对称性在分计算中应用.docVIP

毕业设计(论文) 毕 业 设 计（论文） 题 目：对称性在积分计算中应用 学 院： 数 理 学 院 专业名称： 信息与计算科学 学 号： 0741210102 学生姓名： 鲍 品 指导教师： 张 晓 燕 2011年 对称性在积分计算中的应用 摘 要 对称性的应用很广泛，尤其在数学，物理学，化学等方面都有体现。本论文主要是探讨一下对称性在积分计算中的应用。 积分在微积分学中既是重点又是难点，特别是在解决积分计算问题上，方法比较灵活。常见的积分方法有换元法和分部积分法，这些方法在解决一般的问题上还是奏效的，但是对于复杂的微积分计算和证明问题就显得有些心有余而力不足。假如我们稍仔细地观察题目，很多时候我们会发现积分区域或被积函数具有某种对称性。如果我们将对称性巧妙地应用到解决这类问题中去，不仅简化了计算过程而且还节省计算时间。 利用对称性解题方法比较灵活也十分重要。接下来本论文将从定积分，重积分，曲线积分以及曲面积分四大方面入手，深入探讨对称性在积分计算中的应用。最后分析利用对称性解题的条件与优势，总结出应用相关性质解题时要注意哪些方面。 关键词 定积分，重积分，曲线积分，曲面积分，对称性，奇偶性 Abstract The application of symmetry is very widespread, particularly in mathematics, physics, chemistry and other aspects of embodied. This paper is to explore the symmetry in the integral calculation. Integral calculus is difficult in both the focus, especially in solving the problem of integral calculation, the method more flexible. The common integral method are the substitution of variables and the integration by parts. These methods are effective in the solution general question, but appear regarding the complex calculus computation and the proof question somewhat has more desire than energy. If we carefully observe the subject a little, usually we will find regional integration or product function has a symmetry. If we applied the symmetry skillfully to solve such problems, this not only simplifies the calculation process but also save computing time. More flexible use of problem-solving approach symmetry is also important, Then the paper will be integral, double integral, curve and surface integrals four points in a bid to further investigate the symmetry in the integral calculation. Finally, we solve problems by analyzing the symmetry of the conditions of use and advantages, summed up the nature of problem solving application related to the attention of what. Key words definite integral, heavy integral, curvilinear integral, surface integral, symmetry, parity 目