V2EX isocline

Isocline

定义 Definition

isocline(等斜线):在微分方程的方向场(斜率场)中,把斜率相同(dy/dx 为常数)的点连成的曲线。常用于分析一阶微分方程的解的走势与定性行为。(在地理/气象中也可指“等倾线”,但最常见用法在微分方程。)

发音 Pronunciation

/asklan/

例句 Examples

The isoclines help you sketch the slope field more quickly.
等斜线能帮助你更快地绘制斜率场(方向场)。

By plotting several isoclines where \(dy/dx=c\), we can predict how solution curves bend without solving the differential equation explicitly.
通过绘制若干条满足 \(dy/dx=c\) 的等斜线,我们无需显式求解微分方程,也能预测解曲线如何弯曲。

词源 Etymology

来自 iso-(“相同、等同”,源自希腊语 isos)+ -cline(“倾斜、斜度”,与“incline”同源)。字面意思就是“等斜”,因此用来指“斜率相同的点所形成的曲线”。

相关词 Related Words

文学与著作 Literary Works

  • Differential Equations with Applications and Historical Notes(George F. Simmons)
  • Elementary Differential Equations and Boundary Value Problems(Boyce & DiPrima)
  • Nonlinear Dynamics and Chaos(Steven H. Strogatz)
  • Differential Equations(Shepley L. Ross)
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