{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fourier sine series" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the sine functions $\\sin(n\\pi x)$ for $n=1,2,\\ldots$ on the interval $x \\in [0,1]$, with the \"usual\" function inner product $f(x) \\cdot g(x) = \\int_0^1 f(x) g(x) \\, dx$. It is a remarkable fact that the sine functions are **orthogonal** under this dot product:\n", "\n", "$$\n", "\\sin(m\\pi x) \\cdot \\sin(n\\pi x) = \\int_0^1 \\sin(m\\pi x) \\sin(n\\pi x) \\, dx = \\begin{cases} 0 & m \\ne n \\\\ \\frac{1}{2} & m = n \\end{cases} .\n", "$$\n", "\n", "This can be verified by simply doing the integral, a first-year calculus exercise. (The identity $\\sin A \\sin B = \\frac{1}{2}[\\cos (A-B) - \\cos(A+B)]$ is useful here.)\n", "\n", "Let's plot a few of these functions:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject Text(0.5,1,u'orthogonal sine functions')" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using PyPlot\n", "x = linspace(0,1,200)\n", "plot(x, sin.(π*x), \"-\")\n", "plot(x, sin.(2π*x), \"-\")\n", "plot(x, sin.(3π*x), \"-\")\n", "plot(x, sin.(4π*x), \"-\")\n", "legend([L\"\\sin(\\pi x)\", L\"\\sin(2\\pi x)\", L\"\\sin(3\\pi x)\", L\"\\sin(4\\pi x)\"])\n", "xlabel(L\"x\")\n", "title(\"orthogonal sine functions\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sines as an orthogonal basis\n", "\n", "We can consider the $\\sin(n\\pi x)$ functions as an orthogonal basis for some set of functions, defined by all linear combinations of these $\\sin(n\\pi x)$ functions (their **span**). At first glance, it seems like this should be a rather \"small\" subspace of all functions. One of the most remarkable facts of mathematics, however, is that the span of the sine functions contains nearly all possible functions of practical interest! This was first proposed by Fourier in 1807, but took almost 150 years to make rigorous and precise.\n", "\n", "For a function $f(x)$ defined on $x \\in [0,1]$, the [Fourier sine series](http://en.wikipedia.org/wiki/Fourier_sine_and_cosine_series) writes $f(x)$ as:\n", "\n", "* $f(x) = \\sum_{n=1}^\\infty b_n \\sin(n\\pi x)$\n", "\n", "where the coefficients $b_n$ can be found by integration:\n", "\n", "* $b_m = 2 \\int_0^1 f(x) \\sin(m\\pi x) dx$.\n", "\n", "Let's define a function `sinecoef` in [Julia](http://julialang.org) to compute these [integrals numerically](http://en.wikipedia.org/wiki/Numerical_integration), using Julia's [quadgk](https://github.com/JuliaMath/QuadGK.jl) function We'll use the `abstol` parameter to set an integration tolerance: we want the error to be small compared to $\\sqrt{\\int_0^1 |f(x)|^2 dx}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sinecoef (generic function with 1 method)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Pkg.add(\"QuadGK\") # uncomment to install QuadGK if needed.\n", "using QuadGK\n", "\n", "sinecoef(f, m) = 2 * quadgk(x -> f(x) * sin(m*π*x), 0,1, abstol=1e-8 * sqrt(quadgk(x->abs2(f(x)),0,1)[1]))[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A sine-series example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example, if we have the function $f(x) = 0.5 - |x - 0.5|$, the first 20 coefficients are:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "20-element Array{Float64,1}:\n", " 0.405285 \n", " 5.03187e-18\n", " -0.0450316 \n", " 1.82116e-17\n", " 0.0162114 \n", " -2.0849e-17 \n", " -0.00827112 \n", " -1.25544e-17\n", " 0.00500352 \n", " 4.70332e-17\n", " -0.00334946 \n", " -7.30892e-18\n", " 0.00239813 \n", " -2.34147e-16\n", " -0.00180127 \n", " -8.72534e-17\n", " 0.00140237 \n", " 3.67697e-16\n", " -0.00112267 \n", " -4.11412e-16" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(x) = 0.5 - abs(x - 0.5)\n", "sinecoef.(f, 1:20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(Notice that $b_n = 0$ for *even* $n$, which correspond to *antisymmetric* sine functions that integrate to zero against this *symmetric* $f$.) The coefficients seem to be converging (getting smaller), as we would hope for a convergent series. Let's plot them." