| 引用本文： |
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张浩奇,伍欣叶,张浩敏.基于对称偏导数的多元函数Taylor公式及可微性分析[J].广西科学院学报,2013,29(2):71-74. [点击复制]
- ZHANG Hao-qi,WU Xin-ye,ZHANG Hao-min.Study of Taylor Formula and Differentiability for Multivariate Function based on the Symmetric Partial Derivative[J].Journal of Guangxi Academy of Sciences,2013,29(2):71-74. [点击复制]
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| 摘要: |
| 引入多元函数对称偏导和对称可微的定义,讨论多元函数在对称偏导数意义下的Taylor公式及多元函数对称可微的充分条件和必要条件. |
| 关键词: 对称偏导数 Taylor公式 方向对称导数 对称可微 |
| DOI： |
| 投稿时间：2012-10-30修订日期：2013-01-10 |
| 基金项目:国家自然科学基金项目(11101101);广西教育厅基金项目(200911LX137);桂林理工大学科研启动项目资助。 |
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| Study of Taylor Formula and Differentiability for Multivariate Function based on the Symmetric Partial Derivative |
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ZHANG Hao-qi, WU Xin-ye, ZHANG Hao-min
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| (College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, China) |
| Abstract: |
| First, the definition of the symmetric partial derivative and the symmetric differentiability of multivariate function are introduced in this paper. Second, the Taylor formula for multivariate function based on the symmetric partial derivative is given. Finally, the sufficient condition and the necessary condition for the symmetric differentiability of multivariate function are obtained. |
| Key words: symmetric partial derivative Taylor formula directional symmetric derivative symmetric differentiable |
