二重积分的典例综述.doc

目录 目录 …………………………………………………………………………………………Ⅰ 摘要 …………………………………………………………………………………………Ⅱ 前言 …………………………………………………………………………………………IV 1 二重积分的相关概念……………………………………………………………………1 1.1 二重积分的概念…………………………………………………………………………1 1.2曲线积分、曲面积分的概念……………………………………………………………1 2 二重积分的计算…………………………………………………………………………1 2.1直角坐标系中的计算方法………………………………………………………………极坐标系中的计算法……………………………………………………4 2.3曲线积分、曲面积分的计算?……………………………………………………………5 2.3.1第一类曲线积分………………………………………………………………………5 2.3.2 第二类曲线积分………………………………………………………………………7 2.3.3两类曲线积分的联系…………………………………………………………………7 2.3.4 第一型曲面积分………………………………………………………………………8 2.3.5第二型曲面积分………………………………………………………………………9 参考文献 ……………………………………………………………………………………14 致谢 …………………………………………………………………………………………15 二重积分的典例综述 摘要： 二重积分计算的基本途径是将其转化为二次积分计算，计算二重积分时选择积分次序，交换积分次序以及转换坐标系都是至关重要的问题.为简化二重积分换元公式的推导，利用定积分的换元法及二重积分的有关知识，提出了一种简便的推导方法.本文还介绍了如何利用对称性来计算二重积分，并提出了通过适当改造被积函数和积分区域以利用对称性来简化计算的方法.对积分区域的边界曲线由参数方程表示的二重积分，我们也将给出两种不经消参数而直接计算的方法. 关键字：二重积分; 被积函数；积分限；积分区域； 二次积分; 累次积分；积分次序;换元法；对称性. Double Integral Calculating Abstract: The basic way of calculating double integral is to change it into the quadradic integral,it’s a important problem of choosing the integral order exchanged integral order and conversion coordinate systerm,when we calculating double integral.To simplify the detrusion of the double integral exchange formula,a simple method is derived after using the recevant knowledge of the methed of substitution in definite integral and double integral.The paper introduces the method of calculating double integral with symmetry,and then puts forward a calculating method by rebuilding integrand and domain of integration reasonably. At last,for the double integral which the boundary curve of its domain of integration is denoted by the panameter equation, we will supply a directed method which do not eliminate the parameter. Keyword: Double integral; Integralted function; Integral limit; Integral region; Quadradic integral; Repeated integral; Integral order; Definite integral; Variable substistute; Symmetry