| 微分几何观点下二元函数的极值 |
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| 引用本文： | 安佰玲,卢涛.微分几何观点下二元函数的极值[J].数学学习,2011(4):58-61. |
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| 作者姓名： | 安佰玲 卢涛 |
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| 作者单位： | 淮北师范大学数学科学学院,安徽淮北235000 |
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| 基金项目： | 淮北师范大学教研项目（800623）. |
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| 摘 要： | 利用曲面的局部微分性质给出二元函数极值存在的必要条件和充分条件,并将之运用于具有明显几何特征的曲面对应的二元函数极值的判别问题中.
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| 关 键 词： | 曲面 极值 高斯曲率 平均曲率 |
Differential Geometry and Extreme Values of Functions of Two Variables |
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| AN Bai-ling,LU Tao.Differential Geometry and Extreme Values of Functions of Two Variables[J].Studies In College Mathematics,2011(4):58-61. |
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| Authors: | AN Bai-ling LU Tao |
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| Institution: | - (School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, PRC) |
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| Abstract: | Using the local properties of surface differentials, both sufficient and necessary conditions for the existence of extreme values of the corresponding functions of two variables are given. We apply our results to justify the existence of extreme values for functions with the corresponding surfaces having clear geometric significances. |
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| Keywords: | surface extreme value Gauss curvature mean curvature |
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