微分方程的意思、翻譯和例句

是什麼意思

「微分方程」是數學中的一個重要概念,指的是包含未知函數及其導數的方程。這類方程通常用於描述變化過程,並在物理、工程、生物學等多個領域中有廣泛的應用。微分方程可分為常微分方程和偏微分方程兩大類,前者涉及單一變量的導數,後者則涉及多個變量的導數。解微分方程的過程通常涉及找到一個函數,使得該函數及其導數滿足給定的方程。

依照不同程度的英文解釋

  1. An equation involving rates of change.
  2. An equation that relates a function to its derivatives.
  3. An equation that describes how things change.
  4. An equation that includes functions and their rates of change.
  5. An equation that represents relationships involving derivatives.
  6. An equation that involves an unknown function and its derivatives.
  7. A mathematical statement that describes how a quantity changes.
  8. A mathematical formulation involving a function and its derivatives.
  9. A mathematical equation that expresses the relationship between a function and its derivatives.
  10. A mathematical expression that describes the dynamics of a system.

相關英文單字或片語的差別與用法

1:Differential Equation

用法:

這是數學中一個專門的術語,通常用於描述系統的動態行為或變化過程。在物理學中,它可以用來描述運動、熱傳導、波動等現象。在工程學中,微分方程被用於建模電路、流體流動和結構分析等問題。解這些方程可以幫助預測系統的未來行為或理解其運作原理。

例句及翻譯:

例句 1:

這是一個一階微分方程的例子。

This is an example of a first-order differential equation.

例句 2:

我們需要找到這個微分方程的解。

We need to find the solution to this differential equation.

例句 3:

微分方程在物理學中有著重要的應用。

Differential equations have significant applications in physics.