从“可导点”到“解析点”——复变函数教学中的思政隐喻与价值引领

From “Differentiable Point” to “Analytic Point”—Ideological and Political Metaphors and Value Guidance in Complex Function Teaching

摘要: 本文以“可导点”与“解析点”的概念为切入点，探讨了其中蕴含的“个体优秀”与“整体卓越”的辩证关系。“可导点”指函数仅在这一点可导，是孤立性质，“解析点”指的是函数在该点及其邻域内处处可导，是整体性质，这两个概念既是“局部特性”与“整体属性”的关系，也是“独善其身”与“兼济周边”的恰当隐喻。本文通过“解析”概念所承载的思政价值，阐述了如何引导学生从单纯的知识掌握，升华到对团队协作、责任担当、社会贡献等价值观的理解与认同，实现了专业教育与思政育人的有机融合。

Abstract: Taking the concepts of “differentiable point” and “analytic point” as the starting point, this paper explores the dialectical relationship between “individual excellence” and “collective brilliance” inherent in these concepts. A “differentiable point” refers to a point where a function is differentiable only at that point, representing an isolated property, while an “analytic point” denotes a point where the function is differentiable everywhere in its neighborhood, embodying an overall property. These two concepts not only represent the dialectical unity of “local characteristics” and “global attributes”, but also serve as apt metaphors for “self-improvement” and “benefiting the community”. Through the ideological and political value embodied in the concept of “analytic”, this paper explains how to guide students from mere knowledge acquisition to a deeper understanding and recognition of values such as teamwork, responsibility, and social contribution, achieving the organic integration of professional education and ideological-political education.