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject " ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using PyPlot\n", "n = 1:2:99 # odd integers from 1 to 99\n", "loglog(n, abs.(sinecoef.(f, n)), \"bo\")\n", "xlabel(L\"n\")\n", "ylabel(L\"Fourier sine coefficient $|b_n|$\")\n", "title(L\"Sine series convergence for $f(x) = 0.5 - |x - 0.5|$\")\n", "loglog(n, 1 ./ n.^2, \"b--\")\n", "legend([L\"|b_n|\", L\"1/n^2\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They decay asymptotically as $1/n^2$. It turns out that one can prove this from the fact that $f(x)$ is continuous with a discontinuous slope.\n", "\n", "Now let's plot the series itself and compare it to $f(x)$. We'll use Julia's [Interact package](https://github.com/JuliaLang/Interact.jl) so that we can drag a slider to control the number of terms in the series." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "sinesum (generic function with 1 method)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# First, define a function to evaluate N terms of the sine series, given the coefficients b\n", "function sinesum(b, x)\n", " f = 0.0\n", " for n = 1:length(b)\n", " f += b[n] * sin(n*π*x)\n", " end\n", " return f\n", "end" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "execution_count": 6, "metadata": { "comm_id": "307cfc74-a104-4601-a4a3-3c6dbb6a2b02", "reactive": true }, "output_type": "execute_result" } ], "source": [ "using Interact\n", "fig = figure()\n", "x = linspace(0,1, 1000)\n", "@manipulate for n=1:2:99\n", " withfig(fig) do\n", " plot(x, f.(x), \"k--\")\n", " b = sinecoef.(f, 1:n)\n", " plot(x, [sinesum(b, x) for x in x], \"r-\")\n", " xlabel(L\"$x$\")\n", " legend([\"exact f\", \"$n-term sine series\"])\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In contrast, if we make a smoother function, e.g. $g(x) = \\sin(\\sin(3 \\pi x) + 5\\sin(\\pi x))$, then it eventually converges *much* more quickly (in fact, for a smooth function like this the series converges *exponentially* fast):" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "cd394369-e518-4c38-a7dd-fddc34fdf474", "version_major": 2, "version_minor": 0 } }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [], "text/plain": [ "Interact.Options{:SelectionSlider,Any}(5: \"input-2\" = 19 Any , \"n\", 19, \"19\", 10, Interact.OptionDict(DataStructures.OrderedDict{Any,Any}(\"1\"=>1,\"3\"=>3,\"5\"=>5,\"7\"=>7,\"9\"=>9,\"11\"=>11,\"13\"=>13,\"15\"=>15,\"17\"=>17,\"19\"=>19…), Dict{Any,Any}(Pair{Any,Any}(11, \"11\"),Pair{Any,Any}(21, \"21\"),Pair{Any,Any}(7, \"7\"),Pair{Any,Any}(9, \"9\"),Pair{Any,Any}(25, \"25\"),Pair{Any,Any}(35, \"35\"),Pair{Any,Any}(29, \"29\"),Pair{Any,Any}(19, \"19\"),Pair{Any,Any}(17, \"17\"),Pair{Any,Any}(37, \"37\")…)), Any[], Any[], true, \"horizontal\")" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "PyPlot.Figure(PyObject )" ] }, "execution_count": 7, "metadata": { "comm_id": "c6bc9650-c529-4cc2-8f74-7d5a1640d6f9", "reactive": true }, "output_type": "execute_result" } ], "source": [ "using Interact\n", "fig = figure(figsize=(15,6))\n", "g(x) = sin(sin(3π*x) + 5*sin(π*x))\n", "@manipulate for n=1:2:37\n", " withfig(fig) do\n", " subplot(1,2,1)\n", " plot(x, g.(x), \"k--\")\n", " b = sinecoef.(g, 1:n)\n", " plot(x, [sinesum(b, x) for x in x], \"r-\")\n", " xlabel(L\"x\")\n", " legend([\"exact g\", \"$n-term sine series\"])\n", " \n", " subplot(1,2,2)\n", " semilogy(1:2:n, abs.(b[1:2:n]), \"bo-\")\n", " xlabel(L\"n\")\n", " ylabel(L\"coefficient $|b_n|$\")\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Supplementary material\n", "\n", "The following material goes a bit beyond 18.06 (see e.g. 18.303), but it is provided as a supplement.\n", "\n", "## Solving the heat/diffusion equation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we have the heat equation $\\frac{\\partial^2 u}{\\partial x^2} = \\frac{\\partial u}{\\partial t}$, with Dirichlet boundary conditions $u(0,t) = u(1,t) = 0$, and initial condition $u(x,0) = f(x)$, we can solve the equation by expanding $u(x,t)$ in a Fourier sine series. From class:\n", "\n", "* $u(x,t) = \\sum_{n=0}^\\infty b_n \\sin(n\\pi x) e^{-(n\\pi)^2 t}$\n", "\n", "where $b_n$ are the sine-series coefficients of the initial condition $f(x)$.