| 摘要: |
| 隐函数定理是大学数学分析课程的一个重要定理,该定理在现代数学的许多分支都有重要应用.应用在大学常微分方程课程里学过的有关微分方程解的存在唯一性和解对初值与参数的连续性等定理给出隐函数定理的一个新证明. |
| 关键词: 隐函数定理 微分方程 解的存在唯一性 解对初值与参数的连续性 |
| DOI： |
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| A new proof of the implicit function theorem |
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HAN Maoan, SHENG Lijuan
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College of Mathematics and Science, Shanghai Normal University
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| Abstract: |
| The implicit function theorem plays an important role in the mathematical analysis and many other branches of mathematics. In the college course of Ordinary Differential Equations, we have learnt the theorems on the existence and uniqueness of solutions and dependence on initial values and parameters. In this paper, by using these theorems of differential equations, we give a new proof for the implicit function theorem. |
| Key words: implicit function theorem differential equation existence and uniqueness of solutions dependence on initial conditions and parameters |
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