08_Vector_Calculus.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vector Calculus & `quiver` Plots\n",
    "\n",
    "A lot of the vector calculus questions we will do can be computed without learning anything new. Regardless, it is good practice for the skills we have begun to develop this semester.\n",
    "\n",
    "If you are struggling to understand how to solve the questions, please refer back to the relevant examples in previous notebooks, e.g. `Plotting.ipynb`, `Partial Derivatives.ipynb` and `Riemann Sums.ipynb`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1:\n",
    "\n",
    "(i) Attempt to symbolically plot the parametric line:\n",
    "\n",
    "$$\n",
    "\\mathbf{r}(t) = \\langle t, t^{2}, 1 \\rangle\n",
    "$$\n",
    "\n",
    "where $t \\in [0,1]$. \n",
    "\n",
    "What is the issue? How might this be fixed?\n",
    "\n",
    "(ii) Numerically plot the parametric line (using `plt`).\n",
    "\n",
    "## Answer 1 (i):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Answer 1 (ii):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2: \n",
    "\n",
    "Symbolically calculate the integral:\n",
    "\n",
    "$$\n",
    "\\int_{\\mathcal{C}} \\sqrt{z + 4x^{2}} \\ dx\n",
    "$$\n",
    "\n",
    "over the paramterised curve ($\\mathbf{r}$) in Question 1.\n",
    "\n",
    "## Answer 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating `curl` and `divergence`\n",
    "\n",
    "* Curl ($\\nabla \\times \\mathbf{F}$)\n",
    "* Divergence ($\\nabla^2 \\mathbf{F}$)\n",
    "\n",
    "> (Note that the gradient is not included here as it takes in a scalar function and produces a vector function).\n",
    "\n",
    "The steps are as follows:\n",
    "\n",
    "0. Import the relevant functions `CoordSys3d`, `curl` and `divergence`.\n",
    "1. Set up a coordinate system with variables $x$, $y$ and $z$ being generated by that coordinate system.\n",
    "2. Create a vector field, multiplying each $\\hat{i},\\hat{j},\\hat{k}$ by the relevant functions.\n",
    "3. Pass the vector field into the functions.\n",
    "\n",
    "\n",
    "### Notation\n",
    "\n",
    "* Coordinate System: it should be a capital letter (to be consistent with existing notation). \n",
    "* Vector fields: are usually expressed with bold capital letters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'F is:'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$(\\mathbf{{x}_{N}}^{2} - \\mathbf{{x}_{N}} \\mathbf{{y}_{N}})\\mathbf{\\hat{i}_{N}} + (- \\mathbf{{x}_{N}} \\mathbf{{y}_{N}} + \\mathbf{{y}_{N}}^{2})\\mathbf{\\hat{j}_{N}}$$"
      ],
      "text/plain": [
       "(N.x**2 - N.x*N.y)*N.i + (-N.x*N.y + N.y**2)*N.j"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Curl of F is:'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$(\\mathbf{{x}_{N}} - \\mathbf{{y}_{N}})\\mathbf{\\hat{k}_{N}}$$"
      ],
      "text/plain": [
       "(N.x - N.y)*N.k"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Divergence of F is:'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\mathbf{{x}_{N}} + \\mathbf{{y}_{N}}$$"
      ],
      "text/plain": [
       "N_x + N_y"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'F is conservative:'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Symbol, init_printing, cos, sin, Matrix, pi, exp, plot\n",
    "from sympy.vector import CoordSys3D, curl, divergence, gradient, is_conservative\n",
    "from sympy.plotting import plot3d\n",
    "init_printing()\n",
    "\n",
    "# Create 3D coordinate system\n",
    "N = CoordSys3D('N')  \n",
    "x = N.x\n",
    "y = N.y\n",
    "z = N.z\n",
    "\n",
    "# Create a field.\n",
    "F = N.i*(x**2-x*y) + N.j*(y**2 - x*y)\n",
    "\n",
    "display('F is:')\n",
    "display(F) # Vector Field\n",
    "display('Curl of F is:')\n",
    "display(curl(F)) # Vector Field\n",
    "display('Divergence of F is:')\n",
    "display(divergence(F)) # Scalar number\n",
    "display('F is conservative:')\n",
    "display(is_conservative(F)) # True or False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clarification:\n",
    "Here, $x_N$ is the $x$ variable in the coordinate system, $N$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the $\\mathbf{x_N}$ and $\\mathbf{y_N}$ make it hard for you to interpret your function, you can use the `subs()` method to substitute them for a simpler symbol.\n",
    "\n",
