格林公式及其应用摘要 格林公式是高等数学中是一个重要的结论，它是多元函数积分学中联系二重积分和第二型曲线积分的桥梁.本文首先介绍格林公式的内容、使用条件及注意事项等，并对其本质做了剖析，然后对公式进行了推广，总结了格林公式的一些应用.接着通过利用格林公式在曲线积分与二重积分之间的转化关系，体现格林公式在简化二重积分计算、计算图形面积中的应用.然后介绍了格林公式在物理学中的应用，体现运用格林公式来解决物理方面问题的计算过程.最后，通过整理分析近十五年的考研试题，研究格林公式在考研数学中的应用，总结公式的内涵,体现了格林公式运用的广泛性.文中将牛顿莱-布尼茨公式（Newton's Leibniz formula）与格林公式（Green theorem）相比较.从而加深我们对格林公式的理解，提高运用公式的能力，同时为格林公式的教学提供一定的参考.关键词 格林公式 曲线积分 二重积分 考研数学Green's theorem and its applicationAbstract Green's formula is a very important formula in advanced mathematics, which establishes the relationship between curve integral and double integral, and occupies a very important position in the integration of multivariate functions. This paper will simplify the calculation of curve integral and double integral by introducing the transformation relation between curve integral and double integral and the matters needing attention. At the same time, green's formula is used to understand the process of change in physics. The application of green's formula in higher mathematics or mathematical analysis is studied by analyzing the test questions. Master the structure and form of the formula, learn the process of applying the thought method of analogy to extend the theorem, and analyze the practical application of green's formula.Key words green's formula curve integral application in physical chemistry目录 引言.........................................................................11 格林公式的研究背景....................................................
