升维法在高等数学中的应用

Application of Ascending Dimension Method in Advanced Mathematics

在高等数学学习中,学生的思维总是习惯于由繁到简,但是有时候借助于一种变简为繁的方法,能使一些百思不得其解的问题得到解答。这种方法包括升高函数的次数、行列式(矩阵)的阶数等,我们统称它们为升维法。升维法的运用能增强知识间的纵向和横向联系,培养学生思维的创造性。文章通过举例说明了升维法在高等数学中的应用。

Students are accustomed to thinking about mathematical problems from complicated way to simple way, during study of advanced mathematics, but some problems which are difficult can be solved by thinking them from simple way to complicated way sometimes. This kind of method includes ascending degree of function, order of determinant or matrix, and so on, we call them method of ascending dimension. Application of ascending dimension method may strengthen vertical and horizontal connection with other knowledge, cultivate students＇ creative thinking. Purpose of this article is to expound application of this kind of method in advanced mathematics by giving some examples.