    "e.g."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$(x^{2} - x y)\\mathbf{\\hat{i}_{N}} + (- x y + y^{2})\\mathbf{\\hat{j}_{N}}$$"
      ],
      "text/plain": [
       "(x**2 - x*y)*N.i + (-x*y + y**2)*N.j"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "F = F.subs(x, Symbol('x'))  # Make sure to reassign F equal to the substitution.\n",
    "F = F.subs(y, Symbol('y'))\n",
    "display(F)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 3:\n",
    "\n",
    "(i) Symbolically calculate $\\mathbf{F}$.\n",
    "\n",
    "$$\n",
    "\\mathbf{F} = \\nabla \\phi = \\nabla \\left( x^{2}y + x \\sin\\left(y\\right)\\right)\n",
    "$$\n",
    "\n",
    "(ii) Symbolically calculate $\\nabla \\times \\mathbf{F}$\n",
    "\n",
    "## Answer 3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating `quiver` plots\n",
    "\n",
    "A `quiver` plot is simply a plot of a vector field. It displays arrows on a 2D or 3D space.\n",
    "\n",
    "Running the below cell can give us an idea about how to use the function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function quiver in module matplotlib.pyplot:\n",
      "\n",
      "quiver(*args, data=None, **kw)\n",
      "    Plot a 2-D field of arrows.\n",
      "    \n",
      "    Call signatures::\n",
      "    \n",
      "      quiver(U, V, **kw)\n",
      "      quiver(U, V, C, **kw)\n",
      "      quiver(X, Y, U, V, **kw)\n",
      "      quiver(X, Y, U, V, C, **kw)\n",
      "    \n",
      "    *U* and *V* are the arrow data, *X* and *Y* set the location of the\n",
      "    arrows, and *C* sets the color of the arrows. These arguments may be 1-D or\n",
      "    2-D arrays or sequences.\n",
      "    \n",
      "    If *X* and *Y* are absent, they will be generated as a uniform grid.\n",
      "    If *U* and *V* are 2-D arrays and *X* and *Y* are 1-D, and if ``len(X)`` and\n",
      "    ``len(Y)`` match the column and row dimensions of *U*, then *X* and *Y* will be\n",
      "    expanded with :func:`numpy.meshgrid`.\n",
      "    \n",
      "    The default settings auto-scales the length of the arrows to a reasonable size.\n",
      "    To change this behavior see the *scale* and *scale_units* kwargs.\n",
      "    \n",
      "    The defaults give a slightly swept-back arrow; to make the head a\n",
      "    triangle, make *headaxislength* the same as *headlength*. To make the\n",
      "    arrow more pointed, reduce *headwidth* or increase *headlength* and\n",
      "    *headaxislength*. To make the head smaller relative to the shaft,\n",
      "    scale down all the head parameters. You will probably do best to leave\n",
      "    minshaft alone.\n",
      "    \n",
      "    *linewidths* and *edgecolors* can be used to customize the arrow\n",
      "    outlines.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    X : 1D or 2D array, sequence, optional\n",
      "        The x coordinates of the arrow locations\n",
      "    Y : 1D or 2D array, sequence, optional\n",
      "        The y coordinates of the arrow locations\n",
      "    U : 1D or 2D array or masked array, sequence\n",
      "        The x components of the arrow vectors\n",
      "    V : 1D or 2D array or masked array, sequence\n",
      "        The y components of the arrow vectors\n",
      "    C : 1D or 2D array, sequence, optional\n",
      "        The arrow colors\n",
      "    units : [ 'width' | 'height' | 'dots' | 'inches' | 'x' | 'y' | 'xy' ]\n",
      "        The arrow dimensions (except for *length*) are measured in multiples of\n",
      "        this unit.\n",
      "    \n",
      "        'width' or 'height': the width or height of the axis\n",
      "    \n",
      "        'dots' or 'inches': pixels or inches, based on the figure dpi\n",
      "    \n",
      "        'x', 'y', or 'xy': respectively *X*, *Y*, or :math:`\\sqrt{X^2 + Y^2}`\n",
      "        in data units\n",
      "    \n",
      "        The arrows scale differently depending on the units.  For\n",
      "        'x' or 'y', the arrows get larger as one zooms in; for other\n",
      "        units, the arrow size is independent of the zoom state.  For\n",
      "        'width or 'height', the arrow size increases with the width and\n",
      "        height of the axes, respectively, when the window is resized;\n",
      "        for 'dots' or 'inches', resizing does not change the arrows.\n",
