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    "# Introdution for Transport Equations\n",
    "\n",
    "The transport equation is given by\n",
    "\n",
    "$$\n",
    "\\partial_{t}u+c\\partial_{x}u=0\n",
    "$$(Tansp-Eq-Sup)\n",
    "\n"
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   "source": [
    "<img src=\"corda-naval.gif\" width=\"18%\"> <img src=\"gif-onda-violao.gif\" width=\"20%\"> <img src=\"water.gif\" width=\"18%\"> <img src=\"BOUNCING.gif\" width=\"21%\"> <img src=\"2V4OvG.gif\" width=\"21%\">"
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   "source": [
    "```{figure} wave-transport-Illustration.svg\n",
    "---\n",
    "scale: 80%\n",
    "align: center\n",
    "name: wave-trans-evo\n",
    "---\n",
    "Wave evolution in space and time: a) 2D plots over time; 3D plot in $u\\times x\\times t$.\n",
    "```"
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    "As $u$ is constant through a characteristic line, if we take advective derivative of $u$ evolving over time through the characteristic line, we have\n",
    "\n",
    "$$ \\frac{d u[x,t]}{dt}= \\frac{d u[ct+x_{0},t]}{dt}=0 \\quad \\quad \\rightarrow \\quad \\quad  \\partial_{t}u\\frac{dt}{dt}+\\partial_{x}u\\frac{d(ct+x_{0})}{dt}= \\partial_{t}u +c\\partial_{x}u=0, $$\n",
    "\n",
    "recovering a transport equation."
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   "source": [
    "## Solving Transport Equation"
   ]
  },
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   "metadata": {},
   "source": [
    "<img src=\"sol-sli-1.png\" width=\"45%\"> <img src=\"sol-sli-2.png\" width=\"45%\">"
   ]
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   "source": [
    "## Method of Characteristics"
   ]
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   "metadata": {},
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    "<img src=\"meth-charac-sli-1.png\" width=\"45%\"> <img src=\"meth-charac-sli-2.png\" width=\"45%\">"
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   "source": [
    "### Exercise 1"
   ]
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   "source": [
    "<img src=\"meth-charac-sli-exercise-1.png\" width=\"45%\">"
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