V2EX laplacian

Laplacian

定义 Definition

Laplacian(拉普拉斯算子/拉普拉斯算符):在数学与物理中常指一个二阶微分算子,记作 Δ,用于描述函数的“弯曲程度/扩散趋势”,广泛应用于偏微分方程、热传导、波动、势场与图像处理等领域。在线性代数与图论中也可指 Laplacian 矩阵(图拉普拉斯矩阵)。此外它也可作形容词,表示“与拉普拉斯相关的”。

发音 Pronunciation (IPA)

/lplen/

例句 Examples

The Laplacian of this function is zero.
这个函数的拉普拉斯算子结果为零。

In physics, the Laplacian appears in the heat equation and helps model how temperature spreads over time.
在物理中,拉普拉斯算子出现在热方程里,用来刻画温度如何随时间扩散。

词源 Etymology

Laplacian 源自法国数学家 Pierre-Simon Laplace(皮埃尔-西蒙拉普拉斯) 的姓氏,加上英语形容词/名词后缀 -ian(表示“与……相关的人或事物”)。因此 Laplacian 字面意思就是“拉普拉斯的/与拉普拉斯相关的”,后来专指以他名字命名的算子与相关概念。

相关词 Related Words

文学/名著出处 Notable Works

  • Partial Differential Equations(Lawrence C. Evans)
  • Methods of Mathematical Physics(Richard Courant & David Hilbert)
  • Mathematical Methods for Physicists(Arfken, Weber & Harris)
  • Classical Electrodynamics(J. D. Jackson)
  • Introduction to Graph Theory(Douglas B. West,涉及图拉普拉斯矩阵)
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