      "    angles : [ 'uv' | 'xy' ], array, optional\n",
      "        Method for determining the angle of the arrows. Default is 'uv'.\n",
      "    \n",
      "        'uv': the arrow axis aspect ratio is 1 so that\n",
      "        if *U*==*V* the orientation of the arrow on the plot is 45 degrees\n",
      "        counter-clockwise from the horizontal axis (positive to the right).\n",
      "    \n",
      "        'xy': arrows point from (x,y) to (x+u, y+v).\n",
      "        Use this for plotting a gradient field, for example.\n",
      "    \n",
      "        Alternatively, arbitrary angles may be specified as an array\n",
      "        of values in degrees, counter-clockwise from the horizontal axis.\n",
      "    \n",
      "        Note: inverting a data axis will correspondingly invert the\n",
      "        arrows only with ``angles='xy'``.\n",
      "    scale : None, float, optional\n",
      "        Number of data units per arrow length unit, e.g., m/s per plot width; a\n",
      "        smaller scale parameter makes the arrow longer. Default is *None*.\n",
      "    \n",
      "        If *None*, a simple autoscaling algorithm is used, based on the average\n",
      "        vector length and the number of vectors. The arrow length unit is given by\n",
      "        the *scale_units* parameter\n",
      "    scale_units : [ 'width' | 'height' | 'dots' | 'inches' | 'x' | 'y' | 'xy' ], None, optional\n",
      "        If the *scale* kwarg is *None*, the arrow length unit. Default is *None*.\n",
      "    \n",
      "        e.g. *scale_units* is 'inches', *scale* is 2.0, and\n",
      "        ``(u,v) = (1,0)``, then the vector will be 0.5 inches long.\n",
      "    \n",
      "        If *scale_units* is 'width'/'height', then the vector will be half the\n",
      "        width/height of the axes.\n",
      "    \n",
      "        If *scale_units* is 'x' then the vector will be 0.5 x-axis\n",
      "        units. To plot vectors in the x-y plane, with u and v having\n",
      "        the same units as x and y, use\n",
      "        ``angles='xy', scale_units='xy', scale=1``.\n",
      "    width : scalar, optional\n",
      "        Shaft width in arrow units; default depends on choice of units,\n",
      "        above, and number of vectors; a typical starting value is about\n",
      "        0.005 times the width of the plot.\n",
      "    headwidth : scalar, optional\n",
      "        Head width as multiple of shaft width, default is 3\n",
      "    headlength : scalar, optional\n",
      "        Head length as multiple of shaft width, default is 5\n",
      "    headaxislength : scalar, optional\n",
      "        Head length at shaft intersection, default is 4.5\n",
      "    minshaft : scalar, optional\n",
      "        Length below which arrow scales, in units of head length. Do not\n",
      "        set this to less than 1, or small arrows will look terrible!\n",
      "        Default is 1\n",
      "    minlength : scalar, optional\n",
      "        Minimum length as a multiple of shaft width; if an arrow length\n",
      "        is less than this, plot a dot (hexagon) of this diameter instead.\n",
      "        Default is 1.\n",
      "    pivot : [ 'tail' | 'mid' | 'middle' | 'tip' ], optional\n",
      "        The part of the arrow that is at the grid point; the arrow rotates\n",
      "        about this point, hence the name *pivot*.\n",
      "    color : [ color | color sequence ], optional\n",
      "        This is a synonym for the\n",
      "        :class:`~matplotlib.collections.PolyCollection` facecolor kwarg.\n",
      "        If *C* has been set, *color* has no effect.\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    Additional :class:`~matplotlib.collections.PolyCollection`\n",
      "    keyword arguments:\n",
      "    \n",
      "      agg_filter: a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array \n",
      "      alpha: float or None\n",
      "      animated: bool\n",
      "      antialiased: bool or sequence of bools\n",
      "      array: ndarray\n",
      "      capstyle: {'butt', 'round', 'projecting'}\n",
      "      clim: a length 2 sequence of floats; may be overridden in methods that have ``vmin`` and ``vmax`` kwargs. \n",
      "      clip_box: `.Bbox`\n",
      "      clip_on: bool\n",
      "      clip_path: [(`~matplotlib.path.Path`, `.Transform`) | `.Patch` | None] \n",
