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  "body": "\n## Summary\n\nThe del operator $\\nabla = \\left( \\frac{\\partial}{\\partial x_1}, \\dots, \\frac{\\partial}{\\partial x_n} \\right)$ is a vector of partial derivative operators on $\\mathbb{R}^n$.\nIt gives a short notation for the [[gradient|0ABK9V9Y64]] $\\nabla f$, the [[divergence|0MWV6ZTK6S]] $\\nabla \\cdot F$, the [[curl|0NF6GQNXMY]] $\\nabla \\times F$ in $\\mathbb{R}^3$, and the [[Laplacian|0E0B6RA8K0]] $\\nabla^2 f = \\nabla \\cdot \\nabla f$.\n\n## Remarks\n\nThe notation treats $\\nabla$ like a vector, but it is an operator. For example, $\\nabla \\cdot F$ and $F \\cdot \\nabla$ are different: the first is a function, and the second is the operator $\\sum_i F_i \\, \\partial / \\partial x_i$.\nThe directional derivative of $f$ along $v$ is $(v \\cdot \\nabla) f = v \\cdot \\nabla f$.\nThe symbol $\\nabla$ is called nabla.\n\n## Explanations\n\n### L1 human\n\nDel is a shorthand that makes vector calculus formulas look like vector algebra.\nMultiply it by a function to get the gradient. Dot it with a field to get the divergence, and cross it with a field to get the curl.\n",
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