向量函数隐函数定理之新证明（英文）

A new proof of the implicit function theorem

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.

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.