解的存在唯一性定理蕴涵的数学思想

The Mathematical Thought in the Existence and Uniqueness of Solution Theorem

常微分方程在数学学科的发展中具有很重要的地位,它是许多数学分支产生的动力。常微分方程蕴涵着丰富而深刻的数学思想与方法,通过对解的存在唯一性定理蕴涵的数学思想进行探讨和分析,阐释微分方程本身就是一种数学思想。

Ordinary differential equation is very important in the development of mathematics for it is the basis for many mathematical branches. The ODE contains profound mathematical thought and method, this paper suggests that the ODE itself is a kind of mathematical thought through analyzing the mathematical thought in the existence and uniqueness of solution theorem.