可化为变量分离方程的常微分方程的启发式教学

On the heuristic teaching of some special ordinary differential equations

在理工科的高等数学中,有三类可化为变量分离方程的一阶常微分方程;传统的教学安排,讲解略显零散,不利于学生的学习.本文由现代认知学习理论出发,依次从形式统一、几何直观阐释及例题讲解三个层次给出这三类方程的启发式教学,并强调学生的发现学习.

In advanc ed calculus, the re are thre e kinds of ordina ry differentia l equat ions which can be reduced to variable separation type. The traditional teaching arrangements of these equations are slightly scattered, which is bad for the learning of students in learning advanced calculus. In this paper, based on the modern cognitive learning theory, the author discusses the heuristic teaching of these equations from three different levels and em-phasize discovery learning.