文档介绍：目 录
言……………………………………………………………………………………………2
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定积分的概念………………………………………………………………………………2
曲线积分的概念……………………………………………………………………………3
二重积分的概念……………………………………………………………………………4
曲面积分的概念……………………………………………………………………………4
三重积分的概念……………………………………………………………………………6
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—莱布尼兹公式与格林公式的关系 ………………………………………………10
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结 论………………………………………………………………………………………………13
参考文献 …………………………………………………………………………………………14
致 谢………………………………………………………………………………………………15
各类积分之间关系的研究
某某,某某学院
摘 要:本文从积分的本质属性和积分计算的一致性两个方面探讨了重积分、曲线积分、曲面积分与定积分之间的关系,进而讨论了几个重要的积分公式,即牛顿-莱布尼茨公式、格林公式、高斯公式、斯托克斯公式以及它们之间的联系,最后通过举例说明了这几个积分公式在积分计算中的重要作用.
关键词: 定积分; 重积分; 曲线积分; 曲面积分;
牛顿-莱布尼茨公式;格林公式; 高斯公式; 斯托克斯公式
On the relationship between various types of integral
Siting Liang, School of mathematics and computer science
Abstract: This paper discusses the relationship between the triple integral, curve integral, surface integral and definite integral from the perspective of the essence of integral and the consistency of the integral calculation. Then we discuss several important integral formulas, namely the Newton Leibniz formula, Green formula, Gauss formula, Stokes formula and the relationship between them. Finally, we explain the important roles of these integral formulas in integral calculation through some examples.
Key words: Definite integral; Triple integral; Curve integral; Surface integral;
Newton-Leibniz formula; Green formula; Gauss formula; Stokes formula.
微积分