浅谈高等数学解题的化归策略

Analysis on Strategies to Solve Problems by Induction in Advanced Mathematics

化归是解决数学问题中最一般的原则。通过对几种解决数学问题的化归策略,即一般与特殊的转化、数与形的转化、正面与反面的转化、有限与无限的转化、动与静的转化、由复杂向简单的转化,阐述了在数学解题中运用化归思想可起到开拓思路的作用,使问题的解决达到由难化易、由繁化简的目的。

Induction is the most common method to solve mathematical problems. It is introduced several kinds of inductions such as the transformations from generality to specialty, from number to shape, from reverse to obverse, from definite to indefinite, from motion to rest, from complexity to simplicity. Meanwhile, it is stated that through analyzing these kinds of inductions to solve mathematical problems, the students can expand their minds if they learn to use the method of induction to solve mathematical problems, thus making the difficult problems easy and the complex problems simple to solve.