第二类曲面积分的算法研究

第二类曲面积分是高等数学多元函数积分学中的教学重点和难点,也是考研数学中数学一的必考内容。第二类曲面积分的题目综合性强,难度高,题型多样,方法多变,计算烦琐,学生不易理解和掌握。因此,本文给出六种具有代表性的题型,通过实例分析,从易到难,循序渐进地引导学生思考和探讨各种题型对应的计算方法,加深学生对第二类曲面积分的概念、性质、定理、公式和算法的理解,提高学生运用所学知识分析问题和解决问题的能力,培养学生的创新意识和创新能力。

The surface integral of the second type is an important and difficult point of teaching in integral calculus of multivariate function in Advanced Mathematics,and also one of examination contents of Mathematics A in postgraduate entrance examination.Problems on the surface integral of the second type is comprehensive and difficult,with various types,changeable methods and complex calculation,which makes it difficult for students to understand and master.Therefore,this paper presents six kinds of typical questions,through case analysis,from easy to difficult,guides students to think and explore the corresponding calculation method step by step.This paper aims at deepening students’comprehension of concepts,properties,theorems,formulas and computational methods of surface integral,improving students’ability to analyze and solve problems with the knowledge they have learned,and developing students’consciousness and ability of innovation.