\n", "\n", "Let's plot this for different times $t$ for the $f(x) = 0.5 - |x - 0.5|$ from above, using 199 terms in the series:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "463cf924-496c-4be8-9326-8ee61c0e95e0", "version_major": 2, "version_minor": 0 } }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [], "text/plain": [ "Interact.Slider{Float64}(9: \"input-3\" = 0.0 Float64 , \"time t\", 0.0, 0.0:0.001:1.0, \"horizontal\", true, \".3f\", true)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "execution_count": 8, "metadata": { "comm_id": "0be516ac-62a5-47cd-9ae2-f159ac3f0f94", "reactive": true }, "output_type": "execute_result" } ], "source": [ "fig = figure()\n", "@manipulate for t in slider(0:0.001:1, value=0.0, label=\"time t\")\n", " withfig(fig) do\n", " b = @. sinecoef(f, 1:199) * exp(-((1:199)*π)^2 * t)\n", " plot(x, [sinesum(b, x) for x in x])\n", " xlabel(L\"x\")\n", " title(\"diffusion solution at time $t\")\n", " ylim(0,0.5)\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that the sharp kink (the slope discontinuity) \"diffuses away\" almost immediately, because that sharp kink is created by the high-frequency sine-series terms that decay very rapidly. After a short while, in fact, the solution just looks like $\\sin(\\pi x)$, because it is dominated by the $n=1$ term in the series." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving the wave equation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we have the *wave* equation $\\frac{\\partial^2 u}{\\partial x^2} = \\frac{\\partial^2 u}{\\partial t^2}$, with Dirichlet boundary conditions $u(0,t) = u(1,t) = 0$, and initial conditions $u(x,0) = f(x)$ and $\\dot{u}(x,0) = 0$, we can also solve the equation by expanding $u(x,t)$ in a Fourier sine series. From class:\n", "\n", "* $u(x,t) = \\sum_{n=0}^\\infty b_n \\sin(n\\pi x) \\cos{n\\pi t}$\n", "\n", "where $b_n$ are the sine-series coefficients of the initial condition $f(x)$.\n", "\n", "Let's again plot this for different times $t$ for the $f(x) = 0.5 - |x - 0.5|$ from above, using 199 terms in the series:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "41863d2d-f5e2-4f64-9630-29dc4f37a750", "version_major": 2, "version_minor": 0 } }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [], "text/plain": [ "Interact.Slider{Float64}(13: \"input-4\" = 0.0 Float64 , \"time t\", 0.0, 0.0:0.01:10.0, \"horizontal\", true, \".3f\", true)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "PyPlot.Figure(PyObject )" ] }, "execution_count": 9, "metadata": { "comm_id": "c307e257-249d-400e-8b76-47d96fba5a13", "reactive": true }, "output_type": "execute_result" } ], "source": [ "fig = figure()\n", "@manipulate for t in slider(0:0.01:10, value=0.0, label=\"time t\")\n", " withfig(fig) do\n", " b = @. sinecoef(f, 1:199) * cos(((1:199)*π) * t)\n", " plot(x, [sinesum(b, x) for x in x])\n", " xlabel(L\"x\")\n", " title(\"wave solution at time $t\")\n", " ylim(-0.5,0.5)\n", " grid()\n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we have an oscillating wave, which bounced up and down between two triangle shapes.\n", "\n", "(This may seem unrealistic to you: if you actually stretch a string into a triangle shape and let it go, it doesn't retain the sharp kinks seen here. That is due to an effect called *dispersion* that we are not including in the wave equation...yet.)" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 0.6.0", "language": "julia", "name": "julia-0.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "0.6.0" }, "widgets": { "state": { "0f715249-d955-4474-8ebb-de15454b4eef": { "views": [ { "cell_index": 12 } ] }, "5b9b0707-6132-41e0-a916-593e94d9d59b": { "views": [ { "cell_index": 17 } ] }, "92b6fa17-c0dc-40e6-9e22-9b13eca47f26": { "views": [ { "cell_index": 21 } ] }, "9cdae58e-7be2-481c-a6a6-2fce5b60e8be": { "views": [ { "cell_index": 14 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 1 }