大学数学论文范文.doc

毕业论文 题 目 学 院 专 业 班 级 学 生 学 号 指导教师 二〇一二年月日 摘 要 三重积分在现实中有着广泛的应用.利用三重积分求解不规则物体的体积，不仅仅是当代大学生要学习的基础知识，在很多的大型桥梁，建筑工程中，三重积分也有着不可替代的作用.然而，很多学生不能熟练掌握三重积分的相关知识，因而也不会去应用该知识.为了让学生更好地掌握三重积分的相关知识，以便以后能够熟练巧妙运用，本文系统的总结了三重积分的求解方法.求解三重积分最根本的就是将三重积分化为累次积分.但是化为累次积分时可以有不同的选择，既可以“先二后一”（坐标面投影法），也可以“先一后二”（坐标轴投影法），有的题目还可以巧妙地运用对称性求解，复杂的题目可以选择换元法来求解.不同的方法在不同的情况下适用，对于一个题目来说，具体应该选择哪种方法来求解，则应该进一步分析.三重积分有着广泛的应用，主要是在大型桥梁工程建设中用来计算不规则物体的体积.无论在哪儿应用，都要先抽象成数学模型，再计算.因此本文的应用只是采用了一些简单的例题，关键是让学生去体会不同方法解三重积分的过程. 关键词：三重积分；先一后二；先二后一；换元法；分析应用； ABSTRACT Triple integral in the reality in a wide range of applications. Using triple integral solving the volume of irregular objects, is not only the foundation of contemporary college students to learn knowledge, in many large Bridges, building engineering, triple integral also having the effect that cannot replace. However, many students cant master triple integral related information, and thus wont go with the application of the knowledge. In order to let the student to grasp the triple integral of relevant knowledge, so that later skilled to clever apply, this paper summarized the system triple integral solution. Solving the most fundamental triple integral is will triple integral into LeiCi points. But into LeiCi integral will have different options, already can \after the first one\ (coordinate surface projection method), also can \first after a second\ (a projection method), some questions can also smart use of symmetry solution, complex title can choose for yuan method to solve. Different methods in different situations, applicable, for a topic for, specific should choose which kind of method to solve, it should be further analysis. Triple integral in a wide range of applications, mainly in the large bridge engineering construction is used to calculate the volume of irregular objects. No matter where application, firs