新工科背景下数值分析课程积分方程模块的教学探索

Teaching Exploration of the Integral Equation Module in Numerical Analysis Courses under the Background of Emerging Engineering Education

摘要: 针对新工科对强基础、重实践、善创新人才的培养要求，结合数值分析课程中积分方程求解模块传统教学存在的理论与应用脱节、创新能力培养薄弱问题，提出情境、理论、工具、建模四维融合的教学改革方案。通过重构教学内容、创新教学方法、优化评价体系，将积分方程求解从纯理论推导转向理论解析、数值验证、工程应用的立体化教学，实现学生数学思维、实践技能与创新能力的协同提升。教学实践表明，该方案能有效提高学生对数值分析知识的应用能力，为新工科背景下数学类课程改革提供参考。

Abstract: In response to the training requirements of emerging engineering education for talents with a solid foundation, practical skills, and innovative capabilities, and addressing the disconnection between theory and application as well as the weakness in fostering innovation in the traditional teaching of the integral equation module in numerical analysis courses, this study proposes a teaching reform plan based on the integration of four dimensions: context, theory, tools, and modeling. By restructuring teaching content, innovating teaching methods, and optimizing the evaluation system, the teaching of integral equation solving is shifted from pure theoretical derivation to a multi-dimensional approach encompassing theoretical analysis, numerical verification, and engineering application, thereby achieving coordinated enhancement of students’ mathematical thinking, practical skills, and innovative abilities. Teaching practice shows that this approach can effectively improve students’ ability to apply numerical analysis knowledge, providing a reference for the reform of mathematics courses in the context of emerging engineering education.