几种导数微分及其关系
The Relations of Several Derivatives and Differentials
DOI: 10.12677/AAM.2021.102047, PDF,  被引量    科研立项经费支持
作者: 钟荣花, 王 跃*：贵州大学数学与统计学院，贵州 贵阳；王守财：贵州民族大学数据科学与信息工程学院，贵州 贵阳
关键词: 导数微分；Fréchet导数微分；Gateaux导数微分；弱导数；Derivative Differential； Fréchet Derivative Differential； Gateaux Derivative Differential； Weak Derivative
摘要: 导数微分是微积分中有力的计算工具，占有极其重要的地位。本文通过讨论几类导数微分(普通导数微分、单向导数，Fréchet导数微分和Gâteaux导数微分)的概念，并赋予一些例子对它们进行说明。最后，分析这几类微分之间的关系及通用计算方法，补充弱导数和一些应用。
Abstract: Derivative differential calculus is a powerful tool for calculating in the differential and integral calculus, which has an extremely important position. By discussing the concepts of several types of derivative differentials (ordinary derivative differential, one-way derivative, Fréchet’s derivative differentials and Gâteaux’s derivatives and differential), meanwhile, some examples were given. Finally, it analyzed the relationships among these several differentials and their general algorithm, and supplemented weak derivatives and some applications.
文章引用：钟荣花, 王跃, 王守财. 几种导数微分及其关系[J]. 应用数学进展, 2021, 10(2): 416-425. https://doi.org/10.12677/AAM.2021.102047

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