200918084038YCL论文封面及摘要.doc

淮北师范大学信息学院 2013 届学士学位论文 微积分中轮换对称性的应用 系 别: 数学系 专 业: 数学与应用数学 学 号: 200918084038 姓 名: 杨成玲 指 导 教 师: 崇金凤 指导教师职称: 副教授 2013年5月22日 微积分中轮换对称性的应用 杨成玲 （淮北师范 摘 要 在高等数学中，关于微积分的计算一直是一个难点,在对微积分进行计算时，对于解决一些简单的积分计算若依据较基础的换元法、分部积分法是可行的.但是当遇到复杂的微积分计算和证明，尤其当涉及到三元（及以上）的多元微积分问题时，若仍采用常规的方法解决的话可能会陷入棘手.在这种特殊情况下，如果能够巧妙地借助微积分中函数的轮换对称性来简化微积分的计算则不失为一种行之有效的巧妙方法.同时，有益于人们开拓创造性思维的活跃性以及对判断解题能力的提高.本文主要通过介绍轮换对称性的定义及其应用条件, 归结并列举出了一些相对应的例子，借此加以说明是如何利用轮换对称性对微分、积分进行计算的，同时还通过这些例子进一步体现在微积分的运算问题中如果能够合理运用轮换对称性则可以使微积分的解题过程变得更为简洁、明晰. 关键词：轮换对称性，微分，积分区域，积分 Application of Symmetry Rotation in Calculus Yang Cheng-ling (College of Information of Huaibei Normal University, Huaibei , 235000) Abstract In higher mathematics, computing about calculus is always a difficulty, in the calculation of the calculus, to solve some simple integral calculation according to the more basic change element method, integral method is feasible. But when complex calculus and prove, especially when it comes to ternary?(and above) of multi-variable functions problems, if still using conventional method to solve the words may be involved. In this particular case, at the same time, if the calculation can skillfully to simplify the calculus by means of rotation symmetry calculus function it is an effective method, clever, is beneficial to people develop active creative thinking and problem solving ability to judge the. This paper mainly introduces the definition of rotation symmetry and its application conditions, it lists some corresponding examples, to illustrate how to use rotation symmetry is used to calculate the differential, integral, also through these examples further reflected in the operational problems of calculus if can reasonable use of rotation symmetry can be the problem solving process calculus become more conc