关系-映射-反演方法在高等数学问题解决中的应用

Application of Relationship-Mapping-Inversion Method in the Solving of Higher Mathematics Problem

在高等数学问题解决过程中,用本领域的知识解决一些问题比较困难,但有时将问题转化到其它领域去解决,会使一些百思不得其解的问题得到比较容易的解答.关系-映射-反演方法就是这样一种重要方法.关系-映射-反演方法用于解决高等数学问题有以下几个方面:用几何知识解决代数问题;用代数方法解决几何问题;用积分方法解决级数问题;用概率方法解决高等数学问题;用线性代数方法解决高等数学问题;用计算方法解决高等数学问题;用物理方法解决数学问题等.分别举例对上述应用进行了说明.关系-映射-反演方法的运用能增强知识间的纵向和横向联系,培养学生思维的灵活性和创造性.

During higher mathematics problem - solving, it is more difficult to directly solve some problems, but sometimes the problems are easily solved by using the knowledge and methods on other areas. Relationship - mapping- inversion method is such an important method. Relationship- mapping- inversion method used to solve the higher mathematics in the following areas： using knowledge of geometry to solve algebra problems, using alge- braic methods to solve geometric problems, using the integral method to solve series problems, using probabilistic methods to solve the problem of higher mathematics, using linear algebra methods to solve the problem of higher mathematics, using computational methods to solve the problem of higher mathematics, using physical methods to solve mathematical problems and so on. We have illustrated the above applications by giving some examples respectively.