微元法的一个理解与思考

An Understanding and Consideration of Differential Element Method

摘要: 微元法是分析、解决实际问题的常用方法，也是从部分到整体的思维方法。微元法是一类常用的数学建模方法。本文从微积分的角度出发，给出一个微元法的理解。分析了微元法的难点与关键点。为克服难点，本文提出了从量的定义导出微元法的观点，给出了一个基于量的定义的微元法。该观点可以帮助理解和简化微元法在实际问题中的应用。通过两个定理初步解释了微元法的数学原理。最后通过两个例子，展示了从量的定义导出微元法的优点。

Abstract: Differential element method, widely used in mathematical modeling, is a common method for ana-lyzing and solving practical problems. The main idea of the method is to divide the research object into infinitely many small parts, extract the representative parts for analysis and processing, and then consider it comprehensively from parts to the whole. Firstly, the paper provides an under-standing of the differential element method in the view of calculus and analyzes the key and diffi-cult points of learning this method. In order to overcome the difficult points, the paper derives the differential element method from the definition of quantity, which can help us to understand and simplify the application of the method in practical problems. Then we preliminarily explain the mathematical principles of the method through two main theorems. Finally, the paper presents two examples to demonstrate the advantages of deriving the differential element method from the defi-nition of quantities.