V2EX multivariable calculus

Multivariable Calculus

释义 Definition

多元微积分:研究多个变量的函数的极限、连续、偏导数、梯度、重积分、向量场及线积分/面积分等内容的微积分分支,常用于物理、工程、经济与数据科学建模。(也常简称 multivariable calc

发音 Pronunciation (IPA)

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例句 Examples

Multivariable calculus helps us analyze functions of two or more variables.
多元微积分帮助我们分析包含两个或更多变量的函数。

Using multivariable calculus, the engineer optimized the design by computing gradients and evaluating a triple integral over the region.
工程师运用多元微积分,通过计算梯度并对该区域做三重积分来优化设计。

词源 Etymology

multivariable 由 *multi-*(“多、多重”)+ variable(“变量”)构成,字面意思是“多变量的”。
calculus 源自拉丁语 calculus,原意为“小石子”(古人用小石子计数),后来引申为“计算方法”,在数学中专指“微积分”。合起来即“研究多变量函数的微积分”。

相关词 Related Words

  • Gradient
  • Partial Derivative
  • Directional Derivative
  • Jacobian
  • Hessian
  • Multiple Integral
  • Vector Field
  • Line Integral
  • Surface Integral
  • Divergence
  • 文学与著作 Literary Works

    • James Stewart Calculus: Early Transcendentals(常见教材章节包含 Multivariable Calculus 标题与内容)
    • Tom M. Apostol Calculus, Volume 2(以“多变量微积分与线性代数”为核心主题)
    • Jerrold E. Marsden & Anthony J. Tromba Vector Calculus(覆盖多元微积分的关键工具:梯度、散度、旋度与积分定理)
    • Michael Spivak Calculus on Manifolds(更偏理论,建立在多元微积分之上,涉及多重积分与斯托克斯定理等)
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