基于“双引擎驱动”的微分方程课程体系重构与实践——以信息与计算科学专业为例

Reconstruction and Implementation of a Differential Equations Curriculum System Based on “Double-Engine Drive”—Taking the Information and Computational Science Major as an Example

摘要: 随着智能技术的发展，新工科背景下工程类专业的数学基础课程亟需在教学内容和教学方式上进行调整。针对工程类院校信息与计算科学专业微分方程课程在教学内容与教学方式上的现实困境，本文探索并实施了一种以“AI思想渗透”和“Mathematica平台内嵌”为核心的双引擎驱动教学模式，课程内容围绕“基础建模–理论分析–算法实现–智能拓展”逐步展开，改变了以往以理论推导为主的教学组织方式，并改革过程中，将人工智能相关思想作为理解微分方程方法演进的重要视角，同时将Mathematica科学计算环境融入教学全过程。教学实践表明，该教学改革在一定程度上缓解了理论教学与工程应用之间的脱节问题，有助于提升学生在复杂工程问题中综合运用数学建模、数值计算与智能方法的能力。

Abstract: With the advancement of intelligent technologies, mathematics foundation courses in engineering disciplines under the new engineering education paradigm urgently require adjustments in both content and teaching methods. Addressing the practical challenges in teaching content and methodology for the Differential Equations course in Information and Computational Science majors at engineering universities, this paper proposes and implements a double-engine driven teaching methodology centered on “AI concept integration” and “Mathematica platform integration”. The course content unfolds progressively through “fundamental modeling, theoretical analysis, numerical simulation, intelligent extension”. This approach shifts away from the traditional theory-derivation-centric teaching structure. Throughout the reform, artificial intelligence concepts are integrated as a key perspective for understanding the evolution of differential equation methodologies, while the Mathematica scientific computing environment is embedded throughout the entire teaching and learning process. Teaching evidence demonstrates that this reform partially bridges the gap between theoretical instruction and practical engineering applications, enhancing students’ ability to integrate mathematical modeling, numerical computation, and intelligent methods when tackling complex real-world problems.