100\n", "\n", "u = Euler( 0, f, T, n)\n", "plot( 0:T/n:T , u, label = \"Approximate solution with n = $n\" )" ] }, { "cell_type": "markdown", "id": "b94ee96d", "metadata": {}, "source": [ "
\n", "\n", "We observe $u(t) \\to \\alpha$ as $t\\to\\infty$. Can you compute the value of $\\alpha$?\n", "\n", ":::\n", "\n", "## Math 5486\n", "\n", "* Chapter 1: Initial Value Problems\n", "* Chapter 2: Iterative Methods in Matrix Algebra\n", "* Chapter 3: Finite Differences for Boundary Value Problems\n", "* Chapter 4: Numerical Solution to PDEs\n", "\n", ":::{.callout-tip}\n", "# TO-DO\n", "\n", "* Read: Relevant sections of the lecture notes for Math 5485 if anything from today was unclear,\n", "* Read: Pages 259--268 of @Burden - please come to the lecture next week with any questions you have,\n", "* Assignment 1: Due Wednesday,\n", "* (Sign-up to office hours if you like)\n", "\n", ":::" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.11", "language": "julia", "name": "julia-1.11" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }