mathematical-notebooks-for-the-physical-sciences/16_Complex_Integration.ipynb

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      "source": "Chapter 16 of [A Guided Tour of Mathematical Methods for the Physical Sciences](https://www.cambridge.org/nz/academic/subjects/physics/mathematical-methods/guided-tour-mathematical-methods-physical-sciences-3rd-edition?format=PB&isbn=9781107641600) deals with integration in the complex plane. A very handy tool to solve important problems in physics invokes using the residue theorem. Instead of integrating in the complex plane, we explore the solution of the velocity of a particle in a viscous fluid (syrup, for example). The equation of motion of a particle with mass $m$ in a syrup with viscosity $\\beta$ is $$ m\\frac{d v}{d t} +\\beta v= f(t).$$\nThe force on the particle is described by the source term $f(t)$. In Chapter 16, we use a Fourier transform to turn this differential equation into an algebraic equation, which is much easier to solve. The price we pay is that the algebraic equation is complex. Nevertheless, after solving the algebraic equation, \"all\" we have to do is the inverse Fourier transform to find the velocity of this particle at any time $v(t)$. You can read in the book how the complex integral of the Fourier (back) transform can be solved analytically with the residue theorem:\n\n$$ v(t) = \\int_{-\\infty}^t e^{-(\\beta/m)(t-t')}f(t')dt'.$$"
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      "source": "### Numerical examples\nLet's consider some forcing term $f(t)$ and explore the particle's velocity.\n\n$$ f(t) = 0 \\ \\ \\ \\forall \\ \\ \\ \\ t<0 \\ \\ \\ \\mbox{and} \\ \\ \\ t>1$$\nand\n$$ f(t) = 1 \\ \\ \\ \\ 0 <t<1:$$"
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      "metadata": {},
      "cell_type": "markdown",
      "source": "To evaluate the integral that describes the velocity of the particle, we use a function \"quad\" from the scipy library, based on a Fortran code to do numerical integration:"
    },
    {
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      "cell_type": "code",
      "source": "from scipy import integrate\nimport numpy as np\nimport matplotlib.pyplot as plt\n%matplotlib notebook",
      "execution_count": null,
      "outputs": []
    },
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      "metadata": {
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      "cell_type": "code",
      "source": "# a function to describe the integrand for a constant force function f(t)\ndef const(tprime,t,m,beta,a):\n    \n    if tprime>=-a and tprime<a: # a constant force in a finite interval:\n        ftprime = 1/(2*a)\n    else:\n        ftprime = 0\n    return ftprime*np.exp(-(beta/m)*(t-tprime))",
      "execution_count": null,
      "outputs": []
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      "cell_type": "code",
      "source": "betas = np.logspace(-3,0.5,11)\nm = 1 # normalise the mass\na =2 # half-width of the source force term\n\n# times to consider:\nts = np.linspace(-2*a,8*a,101)\n\n# define the box-car source force term:\nsrc_indices = np.where(np.logical_and(ts > -a,ts <a))\nsource = np.zeros(len(ts))\nsource[src_indices] = 1/(2*a)",
      "execution_count": 46,
      "outputs": []
    },
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      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "plt.figure()\nplt.plot(ts,source,label='source')\nplt.legend()\nplt.xlabel('Time')\nplt.ylabel('Force')\nplt.show()",
      "execution_count": 47,
      "outputs": [
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We want\n     * to control all of the cursor setting manually through the\n     * 'cursor' event from matplotlib */\n    event.preventDefault();\n    return false;\n}\n\nmpl.figure.prototype._key_event_extra = function(event, name) {\n    // Handle any extra behaviour associated with a key event\n}\n\nmpl.figure.prototype.key_event = function(event, name) {\n\n    // Prevent repeat events\n    if (name == 'key_press')\n    {\n        if (event.which === this._key)\n            return;\n        else\n            this._key = event.which;\n    }\n    if (name == 'key_release')\n        this._key = null;\n\n    var value = '';\n    if (event.ctrlKey && event.which != 17)\n        value += \"ctrl+\";\n    if (event.altKey && event.which != 18)\n        value += \"alt+\";\n    if (event.shiftKey && event.which != 16)\n        value += \"shift+\";\n\n    value += 'k';\n    value += event.which.toString();\n\n    this._key_event_extra(event, name);\n\n    this.send_message(name, {key: value,\n                             guiEvent: simpleKeys(event)});\n    return false;\n}\n\nmpl.figure.prototype.toolbar_button_onclick = function(name) {\n    if (name == 'download') {\n        this.handle_save(this, null);\n    } else {\n        this.send_message(\"toolbar_button\", {name: name});\n    }\n};\n\nmpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n    this.message.textContent = tooltip;\n};\nmpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n\nmpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n\nmpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n    // Create a \"websocket\"-like object which calls the given IPython comm\n    // object with the appropriate methods. Currently this is a non binary\n    // socket, so there is still some room for performance tuning.\n    var ws = {};\n\n    ws.close = function() {\n        comm.close()\n    };\n    ws.send = function(m) {\n        //console.log('sending', m);\n        comm.send(m);\n    };\n    // Register the callback with on_msg.\n    comm.on_msg(function(msg) {\n        //console.log('receiving', msg['content']['data'], msg);\n        // Pass the mpl event to the overridden (by mpl) onmessage function.\n        ws.onmessage(msg['content']['data'])\n    });\n    return ws;\n}\n\nmpl.mpl_figure_comm = function(comm, msg) {\n    // This is the function which gets called when the mpl process\n    // starts-up an IPython Comm through the \"matplotlib\" channel.\n\n    var id = msg.content.data.id;\n    // Get hold of the div created by the display call when the Comm\n    // socket was opened in Python.\n    var element = $(\"#\" + id);\n    var ws_proxy = comm_websocket_adapter(comm)\n\n    function ondownload(figure, format) {\n        window.open(figure.imageObj.src);\n    }\n\n    var fig = new mpl.figure(id, ws_proxy,\n                           ondownload,\n                           element.get(0));\n\n    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n    // web socket which is closed, not our websocket->open comm proxy.\n    ws_proxy.onopen();\n\n    fig.parent_element = element.get(0);\n    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n    if (!fig.cell_info) {\n        console.error(\"Failed to find cell for figure\", id, fig);\n        return;\n    }\n\n    var output_index = fig.cell_info[2]\n    var cell = fig.cell_info[0];\n\n};\n\nmpl.figure.prototype.handle_close = function(fig, msg) {\n    var width = fig.canvas.width/mpl.ratio\n    fig.root.unbind('remove')\n\n    // Update the output cell to use the data from the current canvas.\n    fig.push_to_output();\n    var dataURL = fig.canvas.toDataURL();\n    // Re-enable the keyboard manager in IPython - without this line, in FF,\n    // the notebook keyboard shortcuts fail.\n    IPython.keyboard_manager.enable()\n    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n    fig.close_ws(fig, msg);\n}\n\nmpl.figure.prototype.close_ws = function(fig, msg){\n    fig.send_message('closing', msg);\n    // fig.ws.close()\n}\n\nmpl.figure.prototype.push_to_output = function(remove_interactive) {\n    // Turn the data on the canvas into data in the output cell.\n    var width = this.canvas.width/mpl.ratio\n    var dataURL = this.canvas.toDataURL();\n    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n}\n\nmpl.figure.prototype.updated_canvas_event = function() {\n    // Tell IPython that the notebook contents must change.\n    IPython.notebook.set_dirty(true);\n    this.send_message(\"ack\", {});\n    var fig = this;\n    // Wait a second, then push the new image to the DOM so\n    // that it is saved nicely (might be nice to debounce this).\n    setTimeout(function () { fig.push_to_output() }, 1000);\n}\n\nmpl.figure.prototype._init_toolbar = function() {\n    var fig = this;\n\n    var nav_element = $('<div/>')\n    nav_element.attr('style', 'width: 100%');\n    this.root.append(nav_element);\n\n    // Define a callback function for later on.\n    function toolbar_event(event) {\n        return fig.toolbar_button_onclick(event['data']);\n    }\n    function toolbar_mouse_event(event) {\n        return fig.toolbar_button_onmouseover(event['data']);\n    }\n\n    for(var toolbar_ind in mpl.toolbar_items){\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) { continue; };\n\n        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n        button.click(method_name, toolbar_event);\n        button.mouseover(tooltip, toolbar_mouse_event);\n        nav_element.append(button);\n    }\n\n    // Add the status bar.\n    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n    nav_element.append(status_bar);\n    this.message = status_bar[0];\n\n    // Add the close button to the window.\n    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n    button.click(function (evt) { fig.handle_close(fig, {}); } );\n    button.mouseover('Stop Interaction', toolbar_mouse_event);\n    buttongrp.append(button);\n    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n    titlebar.prepend(buttongrp);\n}\n\nmpl.figure.prototype._root_extra_style = function(el){\n    var fig = this\n    el.on(\"remove\", function(){\n\tfig.close_ws(fig, {});\n    });\n}\n\nmpl.figure.prototype._canvas_extra_style = function(el){\n    // this is important to make the div 'focusable\n    el.attr('tabindex', 0)\n    // reach out to IPython and tell the keyboard manager to turn it's self\n    // off when our div gets focus\n\n    // location in version 3\n    if (IPython.notebook.keyboard_manager) {\n        IPython.notebook.keyboard_manager.register_events(el);\n    }\n    else {\n        // location in version 2\n        IPython.keyboard_manager.register_events(el);\n    }\n\n}\n\nmpl.figure.prototype._key_event_extra = function(event, name) {\n    var manager = IPython.notebook.keyboard_manager;\n    if (!manager)\n        manager = IPython.keyboard_manager;\n\n    // Check for shift+enter\n    if (event.shiftKey && event.which == 13) {\n        this.canvas_div.blur();\n        event.shiftKey = false;\n        // Send a \"J\" for go to next cell\n        event.which = 74;\n        event.keyCode = 74;\n        manager.command_mode();\n        manager.handle_keydown(event);\n    }\n}\n\nmpl.figure.prototype.handle_save = function(fig, msg) {\n    fig.ondownload(fig, null);\n}\n\n\nmpl.find_output_cell = function(html_output) {\n    // Return the cell and output element which can be found *uniquely* in the notebook.\n    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n    // IPython event is triggered only after the cells have been serialised, which for\n    // our purposes (turning an active figure into a static one), is too late.\n    var cells = IPython.notebook.get_cells();\n    var ncells = cells.length;\n    for (var i=0; i<ncells; i++) {\n        var cell = cells[i];\n        if (cell.cell_type === 'code'){\n            for (var j=0; j<cell.output_area.outputs.length; j++) {\n                var data = cell.output_area.outputs[j];\n                if (data.data) {\n                    // IPython >= 3 moved mimebundle to data attribute of output\n                    data = data.data;\n                }\n                if (data['text/html'] == html_output) {\n                    return [cell, data, j];\n                }\n            }\n        }\n    }\n}\n\n// Register the function which deals with the matplotlib target/channel.\n// The kernel may be null if the page has been refreshed.\nif (IPython.notebook.kernel != null) {\n    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n}\n",
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    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "plt.figure()\nfor beta in betas:\n    vt = np.array([])\n    \n    for t in ts:\n        integral = integrate.quad(const,-10,t, args=(t,m,beta,a))\n        vt = np.append(vt,integral[0])\n    \n    plt.plot(ts,vt,label=str(round(beta,2)))\nplt.xlabel('time')\nplt.ylabel('velocity')\nplt.legend()\nplt.show()",
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": "/* Put everything inside the global mpl namespace */\nwindow.mpl = {};\n\n\nmpl.get_websocket_type = function() {\n    if (typeof(WebSocket) !== 'undefined') {\n        return WebSocket;\n    } else if (typeof(MozWebSocket) !== 'undefined') {\n        return MozWebSocket;\n    } else {\n        alert('Your browser does not have WebSocket support.' +\n              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n              'Firefox 4 and 5 are also supported but you ' +\n              'have to enable WebSockets in about:config.');\n    };\n}\n\nmpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n    this.id = figure_id;\n\n    this.ws = websocket;\n\n    this.supports_binary = (this.ws.binaryType != undefined);\n\n    if (!this.supports_binary) {\n        var warnings = document.getElementById(\"mpl-warnings\");\n        if (warnings) {\n            warnings.style.display = 'block';\n            warnings.textContent = (\n                \"This browser does not support binary websocket messages. \" +\n                    \"Performance may be slow.\");\n        }\n    }\n\n    this.imageObj = new Image();\n\n    this.context = undefined;\n    this.message = undefined;\n    this.canvas = undefined;\n    this.rubberband_canvas = undefined;\n    this.rubberband_context = undefined;\n    this.format_dropdown = undefined;\n\n    this.image_mode = 'full';\n\n    this.root = $('<div/>');\n    this._root_extra_style(this.root)\n    this.root.attr('style', 'display: inline-block');\n\n    $(parent_element).append(this.root);\n\n    this._init_header(this);\n    this._init_canvas(this);\n    this._init_toolbar(this);\n\n    var fig = this;\n\n    this.waiting = false;\n\n    this.ws.onopen =  function () {\n            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n            fig.send_message(\"send_image_mode\", {});\n            if (mpl.ratio != 1) {\n                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n            }\n            fig.send_message(\"refresh\", {});\n        }\n\n    this.imageObj.onload = function() {\n            if (fig.image_mode == 'full') {\n                // Full images could contain transparency (where diff images\n                // almost always do), so we need to clear the canvas so that\n                // there is no ghosting.\n                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n            }\n            fig.context.drawImage(fig.imageObj, 0, 0);\n        };\n\n    this.imageObj.onunload = function() {\n        fig.ws.close();\n    }\n\n    this.ws.onmessage = this._make_on_message_function(this);\n\n    this.ondownload = ondownload;\n}\n\nmpl.figure.prototype._init_header = function() {\n    var titlebar = $(\n        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n        'ui-helper-clearfix\"/>');\n    var titletext = $(\n        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n        'text-align: center; padding: 3px;\"/>');\n    titlebar.append(titletext)\n    this.root.append(titlebar);\n    this.header = titletext[0];\n}\n\n\n\nmpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n\n}\n\n\nmpl.figure.prototype._root_extra_style = function(canvas_div) {\n\n}\n\nmpl.figure.prototype._init_canvas = function() {\n    var fig = this;\n\n    var canvas_div = $('<div/>');\n\n    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n\n    function canvas_keyboard_event(event) {\n        return fig.key_event(event, event['data']);\n    }\n\n    canvas_div.keydown('key_press', canvas_keyboard_event);\n    canvas_div.keyup('key_release', canvas_keyboard_event);\n    this.canvas_div = canvas_div\n    this._canvas_extra_style(canvas_div)\n    this.root.append(canvas_div);\n\n    var canvas = $('<canvas/>');\n    canvas.addClass('mpl-canvas');\n    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n\n    this.canvas = canvas[0];\n    this.context = canvas[0].getContext(\"2d\");\n\n    var backingStore = this.context.backingStorePixelRatio ||\n\tthis.context.webkitBackingStorePixelRatio ||\n\tthis.context.mozBackingStorePixelRatio ||\n\tthis.context.msBackingStorePixelRatio ||\n\tthis.context.oBackingStorePixelRatio ||\n\tthis.context.backingStorePixelRatio || 1;\n\n    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n\n    var rubberband = $('<canvas/>');\n    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n\n    var pass_mouse_events = true;\n\n    canvas_div.resizable({\n        start: function(event, ui) {\n            pass_mouse_events = false;\n        },\n        resize: function(event, ui) {\n            fig.request_resize(ui.size.width, ui.size.height);\n        },\n        stop: function(event, ui) {\n            pass_mouse_events = true;\n            fig.request_resize(ui.size.width, ui.size.height);\n        },\n    });\n\n    function mouse_event_fn(event) {\n        if (pass_mouse_events)\n            return fig.mouse_event(event, event['data']);\n    }\n\n    rubberband.mousedown('button_press', mouse_event_fn);\n    rubberband.mouseup('button_release', mouse_event_fn);\n    // Throttle sequential mouse events to 1 every 20ms.\n    rubberband.mousemove('motion_notify', mouse_event_fn);\n\n    rubberband.mouseenter('figure_enter', mouse_event_fn);\n    rubberband.mouseleave('figure_leave', mouse_event_fn);\n\n    canvas_div.on(\"wheel\", function (event) {\n        event = event.originalEvent;\n        event['data'] = 'scroll'\n        if (event.deltaY < 0) {\n            event.step = 1;\n        } else {\n            event.step = -1;\n        }\n        mouse_event_fn(event);\n    });\n\n    canvas_div.append(canvas);\n    canvas_div.append(rubberband);\n\n    this.rubberband = rubberband;\n    this.rubberband_canvas = rubberband[0];\n    this.rubberband_context = rubberband[0].getContext(\"2d\");\n    this.rubberband_context.strokeStyle = \"#000000\";\n\n    this._resize_canvas = function(width, height) {\n        // Keep the size of the canvas, canvas container, and rubber band\n        // canvas in synch.\n        canvas_div.css('width', width)\n        canvas_div.css('height', height)\n\n        canvas.attr('width', width * mpl.ratio);\n        canvas.attr('height', height * mpl.ratio);\n        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n\n        rubberband.attr('width', width);\n        rubberband.attr('height', height);\n    }\n\n    // Set the figure to an initial 600x600px, this will subsequently be updated\n    // upon first draw.\n    this._resize_canvas(600, 600);\n\n    // Disable right mouse context menu.\n    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n        return false;\n    });\n\n    function set_focus () {\n        canvas.focus();\n        canvas_div.focus();\n    }\n\n    window.setTimeout(set_focus, 100);\n}\n\nmpl.figure.prototype._init_toolbar = function() {\n    var fig = this;\n\n    var nav_element = $('<div/>')\n    nav_element.attr('style', 'width: 100%');\n    this.root.append(nav_element);\n\n    // Define a callback function for later on.\n    function toolbar_event(event) {\n        return fig.toolbar_button_onclick(event['data']);\n    }\n    function toolbar_mouse_event(event) {\n        return fig.toolbar_button_onmouseover(event['data']);\n    }\n\n    for(var toolbar_ind in mpl.toolbar_items) {\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) {\n            // put a spacer in here.\n            continue;\n        }\n        var button = $('<button/>');\n        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n                        'ui-button-icon-only');\n        button.attr('role', 'button');\n        button.attr('aria-disabled', 'false');\n        button.click(method_name, toolbar_event);\n        button.mouseover(tooltip, toolbar_mouse_event);\n\n        var icon_img = $('<span/>');\n        icon_img.addClass('ui-button-icon-primary ui-icon');\n        icon_img.addClass(image);\n        icon_img.addClass('ui-corner-all');\n\n        var tooltip_span = $('<span/>');\n        tooltip_span.addClass('ui-button-text');\n        tooltip_span.html(tooltip);\n\n        button.append(icon_img);\n        button.append(tooltip_span);\n\n        nav_element.append(button);\n    }\n\n    var fmt_picker_span = $('<span/>');\n\n    var fmt_picker = $('<select/>');\n    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n    fmt_picker_span.append(fmt_picker);\n    nav_element.append(fmt_picker_span);\n    this.format_dropdown = fmt_picker[0];\n\n    for (var ind in mpl.extensions) {\n        var fmt = mpl.extensions[ind];\n        var option = $(\n            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n        fmt_picker.append(option)\n    }\n\n    // Add hover states to the ui-buttons\n    $( \".ui-button\" ).hover(\n        function() { $(this).addClass(\"ui-state-hover\");},\n        function() { $(this).removeClass(\"ui-state-hover\");}\n    );\n\n    var status_bar = $('<span class=\"mpl-message\"/>');\n    nav_element.append(status_bar);\n    this.message = status_bar[0];\n}\n\nmpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n    // which will in turn request a refresh of the image.\n    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n}\n\nmpl.figure.prototype.send_message = function(type, properties) {\n    properties['type'] = type;\n    properties['figure_id'] = this.id;\n    this.ws.send(JSON.stringify(properties));\n}\n\nmpl.figure.prototype.send_draw_message = function() {\n    if (!this.waiting) {\n        this.waiting = true;\n        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n    }\n}\n\n\nmpl.figure.prototype.handle_save = function(fig, msg) {\n    var format_dropdown = fig.format_dropdown;\n    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n    fig.ondownload(fig, format);\n}\n\n\nmpl.figure.prototype.handle_resize = function(fig, msg) {\n    var size = msg['size'];\n    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n        fig._resize_canvas(size[0], size[1]);\n        fig.send_message(\"refresh\", {});\n    };\n}\n\nmpl.figure.prototype.handle_rubberband = function(fig, msg) {\n    var x0 = msg['x0'] / mpl.ratio;\n    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n    var x1 = msg['x1'] / mpl.ratio;\n    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n    x0 = Math.floor(x0) + 0.5;\n    y0 = Math.floor(y0) + 0.5;\n    x1 = Math.floor(x1) + 0.5;\n    y1 = Math.floor(y1) + 0.5;\n    var min_x = Math.min(x0, x1);\n    var min_y = Math.min(y0, y1);\n    var width = Math.abs(x1 - x0);\n    var height = Math.abs(y1 - y0);\n\n    fig.rubberband_context.clearRect(\n        0, 0, fig.canvas.width, fig.canvas.height);\n\n    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n}\n\nmpl.figure.prototype.handle_figure_label = function(fig, msg) {\n    // Updates the figure title.\n    fig.header.textContent = msg['label'];\n}\n\nmpl.figure.prototype.handle_cursor = function(fig, msg) {\n    var cursor = msg['cursor'];\n    switch(cursor)\n    {\n    case 0:\n        cursor = 'pointer';\n        break;\n    case 1:\n        cursor = 'default';\n        break;\n    case 2:\n        cursor = 'crosshair';\n        break;\n    case 3:\n        cursor = 'move';\n        break;\n    }\n    fig.rubberband_canvas.style.cursor = cursor;\n}\n\nmpl.figure.prototype.handle_message = function(fig, msg) {\n    fig.message.textContent = msg['message'];\n}\n\nmpl.figure.prototype.handle_draw = function(fig, msg) {\n    // Request the server to send over a new figure.\n    fig.send_draw_message();\n}\n\nmpl.figure.prototype.handle_image_mode = function(fig, msg) {\n    fig.image_mode = msg['mode'];\n}\n\nmpl.figure.prototype.updated_canvas_event = function() {\n    // Called whenever the canvas gets updated.\n    this.send_message(\"ack\", {});\n}\n\n// A function to construct a web socket function for onmessage handling.\n// Called in the figure constructor.\nmpl.figure.prototype._make_on_message_function = function(fig) {\n    return function socket_on_message(evt) {\n        if (evt.data instanceof Blob) {\n            /* FIXME: We get \"Resource interpreted as Image but\n             * transferred with MIME type text/plain:\" errors on\n             * Chrome.  But how to set the MIME type?  It doesn't seem\n             * to be part of the websocket stream */\n            evt.data.type = \"image/png\";\n\n            /* Free the memory for the previous frames */\n            if (fig.imageObj.src) {\n                (window.URL || window.webkitURL).revokeObjectURL(\n                    fig.imageObj.src);\n            }\n\n            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n                evt.data);\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        }\n        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n            fig.imageObj.src = evt.data;\n            fig.updated_canvas_event();\n            fig.waiting = false;\n            return;\n        }\n\n        var msg = JSON.parse(evt.data);\n        var msg_type = msg['type'];\n\n        // Call the  \"handle_{type}\" callback, which takes\n        // the figure and JSON message as its only arguments.\n        try {\n            var callback = fig[\"handle_\" + msg_type];\n        } catch (e) {\n            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n            return;\n        }\n\n        if (callback) {\n            try {\n                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n                callback(fig, msg);\n            } catch (e) {\n                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n            }\n        }\n    };\n}\n\n// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\nmpl.findpos = function(e) {\n    //this section is from http://www.quirksmode.org/js/events_properties.html\n    var targ;\n    if (!e)\n        e = window.event;\n    if (e.target)\n        targ = e.target;\n    else if (e.srcElement)\n        targ = e.srcElement;\n    if (targ.nodeType == 3) // defeat Safari bug\n        targ = targ.parentNode;\n\n    // jQuery normalizes the pageX and pageY\n    // pageX,Y are the mouse positions relative to the document\n    // offset() returns the position of the element relative to the document\n    var x = e.pageX - $(targ).offset().left;\n    var y = e.pageY - $(targ).offset().top;\n\n    return {\"x\": x, \"y\": y};\n};\n\n/*\n * return a copy of an object with only non-object keys\n * we need this to avoid circular references\n * http://stackoverflow.com/a/24161582/3208463\n */\nfunction simpleKeys (original) {\n  return Object.keys(original).reduce(function (obj, key) {\n    if (typeof original[key] !== 'object')\n        obj[key] = original[key]\n    return obj;\n  }, {});\n}\n\nmpl.figure.prototype.mouse_event = function(event, name) {\n    var canvas_pos = mpl.findpos(event)\n\n    if (name === 'button_press')\n    {\n        this.canvas.focus();\n        this.canvas_div.focus();\n    }\n\n    var x = canvas_pos.x * mpl.ratio;\n    var y = canvas_pos.y * mpl.ratio;\n\n    this.send_message(name, {x: x, y: y, button: event.button,\n                             step: event.step,\n                             guiEvent: simpleKeys(event)});\n\n    /* This prevents the web browser from automatically changing to\n     * the text insertion cursor when the button is pressed.  We want\n     * to control all of the cursor setting manually through the\n     * 'cursor' event from matplotlib */\n    event.preventDefault();\n    return false;\n}\n\nmpl.figure.prototype._key_event_extra = function(event, name) {\n    // Handle any extra behaviour associated with a key event\n}\n\nmpl.figure.prototype.key_event = function(event, name) {\n\n    // Prevent repeat events\n    if (name == 'key_press')\n    {\n        if (event.which === this._key)\n            return;\n        else\n            this._key = event.which;\n    }\n    if (name == 'key_release')\n        this._key = null;\n\n    var value = '';\n    if (event.ctrlKey && event.which != 17)\n        value += \"ctrl+\";\n    if (event.altKey && event.which != 18)\n        value += \"alt+\";\n    if (event.shiftKey && event.which != 16)\n        value += \"shift+\";\n\n    value += 'k';\n    value += event.which.toString();\n\n    this._key_event_extra(event, name);\n\n    this.send_message(name, {key: value,\n                             guiEvent: simpleKeys(event)});\n    return false;\n}\n\nmpl.figure.prototype.toolbar_button_onclick = function(name) {\n    if (name == 'download') {\n        this.handle_save(this, null);\n    } else {\n        this.send_message(\"toolbar_button\", {name: name});\n    }\n};\n\nmpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n    this.message.textContent = tooltip;\n};\nmpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n\nmpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n\nmpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n    // Create a \"websocket\"-like object which calls the given IPython comm\n    // object with the appropriate methods. Currently this is a non binary\n    // socket, so there is still some room for performance tuning.\n    var ws = {};\n\n    ws.close = function() {\n        comm.close()\n    };\n    ws.send = function(m) {\n        //console.log('sending', m);\n        comm.send(m);\n    };\n    // Register the callback with on_msg.\n    comm.on_msg(function(msg) {\n        //console.log('receiving', msg['content']['data'], msg);\n        // Pass the mpl event to the overridden (by mpl) onmessage function.\n        ws.onmessage(msg['content']['data'])\n    });\n    return ws;\n}\n\nmpl.mpl_figure_comm = function(comm, msg) {\n    // This is the function which gets called when the mpl process\n    // starts-up an IPython Comm through the \"matplotlib\" channel.\n\n    var id = msg.content.data.id;\n    // Get hold of the div created by the display call when the Comm\n    // socket was opened in Python.\n    var element = $(\"#\" + id);\n    var ws_proxy = comm_websocket_adapter(comm)\n\n    function ondownload(figure, format) {\n        window.open(figure.imageObj.src);\n    }\n\n    var fig = new mpl.figure(id, ws_proxy,\n                           ondownload,\n                           element.get(0));\n\n    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n    // web socket which is closed, not our websocket->open comm proxy.\n    ws_proxy.onopen();\n\n    fig.parent_element = element.get(0);\n    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n    if (!fig.cell_info) {\n        console.error(\"Failed to find cell for figure\", id, fig);\n        return;\n    }\n\n    var output_index = fig.cell_info[2]\n    var cell = fig.cell_info[0];\n\n};\n\nmpl.figure.prototype.handle_close = function(fig, msg) {\n    var width = fig.canvas.width/mpl.ratio\n    fig.root.unbind('remove')\n\n    // Update the output cell to use the data from the current canvas.\n    fig.push_to_output();\n    var dataURL = fig.canvas.toDataURL();\n    // Re-enable the keyboard manager in IPython - without this line, in FF,\n    // the notebook keyboard shortcuts fail.\n    IPython.keyboard_manager.enable()\n    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n    fig.close_ws(fig, msg);\n}\n\nmpl.figure.prototype.close_ws = function(fig, msg){\n    fig.send_message('closing', msg);\n    // fig.ws.close()\n}\n\nmpl.figure.prototype.push_to_output = function(remove_interactive) {\n    // Turn the data on the canvas into data in the output cell.\n    var width = this.canvas.width/mpl.ratio\n    var dataURL = this.canvas.toDataURL();\n    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n}\n\nmpl.figure.prototype.updated_canvas_event = function() {\n    // Tell IPython that the notebook contents must change.\n    IPython.notebook.set_dirty(true);\n    this.send_message(\"ack\", {});\n    var fig = this;\n    // Wait a second, then push the new image to the DOM so\n    // that it is saved nicely (might be nice to debounce this).\n    setTimeout(function () { fig.push_to_output() }, 1000);\n}\n\nmpl.figure.prototype._init_toolbar = function() {\n    var fig = this;\n\n    var nav_element = $('<div/>')\n    nav_element.attr('style', 'width: 100%');\n    this.root.append(nav_element);\n\n    // Define a callback function for later on.\n    function toolbar_event(event) {\n        return fig.toolbar_button_onclick(event['data']);\n    }\n    function toolbar_mouse_event(event) {\n        return fig.toolbar_button_onmouseover(event['data']);\n    }\n\n    for(var toolbar_ind in mpl.toolbar_items){\n        var name = mpl.toolbar_items[toolbar_ind][0];\n        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n        var image = mpl.toolbar_items[toolbar_ind][2];\n        var method_name = mpl.toolbar_items[toolbar_ind][3];\n\n        if (!name) { continue; };\n\n        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n        button.click(method_name, toolbar_event);\n        button.mouseover(tooltip, toolbar_mouse_event);\n        nav_element.append(button);\n    }\n\n    // Add the status bar.\n    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n    nav_element.append(status_bar);\n    this.message = status_bar[0];\n\n    // Add the close button to the window.\n    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n    button.click(function (evt) { fig.handle_close(fig, {}); } );\n    button.mouseover('Stop Interaction', toolbar_mouse_event);\n    buttongrp.append(button);\n    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n    titlebar.prepend(buttongrp);\n}\n\nmpl.figure.prototype._root_extra_style = function(el){\n    var fig = this\n    el.on(\"remove\", function(){\n\tfig.close_ws(fig, {});\n    });\n}\n\nmpl.figure.prototype._canvas_extra_style = function(el){\n    // this is important to make the div 'focusable\n    el.attr('tabindex', 0)\n    // reach out to IPython and tell the keyboard manager to turn it's self\n    // off when our div gets focus\n\n    // location in version 3\n    if (IPython.notebook.keyboard_manager) {\n        IPython.notebook.keyboard_manager.register_events(el);\n    }\n    else {\n        // location in version 2\n        IPython.keyboard_manager.register_events(el);\n    }\n\n}\n\nmpl.figure.prototype._key_event_extra = function(event, name) {\n    var manager = IPython.notebook.keyboard_manager;\n    if (!manager)\n        manager = IPython.keyboard_manager;\n\n    // Check for shift+enter\n    if (event.shiftKey && event.which == 13) {\n        this.canvas_div.blur();\n        event.shiftKey = false;\n        // Send a \"J\" for go to next cell\n        event.which = 74;\n        event.keyCode = 74;\n        manager.command_mode();\n        manager.handle_keydown(event);\n    }\n}\n\nmpl.figure.prototype.handle_save = function(fig, msg) {\n    fig.ondownload(fig, null);\n}\n\n\nmpl.find_output_cell = function(html_output) {\n    // Return the cell and output element which can be found *uniquely* in the notebook.\n    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n    // IPython event is triggered only after the cells have been serialised, which for\n    // our purposes (turning an active figure into a static one), is too late.\n    var cells = IPython.notebook.get_cells();\n    var ncells = cells.length;\n    for (var i=0; i<ncells; i++) {\n        var cell = cells[i];\n        if (cell.cell_type === 'code'){\n            for (var j=0; j<cell.output_area.outputs.length; j++) {\n                var data = cell.output_area.outputs[j];\n                if (data.data) {\n                    // IPython >= 3 moved mimebundle to data attribute of output\n                    data = data.data;\n                }\n                if (data['text/html'] == html_output) {\n                    return [cell, data, j];\n                }\n            }\n        }\n    }\n}\n\n// Register the function which deals with the matplotlib target/channel.\n// The kernel may be null if the page has been refreshed.\nif (IPython.notebook.kernel != null) {\n    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n}\n",
            "text/plain": "<IPython.core.display.Javascript object>"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
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      "cell_type": "markdown",
      "source": "From an analytic point of view: if the source is an impulse $f(t) = \\delta(t)$, the sifting property of the delta function results in \n$$ v(t) = e^{-(\\beta/m) t},$$\nwhich is the impulse response, or Green's function, for the motion of a particle in syrup. The Dirac Delta function is introduced in Chapter 13, while the Green's function appears in Chapter 17. In Chapter 18, you will see that this Green's function for a particle in syrup is the same Green's function for the heat equation in the wavenumber domain.\n\n#### Excercise\nMake the forcing term shorter and higher amplitude (until the numerical integration breaks) to approximate the Green's function numerically. \n"
    },
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      "cell_type": "markdown",
      "source": "#### Excercise 2\nPlay with different values of the damping parameter $\\beta$, and see if the responses make sense."
    },
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      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
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