微分与积分转换方法及其应用研究摘要 微积分学的创立促进了近代数学的发展，在整个数学领域占有非常重要的地位，我们知道微分与积分是可以通过牛顿—莱布尼兹公式作为工具进行转换的.本文首先回顾了微积分学创立的历史及发展过程，其次给出微积分基本定理即牛顿—莱布尼兹公式，并且以微分中值定理与积分中值定理为基础，给出定理的具体内容然后通过证明说明微分与积分的转换方法.最后给出一些涉及微分与积分转换的例题，将积分问题从微分角度看，通过微分导数的方法解决，反之亦是，通过对比发现一些题目运用转换的思想方法可以简化证明.本文的工作对于我们学生把握微分与积分的关系，以及利用微分与积分可以转换这一特点解决学习中的相关问题有一定的实际价值.关键词 微分 积分 转换 中值定理 Differential and integral transformation method and its applicationsAbstract The calculus has promoted the development of modern mathematics and places an important role in the entire field of mathematics. We know that differential and integral can be converted by Newton-Leibniz formula as a tool. Firstly, we review the history and development process of the calculus. Secondly we give the basic theorem of calculus, the Newton-Leibniz formula. And based on the differential median theorem and the integral median theorem, the specific content of the theorem is given, and then the conversion method of differential and integral is explained. Finally, we give some examples on the conversion of differential and integral. Through comparison, it is found that some topics can be simplified by the conversion of thinking methods. The main work of this thesis is of practical value for our students to grasp the relationship between differential and integral, and to use the relationship to solve related problems in learning.Key words Differential Integral Transformation Mean Value Theorem 目 录1.引言.......................................................................11.1 ...
