基于微积分发展的历史沿革对高等数学课程进行的教学实践

Teaching Practice of Advanced Mathematics Course Based on the Historical Evolution of Calculus Development

摘要: 高等数学在高等教育中占据重要地位，主要教学内容及顺序一般是：极限理论、一元函数微积分、微分方程、空间解析几何、多元函数微积分、无穷级数。但是通过阅读数学史会发现，这些理论的出现和发展顺序其实并不与教学安排的顺序完全一致，那么这种不一致是否会影响学生对理论的理解？研究基于笔者在实际教学活动中进行的思考和探讨，调查这一现象对教学效果可能产生的影响，并在教学中进行了一些尝试。

Abstract: Advanced mathematics plays a pivotal role in higher education, typically taught in the following sequence: limits, single-variable calculus, differential equations, spatial analytic geometry, multivariable calculus, and infinite series. However, a study of mathematical history reveals that the historical development of these theories often diverges from the prescribed teaching order. This discrepancy raises the question: Does it hinder students’ comprehension of the theories? This paper presents reflections and explorations from the author’s teaching practice, examining how this phenomenon might impact instructional effectiveness and proposing practical teaching strategies.