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  "body": "\n## Summary\n\nA partial differential equation, or PDE, is an equation that relates an unknown function of several variables to its [[partial derivatives|09EGC6F8PT]].\nIt is the several-variable counterpart of an [[ordinary differential equation|0NT64JV96A]].\nPDEs describe heat flow, waves, fluids, electromagnetism, quantum mechanics and many other laws of physics, and they are central objects of geometry and probability.\nSee the [[definition|PV8DQ41Q55]].\n\n## Explanations\n\n### L1 human\n\nMany quantities depend on several variables at once, such as the temperature at a point of a room at a given time.\nA law of nature often says how the rates of change of such a quantity in different directions are linked.\nWritten as a formula, this law is a partial differential equation.\nFor example, the temperature $u(t, x)$ in a thin rod obeys $\\partial_t u = \\partial_x^2 u$, the [[heat equation|VP2HN86VAG]].\nSolving the PDE means finding all functions $u$ for which the formula holds.\n",
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