泰勒公式教学的跨学科融通与AI赋能实践研究

Interdisciplinary Integration and AI-Enabled Practical Research in the Teaching of Taylor’s Formula

摘要: 泰勒公式作为高等数学的核心内容，是连接微分学与近似计算及工程应用的关键纽带。针对传统教学中存在的“重推导轻应用、学科壁垒明显”等问题，本文聚焦于“跨学科融通”与“AI赋能”两大核心，展开教学实践研究。通过系统构建泰勒公式的跨学科应用场景，并借助AI工具直观破解教学难点，本方案旨在将知识传授深化为创新能力的培养。实践表明，该改革有效提升了学生的数学素养、工程应用能力与跨学科创新思维，为高等数学课程改革提供了可复制的实践路径。

Abstract: Taylor’s Formula, as a core component of advanced mathematics, serves as a critical link between differential calculus and its applications in approximation methods and engineering. To address issues in traditional teaching, such as overemphasizing derivation while neglecting application and apparent disciplinary barriers, this study centers on two key pillars—interdisciplinary integration and AI empowerment—to conduct practical teaching research. By systematically developing interdisciplinary application scenarios for Taylor’s Formula and leveraging AI tools to intuitively resolve teaching challenges, this approach aims to transform knowledge impartation into the cultivation of innovative capabilities. Practice has demonstrated that this reform effectively enhances students’ mathematical literacy, engineering application skills, and interdisciplinary innovative thinking, providing a replicable practical pathway for the reform of advanced mathematics courses.