V2EX direction field

Direction Field

定义 Definition

direction field方向场(也常叫斜率场)。在微分方程中,用许多小线段/小箭头表示在平面上每一点处解曲线的切线方向(斜率),用来直观地看出解的大致走向。

发音 Pronunciation

/drkn fild/

例句 Examples

A direction field helps you sketch solutions without solving the differential equation.
方向场能帮助你在不求出微分方程解析解的情况下勾画解的图像。

By analyzing the direction field of the system, the researchers identified stable and unstable equilibrium points.
通过分析该系统的方向场,研究人员找出了稳定与不稳定的平衡点。

词源 Etymology

direction 来自拉丁语 directio(引导、指向),与 directus(笔直的、引导的)相关;field 在数学与物理中常用来表示“在空间中每一点都赋有某种量/信息的整体”(如电场、温度场)。合起来 direction field 就是“在每一点给出方向信息的场”,用于描述微分方程解的局部趋势。

相关词 Related Words

文学与著作 Literary Works

  • Elementary Differential Equations and Boundary Value Problems(Boyce & DiPrima)
  • Differential Equations with Applications and Historical Notes(George F. Simmons)
  • Differential Equations, Dynamical Systems, and an Introduction to Chaos(Hirsch, Smale & Devaney)
  • Nonlinear Dynamics and Chaos(Steven H. Strogatz)
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