V2EX ordinary differential equation

Ordinary Differential Equation

释义 Definition

常微分方程(ODE):只涉及一个自变量及其关于该自变量的导数的微分方程,用来描述随时间或某个单一变量变化的系统(如运动、人口增长、电路等)。注:微分方程还有另一大类是偏微分方程(PDE),涉及多个自变量。

发音 Pronunciation (IPA)

/rdnri dfrnl kwen/

例句 Examples

An ordinary differential equation involves derivatives with respect to a single variable.
常微分方程只包含关于单一变量的导数。

We solved the ordinary differential equation using an initial condition to model the system’s behavior over time.
我们利用初始条件求解这个常微分方程,以刻画系统随时间变化的行为。

词源 Etymology

ordinary 在这里不是“普通”的日常含义,而是数学语境中的“常(单变量)”;用来区别于 partial(偏、部分的),即涉及多个自变量的偏微分方程。differential equation 指“含导数的方程”。合起来 ordinary differential equation 就是“关于一个自变量的导数所构成的方程”。

相关词 Related Words

文学与名著用例 Literary Works

  • Ordinary Differential Equations(E. A. Coddington & N. Levinson):经典高阶教材,系统讨论常微分方程理论。
  • Differential Equations and Their Applications(Martin Braun):以应用为导向,常出现 “ordinary differential equation” 的表述。
  • Elementary Differential Equations and Boundary Value Problems(Boyce & DiPrima):入门与工程应用常用教材,频繁使用该术语。
  • Nonlinear Dynamics and Chaos(Steven H. Strogatz):用常微分方程介绍非线性系统、相图与混沌等主题。
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