{
  "aliases": [
    "div"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "02NSMQVQWK"
    },
    {
      "field": "uses",
      "target": "0E0B6RA8K0"
    },
    {
      "field": "uses",
      "target": "0H6DP8CHND"
    },
    {
      "field": "uses",
      "target": "3QWVVM56JF"
    },
    {
      "field": "uses",
      "target": "3XB4PTTK68"
    },
    {
      "field": "uses",
      "target": "46Z1TVS2K6"
    },
    {
      "field": "uses",
      "target": "5WXY2T8JG0"
    },
    {
      "field": "uses",
      "target": "9T7D9ZRWYY"
    },
    {
      "field": "uses",
      "target": "9ZBWK5WSC7"
    },
    {
      "field": "uses",
      "target": "CAB1ARHH31"
    },
    {
      "field": "uses",
      "target": "CM7D3ES438"
    },
    {
      "field": "uses",
      "target": "DBVE636BXN"
    },
    {
      "field": "uses",
      "target": "DKV5J6N6T6"
    },
    {
      "field": "uses",
      "target": "DVB79BK06Y"
    },
    {
      "field": "uses",
      "target": "DX8RV2XG6H"
    },
    {
      "field": "uses",
      "target": "F3DXBJZAME"
    },
    {
      "field": "uses",
      "target": "K76033B5G1"
    },
    {
      "field": "uses",
      "target": "KT0380H39M"
    },
    {
      "field": "uses",
      "target": "M665JWCEXY"
    },
    {
      "field": "uses",
      "target": "MXZHMC2P99"
    },
    {
      "field": "uses",
      "target": "S0QKEJQ1WM"
    }
  ],
  "body": "\n## Summary\n\nThe divergence of a differentiable [[vector field|0299VCW1TH]] is a scalar function. At each point, it measures the net rate of outward flow of the field per unit volume.\nIn Cartesian coordinates it is the sum of the [[partial derivatives|09EGC6F8PT]] $\\partial F_i / \\partial x_i$ of the components.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "div"
    ],
    "kind": "concept",
    "msc": [
      "26B12"
    ],
    "name": "Divergence",
    "same_as": {
      "wikidata": "Q189000",
      "wikipedia": "Divergence"
    },
    "sources": [
      {
        "locator": "Physical interpretation of divergence",
        "url": "https://en.wikipedia.org/wiki/Divergence"
      },
      {
        "locator": "Definition",
        "url": "https://en.wikipedia.org/wiki/Divergence"
      }
    ],
    "tag": "0MWV6ZTK6S",
    "uses": [
      "0299VCW1TH",
      "09EGC6F8PT"
    ]
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0MWV6ZTK6S/",
  "links": [
    {
      "field": "uses",
      "target": "0299VCW1TH"
    },
    {
      "field": "uses",
      "target": "09EGC6F8PT"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0MWV6ZTK6S.md",
  "msc": [
    "26B12"
  ],
  "name": "Divergence",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0MW/0MWV6ZTK6S.md",
  "status": null,
  "tag": "0MWV6ZTK6S",
  "uri": "m2://0MWV6ZTK6S",
  "url": "https://tamnd.github.io/math2/wiki/divergence/",
  "writing": {
    "tag": "0MWV6ZTK6S",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
