V2EX maclaurin

Maclaurin

定义 Definition

Maclaurin(麦克劳林)常用于指麦克劳林级数(Maclaurin series):一种把函数在 x = 0 附近展开为幂级数的表示方法,是泰勒级数在展开点为 0 时的特殊情况(在微积分与近似计算中很常见)。

发音 Pronunciation (IPA)

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例句 Examples

We used a Maclaurin series to approximate sin(x) near zero.
我们用麦克劳林级数来近似计算零点附近的 sin(x)。

In numerical analysis, the Maclaurin expansion provides a practical way to estimate a function when only a few derivatives at 0 are known.
在数值分析中,当只知道函数在 0 处的少数几个导数时,麦克劳林展开能提供一种实用的估算方法。

词源 Etymology

Maclaurin 源自18世纪苏格兰数学家 Colin Maclaurin 的姓氏。以他的名字命名的“麦克劳林级数”用于描述把函数在 0 点附近展开成幂级数的思想与方法。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Calculus: Early Transcendentals(James Stewart):在泰勒/麦克劳林展开章节中频繁出现
  • Calculus(Tom M. Apostol):系统讨论级数展开与收敛性时使用 Maclaurin series
  • Advanced Engineering Mathematics(Erwin Kreyszig):在工程近似与级数解法中使用麦克劳林展开
  • An Introduction to the Theory of Infinite Series(T. J. I’A. Bromwich):在幂级数与函数展开讨论中提及 Maclaurin 展开
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