{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "004FRCXH6M"
    },
    {
      "field": "uses",
      "target": "0ZV14XRNF0"
    },
    {
      "field": "uses",
      "target": "8722T9KCP5"
    },
    {
      "field": "uses",
      "target": "A127WFVYKW"
    },
    {
      "field": "uses",
      "target": "A77EHY9DAN"
    },
    {
      "field": "uses",
      "target": "AME1ZE5HBX"
    },
    {
      "field": "uses",
      "target": "BE9GTWMN0B"
    },
    {
      "field": "uses",
      "target": "G5FAPAB2G2"
    },
    {
      "field": "uses",
      "target": "GRBZT7SWK0"
    },
    {
      "field": "uses",
      "target": "HHKSWC8Y6D"
    },
    {
      "field": "uses",
      "target": "NY1K8FNMPQ"
    },
    {
      "field": "uses",
      "target": "PF83EHMFEG"
    },
    {
      "field": "uses",
      "target": "QP8B74828C"
    },
    {
      "field": "uses",
      "target": "QQ5F8B8DYC"
    },
    {
      "field": "uses",
      "target": "W4B84CGEG1"
    },
    {
      "field": "uses",
      "target": "WA3M3RZDQA"
    },
    {
      "field": "uses",
      "target": "WNSAZD8EZC"
    },
    {
      "field": "uses",
      "target": "X8P0H71EET"
    },
    {
      "field": "uses",
      "target": "Y33AJ7GZ6R"
    },
    {
      "field": "uses",
      "target": "Z0RWBST5BN"
    }
  ],
  "body": "\n## Summary\n\nThe exterior derivative extends the differential of a function to [[differential forms|0E3G0GRPZ6]] of higher degree. It maps $k$-forms to $(k + 1)$-forms.\nIn $\\mathbb{R}^3$ it unifies the gradient, curl and divergence, and it gives a common form of the theorems of Green, Stokes and Gauss. Élie Cartan described it in its current form in 1899.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "70KHYD4XYE"
    ],
    "kind": "concept",
    "msc": [
      "58A10"
    ],
    "name": "Exterior derivative",
    "same_as": {
      "wikidata": "Q1754547",
      "wikipedia": "Exterior derivative"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Exterior_derivative"
      }
    ],
    "tag": "0ZHSTAG8ZY",
    "uses": [
      "0E3G0GRPZ6"
    ]
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0ZHSTAG8ZY/",
  "links": [
    {
      "field": "uses",
      "target": "0E3G0GRPZ6"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0ZHSTAG8ZY.md",
  "msc": [
    "58A10"
  ],
  "name": "Exterior derivative",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0ZH/0ZHSTAG8ZY.md",
  "status": null,
  "tag": "0ZHSTAG8ZY",
  "uri": "m2://0ZHSTAG8ZY",
  "url": "https://tamnd.github.io/math2/wiki/exterior-derivative/",
  "writing": {
    "tag": "0ZHSTAG8ZY",
    "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
      }
    ]
  }
}