      "      cmap: colormap or registered colormap name\n",
      "      color: matplotlib color arg or sequence of rgba tuples\n",
      "      contains: callable\n",
      "      edgecolor: color or sequence of colors\n",
      "      facecolor: color or sequence of colors\n",
      "      figure: `.Figure`\n",
      "      gid: str\n",
      "      hatch: {'/', '\\\\', '|', '-', '+', 'x', 'o', 'O', '.', '*'}\n",
      "      in_layout: bool\n",
      "      joinstyle: {'miter', 'round', 'bevel'}\n",
      "      label: object\n",
      "      linestyle: {'-', '--', '-.', ':', '', (offset, on-off-seq), ...}\n",
      "      linewidth: float or sequence of floats\n",
      "      norm: `.Normalize`\n",
      "      offset_position: {'screen', 'data'}\n",
      "      offsets: float or sequence of floats\n",
      "      path_effects: `.AbstractPathEffect`\n",
      "      picker: None or bool or float or callable\n",
      "      pickradius: unknown\n",
      "      rasterized: bool or None\n",
      "      sketch_params: (scale: float, length: float, randomness: float) \n",
      "      snap: bool or None\n",
      "      transform: `.Transform`\n",
      "      url: str\n",
      "      urls: List[str] or None\n",
      "      visible: bool\n",
      "      zorder: float\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    quiverkey : Add a key to a quiver plot\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "help(plt.quiver)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the `help()` function may have indicated to you that a way to use quiver is:\n",
    "\n",
    "`quiver(X,Y,U,V)`\n",
    "\n",
    "Where:\n",
    "\n",
    "* `X`: Is the $x$-position of the arrow.\n",
    "* `Y`: Is the $y$-position of the arrow.\n",
    "* `U`: Is the $x$-direction of the arrow.\n",
    "* `V`: Is the $y$-direction of the arrow.\n",
    "\n",
    "You _can_ do 3D quiver plots, but we will be sticking to 2D.\n",
    "\n",
    "How to do this is best crystallised by an example.\n",
    "\n",
    "Let's plot \n",
    "\n",
    "$$\n",
    "\\mathbf{F} = -y \\hat{i} + x \\hat{j}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.quiver.Quiver at 0x22554ee2dd8>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure(1)\n",
    "ax = fig.gca()\n",
    "\n",
    "x_ = np.linspace(-10,10,10)\n",
    "y_ = np.linspace(-10,10,10)\n",
    "x, y = np.meshgrid(x_,y_)\n",
    "u = -1*y\n",
    "v = x\n",
    "ax.quiver(x,y,u,v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Making `quiver` plots more interpretable\n",
    "\n",
    "If you have too many points in your vectors, the arrows become impossibly small to see. The ends touch and you have to zoom in to see which direction they are pointing in.\n",
    "\n",
    "Less points results in bigger arrows, which is why the `linspace` vectors above only have 10 values each.\n",
    "\n",
    "## Adding colour to your `quiver` plots\n",
    "\n",
    "We can pass in a fifth variable, which will associate each vector with a colour. Let's use the angle of the arrow set its colour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure(1)\n",
    "ax = fig.gca()\n",
    "\n",
    "x_ = np.linspace(-10,10,10)\n",
    "y_ = np.linspace(-10,10,10)\n",
    "x, y = np.meshgrid(x_,y_)\n",
    "u = -1*y\n",
    "v = x\n",
    "c = np.arctan2(u,v) # Create an array of angles. Each angle is associated with a vector on the plot.\n",
    "ax.quiver(x,y,u,v,c) # Pass the `c` array in as the fifth variable.\n",
    "plt.title('Color Vector Plot')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4:\n",
    "\n",
    "Create a plot of\n",
    "\n",
    "(i) The surface, $\\phi$\n",
    "\n",
    "(ii) The vector field ($\\mathbf{F}$) \n",
    "\n",
    "both as specified in Question 3.\n",
    "\n",
    "## Answer 4:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 5:\n",
    "\n",
    "$\\mathcal{D}$ is defined as the closed region bounded by $y = \\sqrt{x}$ and $y=x^2$.\n",
    "\n",
    "Plot the region in 2D space that is occupied by $\\mathcal{D}$ and symbolically integrate:\n",
    "\n",
    "$$\n",
    "\\int \\int_{\\mathcal{D}} \\left( xy + y^{2} \\right) \\ dA\n",
    "$$\n",
    "\n",
    "Note: You may need to think about what is the upper and lower bound first.\n",
    "\n",
    "## Answer 5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}